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tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/betweenness.py

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+"""Betweenness centrality measures."""
+from collections import deque
+from heapq import heappop, heappush
+from itertools import count
+
+import networkx as nx
+from networkx.algorithms.shortest_paths.weighted import _weight_function
+from networkx.utils import py_random_state
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["betweenness_centrality", "edge_betweenness_centrality"]
+
+
+@py_random_state(5)
+@nx._dispatch(edge_attrs="weight")
+def betweenness_centrality(
+    G, k=None, normalized=True, weight=None, endpoints=False, seed=None
+):
+    r"""Compute the shortest-path betweenness centrality for nodes.
+
+    Betweenness centrality of a node $v$ is the sum of the
+    fraction of all-pairs shortest paths that pass through $v$
+
+    .. math::
+
+       c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}
+
+    where $V$ is the set of nodes, $\sigma(s, t)$ is the number of
+    shortest $(s, t)$-paths,  and $\sigma(s, t|v)$ is the number of
+    those paths  passing through some  node $v$ other than $s, t$.
+    If $s = t$, $\sigma(s, t) = 1$, and if $v \in {s, t}$,
+    $\sigma(s, t|v) = 0$ [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    k : int, optional (default=None)
+      If k is not None use k node samples to estimate betweenness.
+      The value of k <= n where n is the number of nodes in the graph.
+      Higher values give better approximation.
+
+    normalized : bool, optional
+      If True the betweenness values are normalized by `2/((n-1)(n-2))`
+      for graphs, and `1/((n-1)(n-2))` for directed graphs where `n`
+      is the number of nodes in G.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      Weights are used to calculate weighted shortest paths, so they are
+      interpreted as distances.
+
+    endpoints : bool, optional
+      If True include the endpoints in the shortest path counts.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+        Note that this is only used if k is not None.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with betweenness centrality as the value.
+
+    See Also
+    --------
+    edge_betweenness_centrality
+    load_centrality
+
+    Notes
+    -----
+    The algorithm is from Ulrik Brandes [1]_.
+    See [4]_ for the original first published version and [2]_ for details on
+    algorithms for variations and related metrics.
+
+    For approximate betweenness calculations set k=#samples to use
+    k nodes ("pivots") to estimate the betweenness values. For an estimate
+    of the number of pivots needed see [3]_.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    The total number of paths between source and target is counted
+    differently for directed and undirected graphs. Directed paths
+    are easy to count. Undirected paths are tricky: should a path
+    from "u" to "v" count as 1 undirected path or as 2 directed paths?
+
+    For betweenness_centrality we report the number of undirected
+    paths when G is undirected.
+
+    For betweenness_centrality_subset the reporting is different.
+    If the source and target subsets are the same, then we want
+    to count undirected paths. But if the source and target subsets
+    differ -- for example, if sources is {0} and targets is {1},
+    then we are only counting the paths in one direction. They are
+    undirected paths but we are counting them in a directed way.
+    To count them as undirected paths, each should count as half a path.
+
+    This algorithm is not guaranteed to be correct if edge weights
+    are floating point numbers. As a workaround you can use integer
+    numbers by multiplying the relevant edge attributes by a convenient
+    constant factor (eg 100) and converting to integers.
+
+    References
+    ----------
+    .. [1] Ulrik Brandes:
+       A Faster Algorithm for Betweenness Centrality.
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    .. [2] Ulrik Brandes:
+       On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       https://doi.org/10.1016/j.socnet.2007.11.001
+    .. [3] Ulrik Brandes and Christian Pich:
+       Centrality Estimation in Large Networks.
+       International Journal of Bifurcation and Chaos 17(7):2303-2318, 2007.
+       https://dx.doi.org/10.1142/S0218127407018403
+    .. [4] Linton C. Freeman:
+       A set of measures of centrality based on betweenness.
+       Sociometry 40: 35–41, 1977
+       https://doi.org/10.2307/3033543
+    """
+    betweenness = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+    if k is None:
+        nodes = G
+    else:
+        nodes = seed.sample(list(G.nodes()), k)
+    for s in nodes:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = _single_source_shortest_path_basic(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = _single_source_dijkstra_path_basic(G, s, weight)
+        # accumulation
+        if endpoints:
+            betweenness, _ = _accumulate_endpoints(betweenness, S, P, sigma, s)
+        else:
+            betweenness, _ = _accumulate_basic(betweenness, S, P, sigma, s)
+    # rescaling
+    betweenness = _rescale(
+        betweenness,
+        len(G),
+        normalized=normalized,
+        directed=G.is_directed(),
+        k=k,
+        endpoints=endpoints,
+    )
+    return betweenness
+
+
+@py_random_state(4)
+@nx._dispatch(edge_attrs="weight")
+def edge_betweenness_centrality(G, k=None, normalized=True, weight=None, seed=None):
+    r"""Compute betweenness centrality for edges.
+
+    Betweenness centrality of an edge $e$ is the sum of the
+    fraction of all-pairs shortest paths that pass through $e$
+
+    .. math::
+
+       c_B(e) =\sum_{s,t \in V} \frac{\sigma(s, t|e)}{\sigma(s, t)}
+
+    where $V$ is the set of nodes, $\sigma(s, t)$ is the number of
+    shortest $(s, t)$-paths, and $\sigma(s, t|e)$ is the number of
+    those paths passing through edge $e$ [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    k : int, optional (default=None)
+      If k is not None use k node samples to estimate betweenness.
+      The value of k <= n where n is the number of nodes in the graph.
+      Higher values give better approximation.
+
+    normalized : bool, optional
+      If True the betweenness values are normalized by $2/(n(n-1))$
+      for graphs, and $1/(n(n-1))$ for directed graphs where $n$
+      is the number of nodes in G.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      Weights are used to calculate weighted shortest paths, so they are
+      interpreted as distances.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+        Note that this is only used if k is not None.
+
+    Returns
+    -------
+    edges : dictionary
+       Dictionary of edges with betweenness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality
+    edge_load
+
+    Notes
+    -----
+    The algorithm is from Ulrik Brandes [1]_.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    References
+    ----------
+    .. [1]  A Faster Algorithm for Betweenness Centrality. Ulrik Brandes,
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    .. [2] Ulrik Brandes: On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       https://doi.org/10.1016/j.socnet.2007.11.001
+    """
+    betweenness = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+    # b[e]=0 for e in G.edges()
+    betweenness.update(dict.fromkeys(G.edges(), 0.0))
+    if k is None:
+        nodes = G
+    else:
+        nodes = seed.sample(list(G.nodes()), k)
+    for s in nodes:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = _single_source_shortest_path_basic(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = _single_source_dijkstra_path_basic(G, s, weight)
+        # accumulation
+        betweenness = _accumulate_edges(betweenness, S, P, sigma, s)
+    # rescaling
+    for n in G:  # remove nodes to only return edges
+        del betweenness[n]
+    betweenness = _rescale_e(
+        betweenness, len(G), normalized=normalized, directed=G.is_directed()
+    )
+    if G.is_multigraph():
+        betweenness = _add_edge_keys(G, betweenness, weight=weight)
+    return betweenness
+
+
+# helpers for betweenness centrality
+
+
+def _single_source_shortest_path_basic(G, s):
+    S = []
+    P = {}
+    for v in G:
+        P[v] = []
+    sigma = dict.fromkeys(G, 0.0)  # sigma[v]=0 for v in G
+    D = {}
+    sigma[s] = 1.0
+    D[s] = 0
+    Q = deque([s])
+    while Q:  # use BFS to find shortest paths
+        v = Q.popleft()
+        S.append(v)
+        Dv = D[v]
+        sigmav = sigma[v]
+        for w in G[v]:
+            if w not in D:
+                Q.append(w)
+                D[w] = Dv + 1
+            if D[w] == Dv + 1:  # this is a shortest path, count paths
+                sigma[w] += sigmav
+                P[w].append(v)  # predecessors
+    return S, P, sigma, D
+
+
+def _single_source_dijkstra_path_basic(G, s, weight):
+    weight = _weight_function(G, weight)
+    # modified from Eppstein
+    S = []
+    P = {}
+    for v in G:
+        P[v] = []
+    sigma = dict.fromkeys(G, 0.0)  # sigma[v]=0 for v in G
+    D = {}
+    sigma[s] = 1.0
+    push = heappush
+    pop = heappop
+    seen = {s: 0}
+    c = count()
+    Q = []  # use Q as heap with (distance,node id) tuples
+    push(Q, (0, next(c), s, s))
+    while Q:
+        (dist, _, pred, v) = pop(Q)
+        if v in D:
+            continue  # already searched this node.
+        sigma[v] += sigma[pred]  # count paths
+        S.append(v)
+        D[v] = dist
+        for w, edgedata in G[v].items():
+            vw_dist = dist + weight(v, w, edgedata)
+            if w not in D and (w not in seen or vw_dist < seen[w]):
+                seen[w] = vw_dist
+                push(Q, (vw_dist, next(c), v, w))
+                sigma[w] = 0.0
+                P[w] = [v]
+            elif vw_dist == seen[w]:  # handle equal paths
+                sigma[w] += sigma[v]
+                P[w].append(v)
+    return S, P, sigma, D
+
+
+def _accumulate_basic(betweenness, S, P, sigma, s):
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            delta[v] += sigma[v] * coeff
+        if w != s:
+            betweenness[w] += delta[w]
+    return betweenness, delta
+
+
+def _accumulate_endpoints(betweenness, S, P, sigma, s):
+    betweenness[s] += len(S) - 1
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            delta[v] += sigma[v] * coeff
+        if w != s:
+            betweenness[w] += delta[w] + 1
+    return betweenness, delta
+
+
+def _accumulate_edges(betweenness, S, P, sigma, s):
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            c = sigma[v] * coeff
+            if (v, w) not in betweenness:
+                betweenness[(w, v)] += c
+            else:
+                betweenness[(v, w)] += c
+            delta[v] += c
+        if w != s:
+            betweenness[w] += delta[w]
+    return betweenness
+
+
+def _rescale(betweenness, n, normalized, directed=False, k=None, endpoints=False):
+    if normalized:
+        if endpoints:
+            if n < 2:
+                scale = None  # no normalization
+            else:
+                # Scale factor should include endpoint nodes
+                scale = 1 / (n * (n - 1))
+        elif n <= 2:
+            scale = None  # no normalization b=0 for all nodes
+        else:
+            scale = 1 / ((n - 1) * (n - 2))
+    else:  # rescale by 2 for undirected graphs
+        if not directed:
+            scale = 0.5
+        else:
+            scale = None
+    if scale is not None:
+        if k is not None:
+            scale = scale * n / k
+        for v in betweenness:
+            betweenness[v] *= scale
+    return betweenness
+
+
+def _rescale_e(betweenness, n, normalized, directed=False, k=None):
+    if normalized:
+        if n <= 1:
+            scale = None  # no normalization b=0 for all nodes
+        else:
+            scale = 1 / (n * (n - 1))
+    else:  # rescale by 2 for undirected graphs
+        if not directed:
+            scale = 0.5
+        else:
+            scale = None
+    if scale is not None:
+        if k is not None:
+            scale = scale * n / k
+        for v in betweenness:
+            betweenness[v] *= scale
+    return betweenness
+
+
+@not_implemented_for("graph")
+def _add_edge_keys(G, betweenness, weight=None):
+    r"""Adds the corrected betweenness centrality (BC) values for multigraphs.
+
+    Parameters
+    ----------
+    G : NetworkX graph.
+
+    betweenness : dictionary
+        Dictionary mapping adjacent node tuples to betweenness centrality values.
+
+    weight : string or function
+        See `_weight_function` for details. Defaults to `None`.
+
+    Returns
+    -------
+    edges : dictionary
+        The parameter `betweenness` including edges with keys and their
+        betweenness centrality values.
+
+    The BC value is divided among edges of equal weight.
+    """
+    _weight = _weight_function(G, weight)
+
+    edge_bc = dict.fromkeys(G.edges, 0.0)
+    for u, v in betweenness:
+        d = G[u][v]
+        wt = _weight(u, v, d)
+        keys = [k for k in d if _weight(u, v, {k: d[k]}) == wt]
+        bc = betweenness[(u, v)] / len(keys)
+        for k in keys:
+            edge_bc[(u, v, k)] = bc
+
+    return edge_bc

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/closeness.py

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+"""
+Closeness centrality measures.
+"""
+import functools
+
+import networkx as nx
+from networkx.exception import NetworkXError
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["closeness_centrality", "incremental_closeness_centrality"]
+
+
+@nx._dispatch(edge_attrs="distance")
+def closeness_centrality(G, u=None, distance=None, wf_improved=True):
+    r"""Compute closeness centrality for nodes.
+
+    Closeness centrality [1]_ of a node `u` is the reciprocal of the
+    average shortest path distance to `u` over all `n-1` reachable nodes.
+
+    .. math::
+
+        C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where `d(v, u)` is the shortest-path distance between `v` and `u`,
+    and `n-1` is the number of nodes reachable from `u`. Notice that the
+    closeness distance function computes the incoming distance to `u`
+    for directed graphs. To use outward distance, act on `G.reverse()`.
+
+    Notice that higher values of closeness indicate higher centrality.
+
+    Wasserman and Faust propose an improved formula for graphs with
+    more than one connected component. The result is "a ratio of the
+    fraction of actors in the group who are reachable, to the average
+    distance" from the reachable actors [2]_. You might think this
+    scale factor is inverted but it is not. As is, nodes from small
+    components receive a smaller closeness value. Letting `N` denote
+    the number of nodes in the graph,
+
+    .. math::
+
+        C_{WF}(u) = \frac{n-1}{N-1} \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    u : node, optional
+      Return only the value for node u
+
+    distance : edge attribute key, optional (default=None)
+      Use the specified edge attribute as the edge distance in shortest
+      path calculations.  If `None` (the default) all edges have a distance of 1.
+      Absent edge attributes are assigned a distance of 1. Note that no check
+      is performed to ensure that edges have the provided attribute.
+
+    wf_improved : bool, optional (default=True)
+      If True, scale by the fraction of nodes reachable. This gives the
+      Wasserman and Faust improved formula. For single component graphs
+      it is the same as the original formula.
+
+    Returns
+    -------
+    nodes : dictionary
+      Dictionary of nodes with closeness centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.closeness_centrality(G)
+    {0: 1.0, 1: 1.0, 2: 0.75, 3: 0.75}
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality,
+    degree_centrality, incremental_closeness_centrality
+
+    Notes
+    -----
+    The closeness centrality is normalized to `(n-1)/(|G|-1)` where
+    `n` is the number of nodes in the connected part of graph
+    containing the node.  If the graph is not completely connected,
+    this algorithm computes the closeness centrality for each
+    connected part separately scaled by that parts size.
+
+    If the 'distance' keyword is set to an edge attribute key then the
+    shortest-path length will be computed using Dijkstra's algorithm with
+    that edge attribute as the edge weight.
+
+    The closeness centrality uses *inward* distance to a node, not outward.
+    If you want to use outword distances apply the function to `G.reverse()`
+
+    In NetworkX 2.2 and earlier a bug caused Dijkstra's algorithm to use the
+    outward distance rather than the inward distance. If you use a 'distance'
+    keyword and a DiGraph, your results will change between v2.2 and v2.3.
+
+    References
+    ----------
+    .. [1] Linton C. Freeman: Centrality in networks: I.
+       Conceptual clarification. Social Networks 1:215-239, 1979.
+       https://doi.org/10.1016/0378-8733(78)90021-7
+    .. [2] pg. 201 of Wasserman, S. and Faust, K.,
+       Social Network Analysis: Methods and Applications, 1994,
+       Cambridge University Press.
+    """
+    if G.is_directed():
+        G = G.reverse()  # create a reversed graph view
+
+    if distance is not None:
+        # use Dijkstra's algorithm with specified attribute as edge weight
+        path_length = functools.partial(
+            nx.single_source_dijkstra_path_length, weight=distance
+        )
+    else:
+        path_length = nx.single_source_shortest_path_length
+
+    if u is None:
+        nodes = G.nodes
+    else:
+        nodes = [u]
+    closeness_dict = {}
+    for n in nodes:
+        sp = path_length(G, n)
+        totsp = sum(sp.values())
+        len_G = len(G)
+        _closeness_centrality = 0.0
+        if totsp > 0.0 and len_G > 1:
+            _closeness_centrality = (len(sp) - 1.0) / totsp
+            # normalize to number of nodes-1 in connected part
+            if wf_improved:
+                s = (len(sp) - 1.0) / (len_G - 1)
+                _closeness_centrality *= s
+        closeness_dict[n] = _closeness_centrality
+    if u is not None:
+        return closeness_dict[u]
+    return closeness_dict
+
+
+@not_implemented_for("directed")
+@nx._dispatch
+def incremental_closeness_centrality(
+    G, edge, prev_cc=None, insertion=True, wf_improved=True
+):
+    r"""Incremental closeness centrality for nodes.
+
+    Compute closeness centrality for nodes using level-based work filtering
+    as described in Incremental Algorithms for Closeness Centrality by Sariyuce et al.
+
+    Level-based work filtering detects unnecessary updates to the closeness
+    centrality and filters them out.
+
+    ---
+    From "Incremental Algorithms for Closeness Centrality":
+
+    Theorem 1: Let :math:`G = (V, E)` be a graph and u and v be two vertices in V
+    such that there is no edge (u, v) in E. Let :math:`G' = (V, E \cup uv)`
+    Then :math:`cc[s] = cc'[s]` if and only if :math:`\left|dG(s, u) - dG(s, v)\right| \leq 1`.
+
+    Where :math:`dG(u, v)` denotes the length of the shortest path between
+    two vertices u, v in a graph G, cc[s] is the closeness centrality for a
+    vertex s in V, and cc'[s] is the closeness centrality for a
+    vertex s in V, with the (u, v) edge added.
+    ---
+
+    We use Theorem 1 to filter out updates when adding or removing an edge.
+    When adding an edge (u, v), we compute the shortest path lengths from all
+    other nodes to u and to v before the node is added. When removing an edge,
+    we compute the shortest path lengths after the edge is removed. Then we
+    apply Theorem 1 to use previously computed closeness centrality for nodes
+    where :math:`\left|dG(s, u) - dG(s, v)\right| \leq 1`. This works only for
+    undirected, unweighted graphs; the distance argument is not supported.
+
+    Closeness centrality [1]_ of a node `u` is the reciprocal of the
+    sum of the shortest path distances from `u` to all `n-1` other nodes.
+    Since the sum of distances depends on the number of nodes in the
+    graph, closeness is normalized by the sum of minimum possible
+    distances `n-1`.
+
+    .. math::
+
+        C(u) = \frac{n - 1}{\sum_{v=1}^{n-1} d(v, u)},
+
+    where `d(v, u)` is the shortest-path distance between `v` and `u`,
+    and `n` is the number of nodes in the graph.
+
+    Notice that higher values of closeness indicate higher centrality.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    edge : tuple
+      The modified edge (u, v) in the graph.
+
+    prev_cc : dictionary
+      The previous closeness centrality for all nodes in the graph.
+
+    insertion : bool, optional
+      If True (default) the edge was inserted, otherwise it was deleted from the graph.
+
+    wf_improved : bool, optional (default=True)
+      If True, scale by the fraction of nodes reachable. This gives the
+      Wasserman and Faust improved formula. For single component graphs
+      it is the same as the original formula.
+
+    Returns
+    -------
+    nodes : dictionary
+      Dictionary of nodes with closeness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality,
+    degree_centrality, closeness_centrality
+
+    Notes
+    -----
+    The closeness centrality is normalized to `(n-1)/(|G|-1)` where
+    `n` is the number of nodes in the connected part of graph
+    containing the node.  If the graph is not completely connected,
+    this algorithm computes the closeness centrality for each
+    connected part separately.
+
+    References
+    ----------
+    .. [1] Freeman, L.C., 1979. Centrality in networks: I.
+       Conceptual clarification.  Social Networks 1, 215--239.
+       https://doi.org/10.1016/0378-8733(78)90021-7
+    .. [2] Sariyuce, A.E. ; Kaya, K. ; Saule, E. ; Catalyiirek, U.V. Incremental
+       Algorithms for Closeness Centrality. 2013 IEEE International Conference on Big Data
+       http://sariyuce.com/papers/bigdata13.pdf
+    """
+    if prev_cc is not None and set(prev_cc.keys()) != set(G.nodes()):
+        raise NetworkXError("prev_cc and G do not have the same nodes")
+
+    # Unpack edge
+    (u, v) = edge
+    path_length = nx.single_source_shortest_path_length
+
+    if insertion:
+        # For edge insertion, we want shortest paths before the edge is inserted
+        du = path_length(G, u)
+        dv = path_length(G, v)
+
+        G.add_edge(u, v)
+    else:
+        G.remove_edge(u, v)
+
+        # For edge removal, we want shortest paths after the edge is removed
+        du = path_length(G, u)
+        dv = path_length(G, v)
+
+    if prev_cc is None:
+        return nx.closeness_centrality(G)
+
+    nodes = G.nodes()
+    closeness_dict = {}
+    for n in nodes:
+        if n in du and n in dv and abs(du[n] - dv[n]) <= 1:
+            closeness_dict[n] = prev_cc[n]
+        else:
+            sp = path_length(G, n)
+            totsp = sum(sp.values())
+            len_G = len(G)
+            _closeness_centrality = 0.0
+            if totsp > 0.0 and len_G > 1:
+                _closeness_centrality = (len(sp) - 1.0) / totsp
+                # normalize to number of nodes-1 in connected part
+                if wf_improved:
+                    s = (len(sp) - 1.0) / (len_G - 1)
+                    _closeness_centrality *= s
+            closeness_dict[n] = _closeness_centrality
+
+    # Leave the graph as we found it
+    if insertion:
+        G.remove_edge(u, v)
+    else:
+        G.add_edge(u, v)
+
+    return closeness_dict

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/current_flow_betweenness_subset.py

@@ -0,0 +1,226 @@
+"""Current-flow betweenness centrality measures for subsets of nodes."""
+import networkx as nx
+from networkx.algorithms.centrality.flow_matrix import flow_matrix_row
+from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering
+
+__all__ = [
+    "current_flow_betweenness_centrality_subset",
+    "edge_current_flow_betweenness_centrality_subset",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs="weight")
+def current_flow_betweenness_centrality_subset(
+    G, sources, targets, normalized=True, weight=None, dtype=float, solver="lu"
+):
+    r"""Compute current-flow betweenness centrality for subsets of nodes.
+
+    Current-flow betweenness centrality uses an electrical current
+    model for information spreading in contrast to betweenness
+    centrality which uses shortest paths.
+
+    Current-flow betweenness centrality is also known as
+    random-walk betweenness centrality [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    sources: list of nodes
+      Nodes to use as sources for current
+
+    targets: list of nodes
+      Nodes to use as sinks for current
+
+    normalized : bool, optional (default=True)
+      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
+      n is the number of nodes in G.
+
+    weight : string or None, optional (default=None)
+      Key for edge data used as the edge weight.
+      If None, then use 1 as each edge weight.
+      The weight reflects the capacity or the strength of the
+      edge.
+
+    dtype: data type (float)
+      Default data type for internal matrices.
+      Set to np.float32 for lower memory consumption.
+
+    solver: string (default='lu')
+       Type of linear solver to use for computing the flow matrix.
+       Options are "full" (uses most memory), "lu" (recommended), and
+       "cg" (uses least memory).
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with betweenness centrality as the value.
+
+    See Also
+    --------
+    approximate_current_flow_betweenness_centrality
+    betweenness_centrality
+    edge_betweenness_centrality
+    edge_current_flow_betweenness_centrality
+
+    Notes
+    -----
+    Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$
+    time [1]_, where $I(n-1)$ is the time needed to compute the
+    inverse Laplacian.  For a full matrix this is $O(n^3)$ but using
+    sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the
+    Laplacian matrix condition number.
+
+    The space required is $O(nw)$ where $w$ is the width of the sparse
+    Laplacian matrix.  Worse case is $w=n$ for $O(n^2)$.
+
+    If the edges have a 'weight' attribute they will be used as
+    weights in this algorithm.  Unspecified weights are set to 1.
+
+    References
+    ----------
+    .. [1] Centrality Measures Based on Current Flow.
+       Ulrik Brandes and Daniel Fleischer,
+       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
+       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
+       https://doi.org/10.1007/978-3-540-31856-9_44
+
+    .. [2] A measure of betweenness centrality based on random walks,
+       M. E. J. Newman, Social Networks 27, 39-54 (2005).
+    """
+    import numpy as np
+
+    from networkx.utils import reverse_cuthill_mckee_ordering
+
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph not connected.")
+    n = G.number_of_nodes()
+    ordering = list(reverse_cuthill_mckee_ordering(G))
+    # make a copy with integer labels according to rcm ordering
+    # this could be done without a copy if we really wanted to
+    mapping = dict(zip(ordering, range(n)))
+    H = nx.relabel_nodes(G, mapping)
+    betweenness = dict.fromkeys(H, 0.0)  # b[v]=0 for v in H
+    for row, (s, t) in flow_matrix_row(H, weight=weight, dtype=dtype, solver=solver):
+        for ss in sources:
+            i = mapping[ss]
+            for tt in targets:
+                j = mapping[tt]
+                betweenness[s] += 0.5 * np.abs(row[i] - row[j])
+                betweenness[t] += 0.5 * np.abs(row[i] - row[j])
+    if normalized:
+        nb = (n - 1.0) * (n - 2.0)  # normalization factor
+    else:
+        nb = 2.0
+    for v in H:
+        betweenness[v] = betweenness[v] / nb + 1.0 / (2 - n)
+    return {ordering[k]: v for k, v in betweenness.items()}
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs="weight")
+def edge_current_flow_betweenness_centrality_subset(
+    G, sources, targets, normalized=True, weight=None, dtype=float, solver="lu"
+):
+    r"""Compute current-flow betweenness centrality for edges using subsets
+    of nodes.
+
+    Current-flow betweenness centrality uses an electrical current
+    model for information spreading in contrast to betweenness
+    centrality which uses shortest paths.
+
+    Current-flow betweenness centrality is also known as
+    random-walk betweenness centrality [2]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    sources: list of nodes
+      Nodes to use as sources for current
+
+    targets: list of nodes
+      Nodes to use as sinks for current
+
+    normalized : bool, optional (default=True)
+      If True the betweenness values are normalized by b=b/(n-1)(n-2) where
+      n is the number of nodes in G.
+
+    weight : string or None, optional (default=None)
+      Key for edge data used as the edge weight.
+      If None, then use 1 as each edge weight.
+      The weight reflects the capacity or the strength of the
+      edge.
+
+    dtype: data type (float)
+      Default data type for internal matrices.
+      Set to np.float32 for lower memory consumption.
+
+    solver: string (default='lu')
+       Type of linear solver to use for computing the flow matrix.
+       Options are "full" (uses most memory), "lu" (recommended), and
+       "cg" (uses least memory).
+
+    Returns
+    -------
+    nodes : dict
+       Dictionary of edge tuples with betweenness centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality
+    edge_betweenness_centrality
+    current_flow_betweenness_centrality
+
+    Notes
+    -----
+    Current-flow betweenness can be computed in $O(I(n-1)+mn \log n)$
+    time [1]_, where $I(n-1)$ is the time needed to compute the
+    inverse Laplacian.  For a full matrix this is $O(n^3)$ but using
+    sparse methods you can achieve $O(nm{\sqrt k})$ where $k$ is the
+    Laplacian matrix condition number.
+
+    The space required is $O(nw)$ where $w$ is the width of the sparse
+    Laplacian matrix.  Worse case is $w=n$ for $O(n^2)$.
+
+    If the edges have a 'weight' attribute they will be used as
+    weights in this algorithm.  Unspecified weights are set to 1.
+
+    References
+    ----------
+    .. [1] Centrality Measures Based on Current Flow.
+       Ulrik Brandes and Daniel Fleischer,
+       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
+       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
+       https://doi.org/10.1007/978-3-540-31856-9_44
+
+    .. [2] A measure of betweenness centrality based on random walks,
+       M. E. J. Newman, Social Networks 27, 39-54 (2005).
+    """
+    import numpy as np
+
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph not connected.")
+    n = G.number_of_nodes()
+    ordering = list(reverse_cuthill_mckee_ordering(G))
+    # make a copy with integer labels according to rcm ordering
+    # this could be done without a copy if we really wanted to
+    mapping = dict(zip(ordering, range(n)))
+    H = nx.relabel_nodes(G, mapping)
+    edges = (tuple(sorted((u, v))) for u, v in H.edges())
+    betweenness = dict.fromkeys(edges, 0.0)
+    if normalized:
+        nb = (n - 1.0) * (n - 2.0)  # normalization factor
+    else:
+        nb = 2.0
+    for row, (e) in flow_matrix_row(H, weight=weight, dtype=dtype, solver=solver):
+        for ss in sources:
+            i = mapping[ss]
+            for tt in targets:
+                j = mapping[tt]
+                betweenness[e] += 0.5 * np.abs(row[i] - row[j])
+        betweenness[e] /= nb
+    return {(ordering[s], ordering[t]): v for (s, t), v in betweenness.items()}

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/current_flow_closeness.py

@@ -0,0 +1,97 @@
+"""Current-flow closeness centrality measures."""
+import networkx as nx
+from networkx.algorithms.centrality.flow_matrix import (
+    CGInverseLaplacian,
+    FullInverseLaplacian,
+    SuperLUInverseLaplacian,
+)
+from networkx.utils import not_implemented_for, reverse_cuthill_mckee_ordering
+
+__all__ = ["current_flow_closeness_centrality", "information_centrality"]
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs="weight")
+def current_flow_closeness_centrality(G, weight=None, dtype=float, solver="lu"):
+    """Compute current-flow closeness centrality for nodes.
+
+    Current-flow closeness centrality is variant of closeness
+    centrality based on effective resistance between nodes in
+    a network. This metric is also known as information centrality.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      The weight reflects the capacity or the strength of the
+      edge.
+
+    dtype: data type (default=float)
+      Default data type for internal matrices.
+      Set to np.float32 for lower memory consumption.
+
+    solver: string (default='lu')
+       Type of linear solver to use for computing the flow matrix.
+       Options are "full" (uses most memory), "lu" (recommended), and
+       "cg" (uses least memory).
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with current flow closeness centrality as the value.
+
+    See Also
+    --------
+    closeness_centrality
+
+    Notes
+    -----
+    The algorithm is from Brandes [1]_.
+
+    See also [2]_ for the original definition of information centrality.
+
+    References
+    ----------
+    .. [1] Ulrik Brandes and Daniel Fleischer,
+       Centrality Measures Based on Current Flow.
+       Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS '05).
+       LNCS 3404, pp. 533-544. Springer-Verlag, 2005.
+       https://doi.org/10.1007/978-3-540-31856-9_44
+
+    .. [2] Karen Stephenson and Marvin Zelen:
+       Rethinking centrality: Methods and examples.
+       Social Networks 11(1):1-37, 1989.
+       https://doi.org/10.1016/0378-8733(89)90016-6
+    """
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph not connected.")
+    solvername = {
+        "full": FullInverseLaplacian,
+        "lu": SuperLUInverseLaplacian,
+        "cg": CGInverseLaplacian,
+    }
+    n = G.number_of_nodes()
+    ordering = list(reverse_cuthill_mckee_ordering(G))
+    # make a copy with integer labels according to rcm ordering
+    # this could be done without a copy if we really wanted to
+    H = nx.relabel_nodes(G, dict(zip(ordering, range(n))))
+    betweenness = dict.fromkeys(H, 0.0)  # b[v]=0 for v in H
+    n = H.number_of_nodes()
+    L = nx.laplacian_matrix(H, nodelist=range(n), weight=weight).asformat("csc")
+    L = L.astype(dtype)
+    C2 = solvername[solver](L, width=1, dtype=dtype)  # initialize solver
+    for v in H:
+        col = C2.get_row(v)
+        for w in H:
+            betweenness[v] += col[v] - 2 * col[w]
+            betweenness[w] += col[v]
+    for v in H:
+        betweenness[v] = 1 / (betweenness[v])
+    return {ordering[k]: v for k, v in betweenness.items()}
+
+
+information_centrality = current_flow_closeness_centrality

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/degree_alg.py

@@ -0,0 +1,149 @@
+"""Degree centrality measures."""
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = ["degree_centrality", "in_degree_centrality", "out_degree_centrality"]
+
+
+@nx._dispatch
+def degree_centrality(G):
+    """Compute the degree centrality for nodes.
+
+    The degree centrality for a node v is the fraction of nodes it
+    is connected to.
+
+    Parameters
+    ----------
+    G : graph
+      A networkx graph
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with degree centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.degree_centrality(G)
+    {0: 1.0, 1: 1.0, 2: 0.6666666666666666, 3: 0.6666666666666666}
+
+    See Also
+    --------
+    betweenness_centrality, load_centrality, eigenvector_centrality
+
+    Notes
+    -----
+    The degree centrality values are normalized by dividing by the maximum
+    possible degree in a simple graph n-1 where n is the number of nodes in G.
+
+    For multigraphs or graphs with self loops the maximum degree might
+    be higher than n-1 and values of degree centrality greater than 1
+    are possible.
+    """
+    if len(G) <= 1:
+        return {n: 1 for n in G}
+
+    s = 1.0 / (len(G) - 1.0)
+    centrality = {n: d * s for n, d in G.degree()}
+    return centrality
+
+
+@not_implemented_for("undirected")
+@nx._dispatch
+def in_degree_centrality(G):
+    """Compute the in-degree centrality for nodes.
+
+    The in-degree centrality for a node v is the fraction of nodes its
+    incoming edges are connected to.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph
+
+    Returns
+    -------
+    nodes : dictionary
+        Dictionary of nodes with in-degree centrality as values.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.in_degree_centrality(G)
+    {0: 0.0, 1: 0.3333333333333333, 2: 0.6666666666666666, 3: 0.6666666666666666}
+
+    See Also
+    --------
+    degree_centrality, out_degree_centrality
+
+    Notes
+    -----
+    The degree centrality values are normalized by dividing by the maximum
+    possible degree in a simple graph n-1 where n is the number of nodes in G.
+
+    For multigraphs or graphs with self loops the maximum degree might
+    be higher than n-1 and values of degree centrality greater than 1
+    are possible.
+    """
+    if len(G) <= 1:
+        return {n: 1 for n in G}
+
+    s = 1.0 / (len(G) - 1.0)
+    centrality = {n: d * s for n, d in G.in_degree()}
+    return centrality
+
+
+@not_implemented_for("undirected")
+@nx._dispatch
+def out_degree_centrality(G):
+    """Compute the out-degree centrality for nodes.
+
+    The out-degree centrality for a node v is the fraction of nodes its
+    outgoing edges are connected to.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph
+
+    Returns
+    -------
+    nodes : dictionary
+        Dictionary of nodes with out-degree centrality as values.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3)])
+    >>> nx.out_degree_centrality(G)
+    {0: 1.0, 1: 0.6666666666666666, 2: 0.0, 3: 0.0}
+
+    See Also
+    --------
+    degree_centrality, in_degree_centrality
+
+    Notes
+    -----
+    The degree centrality values are normalized by dividing by the maximum
+    possible degree in a simple graph n-1 where n is the number of nodes in G.
+
+    For multigraphs or graphs with self loops the maximum degree might
+    be higher than n-1 and values of degree centrality greater than 1
+    are possible.
+    """
+    if len(G) <= 1:
+        return {n: 1 for n in G}
+
+    s = 1.0 / (len(G) - 1.0)
+    centrality = {n: d * s for n, d in G.out_degree()}
+    return centrality

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/dispersion.py

@@ -0,0 +1,107 @@
+from itertools import combinations
+
+import networkx as nx
+
+__all__ = ["dispersion"]
+
+
+@nx._dispatch
+def dispersion(G, u=None, v=None, normalized=True, alpha=1.0, b=0.0, c=0.0):
+    r"""Calculate dispersion between `u` and `v` in `G`.
+
+    A link between two actors (`u` and `v`) has a high dispersion when their
+    mutual ties (`s` and `t`) are not well connected with each other.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+    u : node, optional
+        The source for the dispersion score (e.g. ego node of the network).
+    v : node, optional
+        The target of the dispersion score if specified.
+    normalized : bool
+        If True (default) normalize by the embeddedness of the nodes (u and v).
+    alpha, b, c : float
+        Parameters for the normalization procedure. When `normalized` is True,
+        the dispersion value is normalized by::
+
+            result = ((dispersion + b) ** alpha) / (embeddedness + c)
+
+        as long as the denominator is nonzero.
+
+    Returns
+    -------
+    nodes : dictionary
+        If u (v) is specified, returns a dictionary of nodes with dispersion
+        score for all "target" ("source") nodes. If neither u nor v is
+        specified, returns a dictionary of dictionaries for all nodes 'u' in the
+        graph with a dispersion score for each node 'v'.
+
+    Notes
+    -----
+    This implementation follows Lars Backstrom and Jon Kleinberg [1]_. Typical
+    usage would be to run dispersion on the ego network $G_u$ if $u$ were
+    specified.  Running :func:`dispersion` with neither $u$ nor $v$ specified
+    can take some time to complete.
+
+    References
+    ----------
+    .. [1] Romantic Partnerships and the Dispersion of Social Ties:
+        A Network Analysis of Relationship Status on Facebook.
+        Lars Backstrom, Jon Kleinberg.
+        https://arxiv.org/pdf/1310.6753v1.pdf
+
+    """
+
+    def _dispersion(G_u, u, v):
+        """dispersion for all nodes 'v' in a ego network G_u of node 'u'"""
+        u_nbrs = set(G_u[u])
+        ST = {n for n in G_u[v] if n in u_nbrs}
+        set_uv = {u, v}
+        # all possible ties of connections that u and b share
+        possib = combinations(ST, 2)
+        total = 0
+        for s, t in possib:
+            # neighbors of s that are in G_u, not including u and v
+            nbrs_s = u_nbrs.intersection(G_u[s]) - set_uv
+            # s and t are not directly connected
+            if t not in nbrs_s:
+                # s and t do not share a connection
+                if nbrs_s.isdisjoint(G_u[t]):
+                    # tick for disp(u, v)
+                    total += 1
+        # neighbors that u and v share
+        embeddedness = len(ST)
+
+        dispersion_val = total
+        if normalized:
+            dispersion_val = (total + b) ** alpha
+            if embeddedness + c != 0:
+                dispersion_val /= embeddedness + c
+
+        return dispersion_val
+
+    if u is None:
+        # v and u are not specified
+        if v is None:
+            results = {n: {} for n in G}
+            for u in G:
+                for v in G[u]:
+                    results[u][v] = _dispersion(G, u, v)
+        # u is not specified, but v is
+        else:
+            results = dict.fromkeys(G[v], {})
+            for u in G[v]:
+                results[u] = _dispersion(G, v, u)
+    else:
+        # u is specified with no target v
+        if v is None:
+            results = dict.fromkeys(G[u], {})
+            for v in G[u]:
+                results[v] = _dispersion(G, u, v)
+        # both u and v are specified
+        else:
+            results = _dispersion(G, u, v)
+
+    return results

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/eigenvector.py

@@ -0,0 +1,341 @@
+"""Functions for computing eigenvector centrality."""
+import math
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["eigenvector_centrality", "eigenvector_centrality_numpy"]
+
+
+@not_implemented_for("multigraph")
+@nx._dispatch(edge_attrs="weight")
+def eigenvector_centrality(G, max_iter=100, tol=1.0e-6, nstart=None, weight=None):
+    r"""Compute the eigenvector centrality for the graph G.
+
+    Eigenvector centrality computes the centrality for a node by adding
+    the centrality of its predecessors. The centrality for node $i$ is the
+    $i$-th element of a left eigenvector associated with the eigenvalue $\lambda$
+    of maximum modulus that is positive. Such an eigenvector $x$ is
+    defined up to a multiplicative constant by the equation
+
+    .. math::
+
+         \lambda x^T = x^T A,
+
+    where $A$ is the adjacency matrix of the graph G. By definition of
+    row-column product, the equation above is equivalent to
+
+    .. math::
+
+        \lambda x_i = \sum_{j\to i}x_j.
+
+    That is, adding the eigenvector centralities of the predecessors of
+    $i$ one obtains the eigenvector centrality of $i$ multiplied by
+    $\lambda$. In the case of undirected graphs, $x$ also solves the familiar
+    right-eigenvector equation $Ax = \lambda x$.
+
+    By virtue of the Perron–Frobenius theorem [1]_, if G is strongly
+    connected there is a unique eigenvector $x$, and all its entries
+    are strictly positive.
+
+    If G is not strongly connected there might be several left
+    eigenvectors associated with $\lambda$, and some of their elements
+    might be zero.
+
+    Parameters
+    ----------
+    G : graph
+      A networkx graph.
+
+    max_iter : integer, optional (default=100)
+      Maximum number of power iterations.
+
+    tol : float, optional (default=1.0e-6)
+      Error tolerance (in Euclidean norm) used to check convergence in
+      power iteration.
+
+    nstart : dictionary, optional (default=None)
+      Starting value of power iteration for each node. Must have a nonzero
+      projection on the desired eigenvector for the power method to converge.
+      If None, this implementation uses an all-ones vector, which is a safe
+      choice.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal. Otherwise holds the
+      name of the edge attribute used as weight. In this measure the
+      weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with eigenvector centrality as the value. The
+       associated vector has unit Euclidean norm and the values are
+       nonegative.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> centrality = nx.eigenvector_centrality(G)
+    >>> sorted((v, f"{c:0.2f}") for v, c in centrality.items())
+    [(0, '0.37'), (1, '0.60'), (2, '0.60'), (3, '0.37')]
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If the graph G is the null graph.
+
+    NetworkXError
+        If each value in `nstart` is zero.
+
+    PowerIterationFailedConvergence
+        If the algorithm fails to converge to the specified tolerance
+        within the specified number of iterations of the power iteration
+        method.
+
+    See Also
+    --------
+    eigenvector_centrality_numpy
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Eigenvector centrality was introduced by Landau [2]_ for chess
+    tournaments. It was later rediscovered by Wei [3]_ and then
+    popularized by Kendall [4]_ in the context of sport ranking. Berge
+    introduced a general definition for graphs based on social connections
+    [5]_. Bonacich [6]_ reintroduced again eigenvector centrality and made
+    it popular in link analysis.
+
+    This function computes the left dominant eigenvector, which corresponds
+    to adding the centrality of predecessors: this is the usual approach.
+    To add the centrality of successors first reverse the graph with
+    ``G.reverse()``.
+
+    The implementation uses power iteration [7]_ to compute a dominant
+    eigenvector starting from the provided vector `nstart`. Convergence is
+    guaranteed as long as `nstart` has a nonzero projection on a dominant
+    eigenvector, which certainly happens using the default value.
+
+    The method stops when the change in the computed vector between two
+    iterations is smaller than an error tolerance of ``G.number_of_nodes()
+    * tol`` or after ``max_iter`` iterations, but in the second case it
+    raises an exception.
+
+    This implementation uses $(A + I)$ rather than the adjacency matrix
+    $A$ because the change preserves eigenvectors, but it shifts the
+    spectrum, thus guaranteeing convergence even for networks with
+    negative eigenvalues of maximum modulus.
+
+    References
+    ----------
+    .. [1] Abraham Berman and Robert J. Plemmons.
+       "Nonnegative Matrices in the Mathematical Sciences."
+       Classics in Applied Mathematics. SIAM, 1994.
+
+    .. [2] Edmund Landau.
+       "Zur relativen Wertbemessung der Turnierresultate."
+       Deutsches Wochenschach, 11:366–369, 1895.
+
+    .. [3] Teh-Hsing Wei.
+       "The Algebraic Foundations of Ranking Theory."
+       PhD thesis, University of Cambridge, 1952.
+
+    .. [4] Maurice G. Kendall.
+       "Further contributions to the theory of paired comparisons."
+       Biometrics, 11(1):43–62, 1955.
+       https://www.jstor.org/stable/3001479
+
+    .. [5] Claude Berge
+       "Théorie des graphes et ses applications."
+       Dunod, Paris, France, 1958.
+
+    .. [6] Phillip Bonacich.
+       "Technique for analyzing overlapping memberships."
+       Sociological Methodology, 4:176–185, 1972.
+       https://www.jstor.org/stable/270732
+
+    .. [7] Power iteration:: https://en.wikipedia.org/wiki/Power_iteration
+
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "cannot compute centrality for the null graph"
+        )
+    # If no initial vector is provided, start with the all-ones vector.
+    if nstart is None:
+        nstart = {v: 1 for v in G}
+    if all(v == 0 for v in nstart.values()):
+        raise nx.NetworkXError("initial vector cannot have all zero values")
+    # Normalize the initial vector so that each entry is in [0, 1]. This is
+    # guaranteed to never have a divide-by-zero error by the previous line.
+    nstart_sum = sum(nstart.values())
+    x = {k: v / nstart_sum for k, v in nstart.items()}
+    nnodes = G.number_of_nodes()
+    # make up to max_iter iterations
+    for _ in range(max_iter):
+        xlast = x
+        x = xlast.copy()  # Start with xlast times I to iterate with (A+I)
+        # do the multiplication y^T = x^T A (left eigenvector)
+        for n in x:
+            for nbr in G[n]:
+                w = G[n][nbr].get(weight, 1) if weight else 1
+                x[nbr] += xlast[n] * w
+        # Normalize the vector. The normalization denominator `norm`
+        # should never be zero by the Perron--Frobenius
+        # theorem. However, in case it is due to numerical error, we
+        # assume the norm to be one instead.
+        norm = math.hypot(*x.values()) or 1
+        x = {k: v / norm for k, v in x.items()}
+        # Check for convergence (in the L_1 norm).
+        if sum(abs(x[n] - xlast[n]) for n in x) < nnodes * tol:
+            return x
+    raise nx.PowerIterationFailedConvergence(max_iter)
+
+
+@nx._dispatch(edge_attrs="weight")
+def eigenvector_centrality_numpy(G, weight=None, max_iter=50, tol=0):
+    r"""Compute the eigenvector centrality for the graph G.
+
+    Eigenvector centrality computes the centrality for a node by adding
+    the centrality of its predecessors. The centrality for node $i$ is the
+    $i$-th element of a left eigenvector associated with the eigenvalue $\lambda$
+    of maximum modulus that is positive. Such an eigenvector $x$ is
+    defined up to a multiplicative constant by the equation
+
+    .. math::
+
+         \lambda x^T = x^T A,
+
+    where $A$ is the adjacency matrix of the graph G. By definition of
+    row-column product, the equation above is equivalent to
+
+    .. math::
+
+        \lambda x_i = \sum_{j\to i}x_j.
+
+    That is, adding the eigenvector centralities of the predecessors of
+    $i$ one obtains the eigenvector centrality of $i$ multiplied by
+    $\lambda$. In the case of undirected graphs, $x$ also solves the familiar
+    right-eigenvector equation $Ax = \lambda x$.
+
+    By virtue of the Perron–Frobenius theorem [1]_, if G is strongly
+    connected there is a unique eigenvector $x$, and all its entries
+    are strictly positive.
+
+    If G is not strongly connected there might be several left
+    eigenvectors associated with $\lambda$, and some of their elements
+    might be zero.
+
+    Parameters
+    ----------
+    G : graph
+      A networkx graph.
+
+    max_iter : integer, optional (default=50)
+      Maximum number of Arnoldi update iterations allowed.
+
+    tol : float, optional (default=0)
+      Relative accuracy for eigenvalues (stopping criterion).
+      The default value of 0 implies machine precision.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal. Otherwise holds the
+      name of the edge attribute used as weight. In this measure the
+      weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with eigenvector centrality as the value. The
+       associated vector has unit Euclidean norm and the values are
+       nonegative.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> centrality = nx.eigenvector_centrality_numpy(G)
+    >>> print([f"{node} {centrality[node]:0.2f}" for node in centrality])
+    ['0 0.37', '1 0.60', '2 0.60', '3 0.37']
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If the graph G is the null graph.
+
+    ArpackNoConvergence
+        When the requested convergence is not obtained. The currently
+        converged eigenvalues and eigenvectors can be found as
+        eigenvalues and eigenvectors attributes of the exception object.
+
+    See Also
+    --------
+    :func:`scipy.sparse.linalg.eigs`
+    eigenvector_centrality
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Eigenvector centrality was introduced by Landau [2]_ for chess
+    tournaments. It was later rediscovered by Wei [3]_ and then
+    popularized by Kendall [4]_ in the context of sport ranking. Berge
+    introduced a general definition for graphs based on social connections
+    [5]_. Bonacich [6]_ reintroduced again eigenvector centrality and made
+    it popular in link analysis.
+
+    This function computes the left dominant eigenvector, which corresponds
+    to adding the centrality of predecessors: this is the usual approach.
+    To add the centrality of successors first reverse the graph with
+    ``G.reverse()``.
+
+    This implementation uses the
+    :func:`SciPy sparse eigenvalue solver<scipy.sparse.linalg.eigs>` (ARPACK)
+    to find the largest eigenvalue/eigenvector pair using Arnoldi iterations
+    [7]_.
+
+    References
+    ----------
+    .. [1] Abraham Berman and Robert J. Plemmons.
+       "Nonnegative Matrices in the Mathematical Sciences."
+       Classics in Applied Mathematics. SIAM, 1994.
+
+    .. [2] Edmund Landau.
+       "Zur relativen Wertbemessung der Turnierresultate."
+       Deutsches Wochenschach, 11:366–369, 1895.
+
+    .. [3] Teh-Hsing Wei.
+       "The Algebraic Foundations of Ranking Theory."
+       PhD thesis, University of Cambridge, 1952.
+
+    .. [4] Maurice G. Kendall.
+       "Further contributions to the theory of paired comparisons."
+       Biometrics, 11(1):43–62, 1955.
+       https://www.jstor.org/stable/3001479
+
+    .. [5] Claude Berge
+       "Théorie des graphes et ses applications."
+       Dunod, Paris, France, 1958.
+
+    .. [6] Phillip Bonacich.
+       "Technique for analyzing overlapping memberships."
+       Sociological Methodology, 4:176–185, 1972.
+       https://www.jstor.org/stable/270732
+
+    .. [7] Arnoldi iteration:: https://en.wikipedia.org/wiki/Arnoldi_iteration
+
+    """
+    import numpy as np
+    import scipy as sp
+
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            "cannot compute centrality for the null graph"
+        )
+    M = nx.to_scipy_sparse_array(G, nodelist=list(G), weight=weight, dtype=float)
+    _, eigenvector = sp.sparse.linalg.eigs(
+        M.T, k=1, which="LR", maxiter=max_iter, tol=tol
+    )
+    largest = eigenvector.flatten().real
+    norm = np.sign(largest.sum()) * sp.linalg.norm(largest)
+    return dict(zip(G, largest / norm))

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/flow_matrix.py

@@ -0,0 +1,130 @@
+# Helpers for current-flow betweenness and current-flow closeness
+# Lazy computations for inverse Laplacian and flow-matrix rows.
+import networkx as nx
+
+
+@nx._dispatch(edge_attrs="weight")
+def flow_matrix_row(G, weight=None, dtype=float, solver="lu"):
+    # Generate a row of the current-flow matrix
+    import numpy as np
+
+    solvername = {
+        "full": FullInverseLaplacian,
+        "lu": SuperLUInverseLaplacian,
+        "cg": CGInverseLaplacian,
+    }
+    n = G.number_of_nodes()
+    L = nx.laplacian_matrix(G, nodelist=range(n), weight=weight).asformat("csc")
+    L = L.astype(dtype)
+    C = solvername[solver](L, dtype=dtype)  # initialize solver
+    w = C.w  # w is the Laplacian matrix width
+    # row-by-row flow matrix
+    for u, v in sorted(sorted((u, v)) for u, v in G.edges()):
+        B = np.zeros(w, dtype=dtype)
+        c = G[u][v].get(weight, 1.0)
+        B[u % w] = c
+        B[v % w] = -c
+        # get only the rows needed in the inverse laplacian
+        # and multiply to get the flow matrix row
+        row = B @ C.get_rows(u, v)
+        yield row, (u, v)
+
+
+# Class to compute the inverse laplacian only for specified rows
+# Allows computation of the current-flow matrix without storing entire
+# inverse laplacian matrix
+class InverseLaplacian:
+    def __init__(self, L, width=None, dtype=None):
+        global np
+        import numpy as np
+
+        (n, n) = L.shape
+        self.dtype = dtype
+        self.n = n
+        if width is None:
+            self.w = self.width(L)
+        else:
+            self.w = width
+        self.C = np.zeros((self.w, n), dtype=dtype)
+        self.L1 = L[1:, 1:]
+        self.init_solver(L)
+
+    def init_solver(self, L):
+        pass
+
+    def solve(self, r):
+        raise nx.NetworkXError("Implement solver")
+
+    def solve_inverse(self, r):
+        raise nx.NetworkXError("Implement solver")
+
+    def get_rows(self, r1, r2):
+        for r in range(r1, r2 + 1):
+            self.C[r % self.w, 1:] = self.solve_inverse(r)
+        return self.C
+
+    def get_row(self, r):
+        self.C[r % self.w, 1:] = self.solve_inverse(r)
+        return self.C[r % self.w]
+
+    def width(self, L):
+        m = 0
+        for i, row in enumerate(L):
+            w = 0
+            x, y = np.nonzero(row)
+            if len(y) > 0:
+                v = y - i
+                w = v.max() - v.min() + 1
+                m = max(w, m)
+        return m
+
+
+class FullInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        self.IL = np.zeros(L.shape, dtype=self.dtype)
+        self.IL[1:, 1:] = np.linalg.inv(self.L1.todense())
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s = self.IL @ rhs
+        return s
+
+    def solve_inverse(self, r):
+        return self.IL[r, 1:]
+
+
+class SuperLUInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        import scipy as sp
+
+        self.lusolve = sp.sparse.linalg.factorized(self.L1.tocsc())
+
+    def solve_inverse(self, r):
+        rhs = np.zeros(self.n, dtype=self.dtype)
+        rhs[r] = 1
+        return self.lusolve(rhs[1:])
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s[1:] = self.lusolve(rhs[1:])
+        return s
+
+
+class CGInverseLaplacian(InverseLaplacian):
+    def init_solver(self, L):
+        global sp
+        import scipy as sp
+
+        ilu = sp.sparse.linalg.spilu(self.L1.tocsc())
+        n = self.n - 1
+        self.M = sp.sparse.linalg.LinearOperator(shape=(n, n), matvec=ilu.solve)
+
+    def solve(self, rhs):
+        s = np.zeros(rhs.shape, dtype=self.dtype)
+        s[1:] = sp.sparse.linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]
+        return s
+
+    def solve_inverse(self, r):
+        rhs = np.zeros(self.n, self.dtype)
+        rhs[r] = 1
+        return sp.sparse.linalg.cg(self.L1, rhs[1:], M=self.M, atol=0)[0]

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/group.py

@@ -0,0 +1,785 @@
+"""Group centrality measures."""
+from copy import deepcopy
+
+import networkx as nx
+from networkx.algorithms.centrality.betweenness import (
+    _accumulate_endpoints,
+    _single_source_dijkstra_path_basic,
+    _single_source_shortest_path_basic,
+)
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "group_betweenness_centrality",
+    "group_closeness_centrality",
+    "group_degree_centrality",
+    "group_in_degree_centrality",
+    "group_out_degree_centrality",
+    "prominent_group",
+]
+
+
+@nx._dispatch(edge_attrs="weight")
+def group_betweenness_centrality(G, C, normalized=True, weight=None, endpoints=False):
+    r"""Compute the group betweenness centrality for a group of nodes.
+
+    Group betweenness centrality of a group of nodes $C$ is the sum of the
+    fraction of all-pairs shortest paths that pass through any vertex in $C$
+
+    .. math::
+
+       c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}
+
+    where $V$ is the set of nodes, $\sigma(s, t)$ is the number of
+    shortest $(s, t)$-paths, and $\sigma(s, t|C)$ is the number of
+    those paths passing through some node in group $C$. Note that
+    $(s, t)$ are not members of the group ($V-C$ is the set of nodes
+    in $V$ that are not in $C$).
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    C : list or set or list of lists or list of sets
+      A group or a list of groups containing nodes which belong to G, for which group betweenness
+      centrality is to be calculated.
+
+    normalized : bool, optional (default=True)
+      If True, group betweenness is normalized by `1/((|V|-|C|)(|V|-|C|-1))`
+      where `|V|` is the number of nodes in G and `|C|` is the number of nodes in C.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      The weight of an edge is treated as the length or distance between the two sides.
+
+    endpoints : bool, optional (default=False)
+      If True include the endpoints in the shortest path counts.
+
+    Raises
+    ------
+    NodeNotFound
+       If node(s) in C are not present in G.
+
+    Returns
+    -------
+    betweenness : list of floats or float
+       If C is a single group then return a float. If C is a list with
+       several groups then return a list of group betweenness centralities.
+
+    See Also
+    --------
+    betweenness_centrality
+
+    Notes
+    -----
+    Group betweenness centrality is described in [1]_ and its importance discussed in [3]_.
+    The initial implementation of the algorithm is mentioned in [2]_. This function uses
+    an improved algorithm presented in [4]_.
+
+    The number of nodes in the group must be a maximum of n - 2 where `n`
+    is the total number of nodes in the graph.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    The total number of paths between source and target is counted
+    differently for directed and undirected graphs. Directed paths
+    between "u" and "v" are counted as two possible paths (one each
+    direction) while undirected paths between "u" and "v" are counted
+    as one path. Said another way, the sum in the expression above is
+    over all ``s != t`` for directed graphs and for ``s < t`` for undirected graphs.
+
+
+    References
+    ----------
+    .. [1] M G Everett and S P Borgatti:
+       The Centrality of Groups and Classes.
+       Journal of Mathematical Sociology. 23(3): 181-201. 1999.
+       http://www.analytictech.com/borgatti/group_centrality.htm
+    .. [2] Ulrik Brandes:
+       On Variants of Shortest-Path Betweenness
+       Centrality and their Generic Computation.
+       Social Networks 30(2):136-145, 2008.
+       http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.9610&rep=rep1&type=pdf
+    .. [3] Sourav Medya et. al.:
+       Group Centrality Maximization via Network Design.
+       SIAM International Conference on Data Mining, SDM 2018, 126–134.
+       https://sites.cs.ucsb.edu/~arlei/pubs/sdm18.pdf
+    .. [4] Rami Puzis, Yuval Elovici, and Shlomi Dolev.
+       "Fast algorithm for successive computation of group betweenness centrality."
+       https://journals.aps.org/pre/pdf/10.1103/PhysRevE.76.056709
+
+    """
+    GBC = []  # initialize betweenness
+    list_of_groups = True
+    #  check weather C contains one or many groups
+    if any(el in G for el in C):
+        C = [C]
+        list_of_groups = False
+    set_v = {node for group in C for node in group}
+    if set_v - G.nodes:  # element(s) of C not in G
+        raise nx.NodeNotFound(f"The node(s) {set_v - G.nodes} are in C but not in G.")
+
+    # pre-processing
+    PB, sigma, D = _group_preprocessing(G, set_v, weight)
+
+    # the algorithm for each group
+    for group in C:
+        group = set(group)  # set of nodes in group
+        # initialize the matrices of the sigma and the PB
+        GBC_group = 0
+        sigma_m = deepcopy(sigma)
+        PB_m = deepcopy(PB)
+        sigma_m_v = deepcopy(sigma_m)
+        PB_m_v = deepcopy(PB_m)
+        for v in group:
+            GBC_group += PB_m[v][v]
+            for x in group:
+                for y in group:
+                    dxvy = 0
+                    dxyv = 0
+                    dvxy = 0
+                    if not (
+                        sigma_m[x][y] == 0 or sigma_m[x][v] == 0 or sigma_m[v][y] == 0
+                    ):
+                        if D[x][v] == D[x][y] + D[y][v]:
+                            dxyv = sigma_m[x][y] * sigma_m[y][v] / sigma_m[x][v]
+                        if D[x][y] == D[x][v] + D[v][y]:
+                            dxvy = sigma_m[x][v] * sigma_m[v][y] / sigma_m[x][y]
+                        if D[v][y] == D[v][x] + D[x][y]:
+                            dvxy = sigma_m[v][x] * sigma[x][y] / sigma[v][y]
+                    sigma_m_v[x][y] = sigma_m[x][y] * (1 - dxvy)
+                    PB_m_v[x][y] = PB_m[x][y] - PB_m[x][y] * dxvy
+                    if y != v:
+                        PB_m_v[x][y] -= PB_m[x][v] * dxyv
+                    if x != v:
+                        PB_m_v[x][y] -= PB_m[v][y] * dvxy
+            sigma_m, sigma_m_v = sigma_m_v, sigma_m
+            PB_m, PB_m_v = PB_m_v, PB_m
+
+        # endpoints
+        v, c = len(G), len(group)
+        if not endpoints:
+            scale = 0
+            # if the graph is connected then subtract the endpoints from
+            # the count for all the nodes in the graph. else count how many
+            # nodes are connected to the group's nodes and subtract that.
+            if nx.is_directed(G):
+                if nx.is_strongly_connected(G):
+                    scale = c * (2 * v - c - 1)
+            elif nx.is_connected(G):
+                scale = c * (2 * v - c - 1)
+            if scale == 0:
+                for group_node1 in group:
+                    for node in D[group_node1]:
+                        if node != group_node1:
+                            if node in group:
+                                scale += 1
+                            else:
+                                scale += 2
+            GBC_group -= scale
+
+        # normalized
+        if normalized:
+            scale = 1 / ((v - c) * (v - c - 1))
+            GBC_group *= scale
+
+        # If undirected than count only the undirected edges
+        elif not G.is_directed():
+            GBC_group /= 2
+
+        GBC.append(GBC_group)
+    if list_of_groups:
+        return GBC
+    return GBC[0]
+
+
+def _group_preprocessing(G, set_v, weight):
+    sigma = {}
+    delta = {}
+    D = {}
+    betweenness = dict.fromkeys(G, 0)
+    for s in G:
+        if weight is None:  # use BFS
+            S, P, sigma[s], D[s] = _single_source_shortest_path_basic(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma[s], D[s] = _single_source_dijkstra_path_basic(G, s, weight)
+        betweenness, delta[s] = _accumulate_endpoints(betweenness, S, P, sigma[s], s)
+        for i in delta[s]:  # add the paths from s to i and rescale sigma
+            if s != i:
+                delta[s][i] += 1
+            if weight is not None:
+                sigma[s][i] = sigma[s][i] / 2
+    # building the path betweenness matrix only for nodes that appear in the group
+    PB = dict.fromkeys(G)
+    for group_node1 in set_v:
+        PB[group_node1] = dict.fromkeys(G, 0.0)
+        for group_node2 in set_v:
+            if group_node2 not in D[group_node1]:
+                continue
+            for node in G:
+                # if node is connected to the two group nodes than continue
+                if group_node2 in D[node] and group_node1 in D[node]:
+                    if (
+                        D[node][group_node2]
+                        == D[node][group_node1] + D[group_node1][group_node2]
+                    ):
+                        PB[group_node1][group_node2] += (
+                            delta[node][group_node2]
+                            * sigma[node][group_node1]
+                            * sigma[group_node1][group_node2]
+                            / sigma[node][group_node2]
+                        )
+    return PB, sigma, D
+
+
+@nx._dispatch(edge_attrs="weight")
+def prominent_group(
+    G, k, weight=None, C=None, endpoints=False, normalized=True, greedy=False
+):
+    r"""Find the prominent group of size $k$ in graph $G$. The prominence of the
+    group is evaluated by the group betweenness centrality.
+
+    Group betweenness centrality of a group of nodes $C$ is the sum of the
+    fraction of all-pairs shortest paths that pass through any vertex in $C$
+
+    .. math::
+
+       c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}
+
+    where $V$ is the set of nodes, $\sigma(s, t)$ is the number of
+    shortest $(s, t)$-paths, and $\sigma(s, t|C)$ is the number of
+    those paths passing through some node in group $C$. Note that
+    $(s, t)$ are not members of the group ($V-C$ is the set of nodes
+    in $V$ that are not in $C$).
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph.
+
+    k : int
+       The number of nodes in the group.
+
+    normalized : bool, optional (default=True)
+       If True, group betweenness is normalized by ``1/((|V|-|C|)(|V|-|C|-1))``
+       where ``|V|`` is the number of nodes in G and ``|C|`` is the number of
+       nodes in C.
+
+    weight : None or string, optional (default=None)
+       If None, all edge weights are considered equal.
+       Otherwise holds the name of the edge attribute used as weight.
+       The weight of an edge is treated as the length or distance between the two sides.
+
+    endpoints : bool, optional (default=False)
+       If True include the endpoints in the shortest path counts.
+
+    C : list or set, optional (default=None)
+       list of nodes which won't be candidates of the prominent group.
+
+    greedy : bool, optional (default=False)
+       Using a naive greedy algorithm in order to find non-optimal prominent
+       group. For scale free networks the results are negligibly below the optimal
+       results.
+
+    Raises
+    ------
+    NodeNotFound
+       If node(s) in C are not present in G.
+
+    Returns
+    -------
+    max_GBC : float
+       The group betweenness centrality of the prominent group.
+
+    max_group : list
+        The list of nodes in the prominent group.
+
+    See Also
+    --------
+    betweenness_centrality, group_betweenness_centrality
+
+    Notes
+    -----
+    Group betweenness centrality is described in [1]_ and its importance discussed in [3]_.
+    The algorithm is described in [2]_ and is based on techniques mentioned in [4]_.
+
+    The number of nodes in the group must be a maximum of ``n - 2`` where ``n``
+    is the total number of nodes in the graph.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    The total number of paths between source and target is counted
+    differently for directed and undirected graphs. Directed paths
+    between "u" and "v" are counted as two possible paths (one each
+    direction) while undirected paths between "u" and "v" are counted
+    as one path. Said another way, the sum in the expression above is
+    over all ``s != t`` for directed graphs and for ``s < t`` for undirected graphs.
+
+    References
+    ----------
+    .. [1] M G Everett and S P Borgatti:
+       The Centrality of Groups and Classes.
+       Journal of Mathematical Sociology. 23(3): 181-201. 1999.
+       http://www.analytictech.com/borgatti/group_centrality.htm
+    .. [2] Rami Puzis, Yuval Elovici, and Shlomi Dolev:
+       "Finding the Most Prominent Group in Complex Networks"
+       AI communications 20(4): 287-296, 2007.
+       https://www.researchgate.net/profile/Rami_Puzis2/publication/220308855
+    .. [3] Sourav Medya et. al.:
+       Group Centrality Maximization via Network Design.
+       SIAM International Conference on Data Mining, SDM 2018, 126–134.
+       https://sites.cs.ucsb.edu/~arlei/pubs/sdm18.pdf
+    .. [4] Rami Puzis, Yuval Elovici, and Shlomi Dolev.
+       "Fast algorithm for successive computation of group betweenness centrality."
+       https://journals.aps.org/pre/pdf/10.1103/PhysRevE.76.056709
+    """
+    import numpy as np
+    import pandas as pd
+
+    if C is not None:
+        C = set(C)
+        if C - G.nodes:  # element(s) of C not in G
+            raise nx.NodeNotFound(f"The node(s) {C - G.nodes} are in C but not in G.")
+        nodes = list(G.nodes - C)
+    else:
+        nodes = list(G.nodes)
+    DF_tree = nx.Graph()
+    PB, sigma, D = _group_preprocessing(G, nodes, weight)
+    betweenness = pd.DataFrame.from_dict(PB)
+    if C is not None:
+        for node in C:
+            # remove from the betweenness all the nodes not part of the group
+            betweenness.drop(index=node, inplace=True)
+            betweenness.drop(columns=node, inplace=True)
+    CL = [node for _, node in sorted(zip(np.diag(betweenness), nodes), reverse=True)]
+    max_GBC = 0
+    max_group = []
+    DF_tree.add_node(
+        1,
+        CL=CL,
+        betweenness=betweenness,
+        GBC=0,
+        GM=[],
+        sigma=sigma,
+        cont=dict(zip(nodes, np.diag(betweenness))),
+    )
+
+    # the algorithm
+    DF_tree.nodes[1]["heu"] = 0
+    for i in range(k):
+        DF_tree.nodes[1]["heu"] += DF_tree.nodes[1]["cont"][DF_tree.nodes[1]["CL"][i]]
+    max_GBC, DF_tree, max_group = _dfbnb(
+        G, k, DF_tree, max_GBC, 1, D, max_group, nodes, greedy
+    )
+
+    v = len(G)
+    if not endpoints:
+        scale = 0
+        # if the graph is connected then subtract the endpoints from
+        # the count for all the nodes in the graph. else count how many
+        # nodes are connected to the group's nodes and subtract that.
+        if nx.is_directed(G):
+            if nx.is_strongly_connected(G):
+                scale = k * (2 * v - k - 1)
+        elif nx.is_connected(G):
+            scale = k * (2 * v - k - 1)
+        if scale == 0:
+            for group_node1 in max_group:
+                for node in D[group_node1]:
+                    if node != group_node1:
+                        if node in max_group:
+                            scale += 1
+                        else:
+                            scale += 2
+        max_GBC -= scale
+
+    # normalized
+    if normalized:
+        scale = 1 / ((v - k) * (v - k - 1))
+        max_GBC *= scale
+
+    # If undirected then count only the undirected edges
+    elif not G.is_directed():
+        max_GBC /= 2
+    max_GBC = float("%.2f" % max_GBC)
+    return max_GBC, max_group
+
+
+def _dfbnb(G, k, DF_tree, max_GBC, root, D, max_group, nodes, greedy):
+    # stopping condition - if we found a group of size k and with higher GBC then prune
+    if len(DF_tree.nodes[root]["GM"]) == k and DF_tree.nodes[root]["GBC"] > max_GBC:
+        return DF_tree.nodes[root]["GBC"], DF_tree, DF_tree.nodes[root]["GM"]
+    # stopping condition - if the size of group members equal to k or there are less than
+    # k - |GM| in the candidate list or the heuristic function plus the GBC is below the
+    # maximal GBC found then prune
+    if (
+        len(DF_tree.nodes[root]["GM"]) == k
+        or len(DF_tree.nodes[root]["CL"]) <= k - len(DF_tree.nodes[root]["GM"])
+        or DF_tree.nodes[root]["GBC"] + DF_tree.nodes[root]["heu"] <= max_GBC
+    ):
+        return max_GBC, DF_tree, max_group
+
+    # finding the heuristic of both children
+    node_p, node_m, DF_tree = _heuristic(k, root, DF_tree, D, nodes, greedy)
+
+    # finding the child with the bigger heuristic + GBC and expand
+    # that node first if greedy then only expand the plus node
+    if greedy:
+        max_GBC, DF_tree, max_group = _dfbnb(
+            G, k, DF_tree, max_GBC, node_p, D, max_group, nodes, greedy
+        )
+
+    elif (
+        DF_tree.nodes[node_p]["GBC"] + DF_tree.nodes[node_p]["heu"]
+        > DF_tree.nodes[node_m]["GBC"] + DF_tree.nodes[node_m]["heu"]
+    ):
+        max_GBC, DF_tree, max_group = _dfbnb(
+            G, k, DF_tree, max_GBC, node_p, D, max_group, nodes, greedy
+        )
+        max_GBC, DF_tree, max_group = _dfbnb(
+            G, k, DF_tree, max_GBC, node_m, D, max_group, nodes, greedy
+        )
+    else:
+        max_GBC, DF_tree, max_group = _dfbnb(
+            G, k, DF_tree, max_GBC, node_m, D, max_group, nodes, greedy
+        )
+        max_GBC, DF_tree, max_group = _dfbnb(
+            G, k, DF_tree, max_GBC, node_p, D, max_group, nodes, greedy
+        )
+    return max_GBC, DF_tree, max_group
+
+
+def _heuristic(k, root, DF_tree, D, nodes, greedy):
+    import numpy as np
+
+    # This helper function add two nodes to DF_tree - one left son and the
+    # other right son, finds their heuristic, CL, GBC, and GM
+    node_p = DF_tree.number_of_nodes() + 1
+    node_m = DF_tree.number_of_nodes() + 2
+    added_node = DF_tree.nodes[root]["CL"][0]
+
+    # adding the plus node
+    DF_tree.add_nodes_from([(node_p, deepcopy(DF_tree.nodes[root]))])
+    DF_tree.nodes[node_p]["GM"].append(added_node)
+    DF_tree.nodes[node_p]["GBC"] += DF_tree.nodes[node_p]["cont"][added_node]
+    root_node = DF_tree.nodes[root]
+    for x in nodes:
+        for y in nodes:
+            dxvy = 0
+            dxyv = 0
+            dvxy = 0
+            if not (
+                root_node["sigma"][x][y] == 0
+                or root_node["sigma"][x][added_node] == 0
+                or root_node["sigma"][added_node][y] == 0
+            ):
+                if D[x][added_node] == D[x][y] + D[y][added_node]:
+                    dxyv = (
+                        root_node["sigma"][x][y]
+                        * root_node["sigma"][y][added_node]
+                        / root_node["sigma"][x][added_node]
+                    )
+                if D[x][y] == D[x][added_node] + D[added_node][y]:
+                    dxvy = (
+                        root_node["sigma"][x][added_node]
+                        * root_node["sigma"][added_node][y]
+                        / root_node["sigma"][x][y]
+                    )
+                if D[added_node][y] == D[added_node][x] + D[x][y]:
+                    dvxy = (
+                        root_node["sigma"][added_node][x]
+                        * root_node["sigma"][x][y]
+                        / root_node["sigma"][added_node][y]
+                    )
+            DF_tree.nodes[node_p]["sigma"][x][y] = root_node["sigma"][x][y] * (1 - dxvy)
+            DF_tree.nodes[node_p]["betweenness"][x][y] = (
+                root_node["betweenness"][x][y] - root_node["betweenness"][x][y] * dxvy
+            )
+            if y != added_node:
+                DF_tree.nodes[node_p]["betweenness"][x][y] -= (
+                    root_node["betweenness"][x][added_node] * dxyv
+                )
+            if x != added_node:
+                DF_tree.nodes[node_p]["betweenness"][x][y] -= (
+                    root_node["betweenness"][added_node][y] * dvxy
+                )
+
+    DF_tree.nodes[node_p]["CL"] = [
+        node
+        for _, node in sorted(
+            zip(np.diag(DF_tree.nodes[node_p]["betweenness"]), nodes), reverse=True
+        )
+        if node not in DF_tree.nodes[node_p]["GM"]
+    ]
+    DF_tree.nodes[node_p]["cont"] = dict(
+        zip(nodes, np.diag(DF_tree.nodes[node_p]["betweenness"]))
+    )
+    DF_tree.nodes[node_p]["heu"] = 0
+    for i in range(k - len(DF_tree.nodes[node_p]["GM"])):
+        DF_tree.nodes[node_p]["heu"] += DF_tree.nodes[node_p]["cont"][
+            DF_tree.nodes[node_p]["CL"][i]
+        ]
+
+    # adding the minus node - don't insert the first node in the CL to GM
+    # Insert minus node only if isn't greedy type algorithm
+    if not greedy:
+        DF_tree.add_nodes_from([(node_m, deepcopy(DF_tree.nodes[root]))])
+        DF_tree.nodes[node_m]["CL"].pop(0)
+        DF_tree.nodes[node_m]["cont"].pop(added_node)
+        DF_tree.nodes[node_m]["heu"] = 0
+        for i in range(k - len(DF_tree.nodes[node_m]["GM"])):
+            DF_tree.nodes[node_m]["heu"] += DF_tree.nodes[node_m]["cont"][
+                DF_tree.nodes[node_m]["CL"][i]
+            ]
+    else:
+        node_m = None
+
+    return node_p, node_m, DF_tree
+
+
+@nx._dispatch(edge_attrs="weight")
+def group_closeness_centrality(G, S, weight=None):
+    r"""Compute the group closeness centrality for a group of nodes.
+
+    Group closeness centrality of a group of nodes $S$ is a measure
+    of how close the group is to the other nodes in the graph.
+
+    .. math::
+
+       c_{close}(S) = \frac{|V-S|}{\sum_{v \in V-S} d_{S, v}}
+
+       d_{S, v} = min_{u \in S} (d_{u, v})
+
+    where $V$ is the set of nodes, $d_{S, v}$ is the distance of
+    the group $S$ from $v$ defined as above. ($V-S$ is the set of nodes
+    in $V$ that are not in $S$).
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph.
+
+    S : list or set
+       S is a group of nodes which belong to G, for which group closeness
+       centrality is to be calculated.
+
+    weight : None or string, optional (default=None)
+       If None, all edge weights are considered equal.
+       Otherwise holds the name of the edge attribute used as weight.
+       The weight of an edge is treated as the length or distance between the two sides.
+
+    Raises
+    ------
+    NodeNotFound
+       If node(s) in S are not present in G.
+
+    Returns
+    -------
+    closeness : float
+       Group closeness centrality of the group S.
+
+    See Also
+    --------
+    closeness_centrality
+
+    Notes
+    -----
+    The measure was introduced in [1]_.
+    The formula implemented here is described in [2]_.
+
+    Higher values of closeness indicate greater centrality.
+
+    It is assumed that 1 / 0 is 0 (required in the case of directed graphs,
+    or when a shortest path length is 0).
+
+    The number of nodes in the group must be a maximum of n - 1 where `n`
+    is the total number of nodes in the graph.
+
+    For directed graphs, the incoming distance is utilized here. To use the
+    outward distance, act on `G.reverse()`.
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    References
+    ----------
+    .. [1] M G Everett and S P Borgatti:
+       The Centrality of Groups and Classes.
+       Journal of Mathematical Sociology. 23(3): 181-201. 1999.
+       http://www.analytictech.com/borgatti/group_centrality.htm
+    .. [2] J. Zhao et. al.:
+       Measuring and Maximizing Group Closeness Centrality over
+       Disk Resident Graphs.
+       WWWConference Proceedings, 2014. 689-694.
+       https://doi.org/10.1145/2567948.2579356
+    """
+    if G.is_directed():
+        G = G.reverse()  # reverse view
+    closeness = 0  # initialize to 0
+    V = set(G)  # set of nodes in G
+    S = set(S)  # set of nodes in group S
+    V_S = V - S  # set of nodes in V but not S
+    shortest_path_lengths = nx.multi_source_dijkstra_path_length(G, S, weight=weight)
+    # accumulation
+    for v in V_S:
+        try:
+            closeness += shortest_path_lengths[v]
+        except KeyError:  # no path exists
+            closeness += 0
+    try:
+        closeness = len(V_S) / closeness
+    except ZeroDivisionError:  # 1 / 0 assumed as 0
+        closeness = 0
+    return closeness
+
+
+@nx._dispatch
+def group_degree_centrality(G, S):
+    """Compute the group degree centrality for a group of nodes.
+
+    Group degree centrality of a group of nodes $S$ is the fraction
+    of non-group members connected to group members.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph.
+
+    S : list or set
+       S is a group of nodes which belong to G, for which group degree
+       centrality is to be calculated.
+
+    Raises
+    ------
+    NetworkXError
+       If node(s) in S are not in G.
+
+    Returns
+    -------
+    centrality : float
+       Group degree centrality of the group S.
+
+    See Also
+    --------
+    degree_centrality
+    group_in_degree_centrality
+    group_out_degree_centrality
+
+    Notes
+    -----
+    The measure was introduced in [1]_.
+
+    The number of nodes in the group must be a maximum of n - 1 where `n`
+    is the total number of nodes in the graph.
+
+    References
+    ----------
+    .. [1] M G Everett and S P Borgatti:
+       The Centrality of Groups and Classes.
+       Journal of Mathematical Sociology. 23(3): 181-201. 1999.
+       http://www.analytictech.com/borgatti/group_centrality.htm
+    """
+    centrality = len(set().union(*[set(G.neighbors(i)) for i in S]) - set(S))
+    centrality /= len(G.nodes()) - len(S)
+    return centrality
+
+
+@not_implemented_for("undirected")
+@nx._dispatch
+def group_in_degree_centrality(G, S):
+    """Compute the group in-degree centrality for a group of nodes.
+
+    Group in-degree centrality of a group of nodes $S$ is the fraction
+    of non-group members connected to group members by incoming edges.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph.
+
+    S : list or set
+       S is a group of nodes which belong to G, for which group in-degree
+       centrality is to be calculated.
+
+    Returns
+    -------
+    centrality : float
+       Group in-degree centrality of the group S.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+       If G is undirected.
+
+    NodeNotFound
+       If node(s) in S are not in G.
+
+    See Also
+    --------
+    degree_centrality
+    group_degree_centrality
+    group_out_degree_centrality
+
+    Notes
+    -----
+    The number of nodes in the group must be a maximum of n - 1 where `n`
+    is the total number of nodes in the graph.
+
+    `G.neighbors(i)` gives nodes with an outward edge from i, in a DiGraph,
+    so for group in-degree centrality, the reverse graph is used.
+    """
+    return group_degree_centrality(G.reverse(), S)
+
+
+@not_implemented_for("undirected")
+@nx._dispatch
+def group_out_degree_centrality(G, S):
+    """Compute the group out-degree centrality for a group of nodes.
+
+    Group out-degree centrality of a group of nodes $S$ is the fraction
+    of non-group members connected to group members by outgoing edges.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph.
+
+    S : list or set
+       S is a group of nodes which belong to G, for which group in-degree
+       centrality is to be calculated.
+
+    Returns
+    -------
+    centrality : float
+       Group out-degree centrality of the group S.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+       If G is undirected.
+
+    NodeNotFound
+       If node(s) in S are not in G.
+
+    See Also
+    --------
+    degree_centrality
+    group_degree_centrality
+    group_in_degree_centrality
+
+    Notes
+    -----
+    The number of nodes in the group must be a maximum of n - 1 where `n`
+    is the total number of nodes in the graph.
+
+    `G.neighbors(i)` gives nodes with an outward edge from i, in a DiGraph,
+    so for group out-degree centrality, the graph itself is used.
+    """
+    return group_degree_centrality(G, S)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/katz.py

@@ -0,0 +1,331 @@
+"""Katz centrality."""
+import math
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["katz_centrality", "katz_centrality_numpy"]
+
+
+@not_implemented_for("multigraph")
+@nx._dispatch(edge_attrs="weight")
+def katz_centrality(
+    G,
+    alpha=0.1,
+    beta=1.0,
+    max_iter=1000,
+    tol=1.0e-6,
+    nstart=None,
+    normalized=True,
+    weight=None,
+):
+    r"""Compute the Katz centrality for the nodes of the graph G.
+
+    Katz centrality computes the centrality for a node based on the centrality
+    of its neighbors. It is a generalization of the eigenvector centrality. The
+    Katz centrality for node $i$ is
+
+    .. math::
+
+        x_i = \alpha \sum_{j} A_{ij} x_j + \beta,
+
+    where $A$ is the adjacency matrix of graph G with eigenvalues $\lambda$.
+
+    The parameter $\beta$ controls the initial centrality and
+
+    .. math::
+
+        \alpha < \frac{1}{\lambda_{\max}}.
+
+    Katz centrality computes the relative influence of a node within a
+    network by measuring the number of the immediate neighbors (first
+    degree nodes) and also all other nodes in the network that connect
+    to the node under consideration through these immediate neighbors.
+
+    Extra weight can be provided to immediate neighbors through the
+    parameter $\beta$.  Connections made with distant neighbors
+    are, however, penalized by an attenuation factor $\alpha$ which
+    should be strictly less than the inverse largest eigenvalue of the
+    adjacency matrix in order for the Katz centrality to be computed
+    correctly. More information is provided in [1]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    alpha : float, optional (default=0.1)
+      Attenuation factor
+
+    beta : scalar or dictionary, optional (default=1.0)
+      Weight attributed to the immediate neighborhood. If not a scalar, the
+      dictionary must have an value for every node.
+
+    max_iter : integer, optional (default=1000)
+      Maximum number of iterations in power method.
+
+    tol : float, optional (default=1.0e-6)
+      Error tolerance used to check convergence in power method iteration.
+
+    nstart : dictionary, optional
+      Starting value of Katz iteration for each node.
+
+    normalized : bool, optional (default=True)
+      If True normalize the resulting values.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      In this measure the weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with Katz centrality as the value.
+
+    Raises
+    ------
+    NetworkXError
+       If the parameter `beta` is not a scalar but lacks a value for at least
+       one node
+
+    PowerIterationFailedConvergence
+        If the algorithm fails to converge to the specified tolerance
+        within the specified number of iterations of the power iteration
+        method.
+
+    Examples
+    --------
+    >>> import math
+    >>> G = nx.path_graph(4)
+    >>> phi = (1 + math.sqrt(5)) / 2.0  # largest eigenvalue of adj matrix
+    >>> centrality = nx.katz_centrality(G, 1 / phi - 0.01)
+    >>> for n, c in sorted(centrality.items()):
+    ...     print(f"{n} {c:.2f}")
+    0 0.37
+    1 0.60
+    2 0.60
+    3 0.37
+
+    See Also
+    --------
+    katz_centrality_numpy
+    eigenvector_centrality
+    eigenvector_centrality_numpy
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Katz centrality was introduced by [2]_.
+
+    This algorithm it uses the power method to find the eigenvector
+    corresponding to the largest eigenvalue of the adjacency matrix of ``G``.
+    The parameter ``alpha`` should be strictly less than the inverse of largest
+    eigenvalue of the adjacency matrix for the algorithm to converge.
+    You can use ``max(nx.adjacency_spectrum(G))`` to get $\lambda_{\max}$ the largest
+    eigenvalue of the adjacency matrix.
+    The iteration will stop after ``max_iter`` iterations or an error tolerance of
+    ``number_of_nodes(G) * tol`` has been reached.
+
+    When $\alpha = 1/\lambda_{\max}$ and $\beta=0$, Katz centrality is the same
+    as eigenvector centrality.
+
+    For directed graphs this finds "left" eigenvectors which corresponds
+    to the in-edges in the graph. For out-edges Katz centrality
+    first reverse the graph with ``G.reverse()``.
+
+    References
+    ----------
+    .. [1] Mark E. J. Newman:
+       Networks: An Introduction.
+       Oxford University Press, USA, 2010, p. 720.
+    .. [2] Leo Katz:
+       A New Status Index Derived from Sociometric Index.
+       Psychometrika 18(1):39–43, 1953
+       https://link.springer.com/content/pdf/10.1007/BF02289026.pdf
+    """
+    if len(G) == 0:
+        return {}
+
+    nnodes = G.number_of_nodes()
+
+    if nstart is None:
+        # choose starting vector with entries of 0
+        x = {n: 0 for n in G}
+    else:
+        x = nstart
+
+    try:
+        b = dict.fromkeys(G, float(beta))
+    except (TypeError, ValueError, AttributeError) as err:
+        b = beta
+        if set(beta) != set(G):
+            raise nx.NetworkXError(
+                "beta dictionary " "must have a value for every node"
+            ) from err
+
+    # make up to max_iter iterations
+    for _ in range(max_iter):
+        xlast = x
+        x = dict.fromkeys(xlast, 0)
+        # do the multiplication y^T = Alpha * x^T A + Beta
+        for n in x:
+            for nbr in G[n]:
+                x[nbr] += xlast[n] * G[n][nbr].get(weight, 1)
+        for n in x:
+            x[n] = alpha * x[n] + b[n]
+
+        # check convergence
+        error = sum(abs(x[n] - xlast[n]) for n in x)
+        if error < nnodes * tol:
+            if normalized:
+                # normalize vector
+                try:
+                    s = 1.0 / math.hypot(*x.values())
+                # this should never be zero?
+                except ZeroDivisionError:
+                    s = 1.0
+            else:
+                s = 1
+            for n in x:
+                x[n] *= s
+            return x
+    raise nx.PowerIterationFailedConvergence(max_iter)
+
+
+@not_implemented_for("multigraph")
+@nx._dispatch(edge_attrs="weight")
+def katz_centrality_numpy(G, alpha=0.1, beta=1.0, normalized=True, weight=None):
+    r"""Compute the Katz centrality for the graph G.
+
+    Katz centrality computes the centrality for a node based on the centrality
+    of its neighbors. It is a generalization of the eigenvector centrality. The
+    Katz centrality for node $i$ is
+
+    .. math::
+
+        x_i = \alpha \sum_{j} A_{ij} x_j + \beta,
+
+    where $A$ is the adjacency matrix of graph G with eigenvalues $\lambda$.
+
+    The parameter $\beta$ controls the initial centrality and
+
+    .. math::
+
+        \alpha < \frac{1}{\lambda_{\max}}.
+
+    Katz centrality computes the relative influence of a node within a
+    network by measuring the number of the immediate neighbors (first
+    degree nodes) and also all other nodes in the network that connect
+    to the node under consideration through these immediate neighbors.
+
+    Extra weight can be provided to immediate neighbors through the
+    parameter $\beta$.  Connections made with distant neighbors
+    are, however, penalized by an attenuation factor $\alpha$ which
+    should be strictly less than the inverse largest eigenvalue of the
+    adjacency matrix in order for the Katz centrality to be computed
+    correctly. More information is provided in [1]_.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph
+
+    alpha : float
+      Attenuation factor
+
+    beta : scalar or dictionary, optional (default=1.0)
+      Weight attributed to the immediate neighborhood. If not a scalar the
+      dictionary must have an value for every node.
+
+    normalized : bool
+      If True normalize the resulting values.
+
+    weight : None or string, optional
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      In this measure the weight is interpreted as the connection strength.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with Katz centrality as the value.
+
+    Raises
+    ------
+    NetworkXError
+       If the parameter `beta` is not a scalar but lacks a value for at least
+       one node
+
+    Examples
+    --------
+    >>> import math
+    >>> G = nx.path_graph(4)
+    >>> phi = (1 + math.sqrt(5)) / 2.0  # largest eigenvalue of adj matrix
+    >>> centrality = nx.katz_centrality_numpy(G, 1 / phi)
+    >>> for n, c in sorted(centrality.items()):
+    ...     print(f"{n} {c:.2f}")
+    0 0.37
+    1 0.60
+    2 0.60
+    3 0.37
+
+    See Also
+    --------
+    katz_centrality
+    eigenvector_centrality_numpy
+    eigenvector_centrality
+    :func:`~networkx.algorithms.link_analysis.pagerank_alg.pagerank`
+    :func:`~networkx.algorithms.link_analysis.hits_alg.hits`
+
+    Notes
+    -----
+    Katz centrality was introduced by [2]_.
+
+    This algorithm uses a direct linear solver to solve the above equation.
+    The parameter ``alpha`` should be strictly less than the inverse of largest
+    eigenvalue of the adjacency matrix for there to be a solution.
+    You can use ``max(nx.adjacency_spectrum(G))`` to get $\lambda_{\max}$ the largest
+    eigenvalue of the adjacency matrix.
+
+    When $\alpha = 1/\lambda_{\max}$ and $\beta=0$, Katz centrality is the same
+    as eigenvector centrality.
+
+    For directed graphs this finds "left" eigenvectors which corresponds
+    to the in-edges in the graph. For out-edges Katz centrality
+    first reverse the graph with ``G.reverse()``.
+
+    References
+    ----------
+    .. [1] Mark E. J. Newman:
+       Networks: An Introduction.
+       Oxford University Press, USA, 2010, p. 173.
+    .. [2] Leo Katz:
+       A New Status Index Derived from Sociometric Index.
+       Psychometrika 18(1):39–43, 1953
+       https://link.springer.com/content/pdf/10.1007/BF02289026.pdf
+    """
+    import numpy as np
+
+    if len(G) == 0:
+        return {}
+    try:
+        nodelist = beta.keys()
+        if set(nodelist) != set(G):
+            raise nx.NetworkXError("beta dictionary must have a value for every node")
+        b = np.array(list(beta.values()), dtype=float)
+    except AttributeError:
+        nodelist = list(G)
+        try:
+            b = np.ones((len(nodelist), 1)) * beta
+        except (TypeError, ValueError, AttributeError) as err:
+            raise nx.NetworkXError("beta must be a number") from err
+
+    A = nx.adjacency_matrix(G, nodelist=nodelist, weight=weight).todense().T
+    n = A.shape[0]
+    centrality = np.linalg.solve(np.eye(n, n) - (alpha * A), b).squeeze()
+
+    # Normalize: rely on truediv to cast to float
+    norm = np.sign(sum(centrality)) * np.linalg.norm(centrality) if normalized else 1
+    return dict(zip(nodelist, centrality / norm))

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/laplacian.py

@@ -0,0 +1,146 @@
+"""
+Laplacian centrality measures.
+"""
+import networkx as nx
+
+__all__ = ["laplacian_centrality"]
+
+
+@nx._dispatch(edge_attrs="weight")
+def laplacian_centrality(
+    G, normalized=True, nodelist=None, weight="weight", walk_type=None, alpha=0.95
+):
+    r"""Compute the Laplacian centrality for nodes in the graph `G`.
+
+    The Laplacian Centrality of a node ``i`` is measured by the drop in the
+    Laplacian Energy after deleting node ``i`` from the graph. The Laplacian Energy
+    is the sum of the squared eigenvalues of a graph's Laplacian matrix.
+
+    .. math::
+
+        C_L(u_i,G) = \frac{(\Delta E)_i}{E_L (G)} = \frac{E_L (G)-E_L (G_i)}{E_L (G)}
+
+        E_L (G) = \sum_{i=0}^n \lambda_i^2
+
+    Where $E_L (G)$ is the Laplacian energy of graph `G`,
+    E_L (G_i) is the Laplacian energy of graph `G` after deleting node ``i``
+    and $\lambda_i$ are the eigenvalues of `G`'s Laplacian matrix.
+    This formula shows the normalized value. Without normalization,
+    the numerator on the right side is returned.
+
+    Parameters
+    ----------
+    G : graph
+        A networkx graph
+
+    normalized : bool (default = True)
+        If True the centrality score is scaled so the sum over all nodes is 1.
+        If False the centrality score for each node is the drop in Laplacian
+        energy when that node is removed.
+
+    nodelist : list, optional (default = None)
+        The rows and columns are ordered according to the nodes in nodelist.
+        If nodelist is None, then the ordering is produced by G.nodes().
+
+    weight: string or None, optional (default=`weight`)
+        Optional parameter `weight` to compute the Laplacian matrix.
+        The edge data key used to compute each value in the matrix.
+        If None, then each edge has weight 1.
+
+    walk_type : string or None, optional (default=None)
+        Optional parameter `walk_type` used when calling
+        :func:`directed_laplacian_matrix <networkx.directed_laplacian_matrix>`.
+        If None, the transition matrix is selected depending on the properties
+        of the graph. Otherwise can be `random`, `lazy`, or `pagerank`.
+
+    alpha : real (default = 0.95)
+        Optional parameter `alpha` used when calling
+        :func:`directed_laplacian_matrix <networkx.directed_laplacian_matrix>`.
+        (1 - alpha) is the teleportation probability used with pagerank.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with Laplacian centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> edges = [(0, 1, 4), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2), (4, 5, 1)]
+    >>> G.add_weighted_edges_from(edges)
+    >>> sorted((v, f"{c:0.2f}") for v, c in laplacian_centrality(G).items())
+    [(0, '0.70'), (1, '0.90'), (2, '0.28'), (3, '0.22'), (4, '0.26'), (5, '0.04')]
+
+    Notes
+    -----
+    The algorithm is implemented based on [1]_ with an extension to directed graphs
+    using the ``directed_laplacian_matrix`` function.
+
+    Raises
+    ------
+    NetworkXPointlessConcept
+        If the graph `G` is the null graph.
+    ZeroDivisionError
+        If the graph `G` has no edges (is empty) and normalization is requested.
+
+    References
+    ----------
+    .. [1] Qi, X., Fuller, E., Wu, Q., Wu, Y., and Zhang, C.-Q. (2012).
+       Laplacian centrality: A new centrality measure for weighted networks.
+       Information Sciences, 194:240-253.
+       https://math.wvu.edu/~cqzhang/Publication-files/my-paper/INS-2012-Laplacian-W.pdf
+
+    See Also
+    --------
+    :func:`~networkx.linalg.laplacianmatrix.directed_laplacian_matrix`
+    :func:`~networkx.linalg.laplacianmatrix.laplacian_matrix`
+    """
+    import numpy as np
+    import scipy as sp
+
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept("null graph has no centrality defined")
+    if G.size(weight=weight) == 0:
+        if normalized:
+            raise ZeroDivisionError("graph with no edges has zero full energy")
+        return {n: 0 for n in G}
+
+    if nodelist is not None:
+        nodeset = set(G.nbunch_iter(nodelist))
+        if len(nodeset) != len(nodelist):
+            raise nx.NetworkXError("nodelist has duplicate nodes or nodes not in G")
+        nodes = nodelist + [n for n in G if n not in nodeset]
+    else:
+        nodelist = nodes = list(G)
+
+    if G.is_directed():
+        lap_matrix = nx.directed_laplacian_matrix(G, nodes, weight, walk_type, alpha)
+    else:
+        lap_matrix = nx.laplacian_matrix(G, nodes, weight).toarray()
+
+    full_energy = np.power(sp.linalg.eigh(lap_matrix, eigvals_only=True), 2).sum()
+
+    # calculate laplacian centrality
+    laplace_centralities_dict = {}
+    for i, node in enumerate(nodelist):
+        # remove row and col i from lap_matrix
+        all_but_i = list(np.arange(lap_matrix.shape[0]))
+        all_but_i.remove(i)
+        A_2 = lap_matrix[all_but_i, :][:, all_but_i]
+
+        # Adjust diagonal for removed row
+        new_diag = lap_matrix.diagonal() - abs(lap_matrix[:, i])
+        np.fill_diagonal(A_2, new_diag[all_but_i])
+
+        if len(all_but_i) > 0:  # catches degenerate case of single node
+            new_energy = np.power(sp.linalg.eigh(A_2, eigvals_only=True), 2).sum()
+        else:
+            new_energy = 0.0
+
+        lapl_cent = full_energy - new_energy
+        if normalized:
+            lapl_cent = lapl_cent / full_energy
+
+        laplace_centralities_dict[node] = lapl_cent
+
+    return laplace_centralities_dict

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/percolation.py

@@ -0,0 +1,128 @@
+"""Percolation centrality measures."""
+
+import networkx as nx
+from networkx.algorithms.centrality.betweenness import (
+    _single_source_dijkstra_path_basic as dijkstra,
+)
+from networkx.algorithms.centrality.betweenness import (
+    _single_source_shortest_path_basic as shortest_path,
+)
+
+__all__ = ["percolation_centrality"]
+
+
+@nx._dispatch(node_attrs="attribute", edge_attrs="weight")
+def percolation_centrality(G, attribute="percolation", states=None, weight=None):
+    r"""Compute the percolation centrality for nodes.
+
+    Percolation centrality of a node $v$, at a given time, is defined
+    as the proportion of ‘percolated paths’ that go through that node.
+
+    This measure quantifies relative impact of nodes based on their
+    topological connectivity, as well as their percolation states.
+
+    Percolation states of nodes are used to depict network percolation
+    scenarios (such as during infection transmission in a social network
+    of individuals, spreading of computer viruses on computer networks, or
+    transmission of disease over a network of towns) over time. In this
+    measure usually the percolation state is expressed as a decimal
+    between 0.0 and 1.0.
+
+    When all nodes are in the same percolated state this measure is
+    equivalent to betweenness centrality.
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX graph.
+
+    attribute : None or string, optional (default='percolation')
+      Name of the node attribute to use for percolation state, used
+      if `states` is None. If a node does not set the attribute the
+      state of that node will be set to the default value of 1.
+      If all nodes do not have the attribute all nodes will be set to
+      1 and the centrality measure will be equivalent to betweenness centrality.
+
+    states : None or dict, optional (default=None)
+      Specify percolation states for the nodes, nodes as keys states
+      as values.
+
+    weight : None or string, optional (default=None)
+      If None, all edge weights are considered equal.
+      Otherwise holds the name of the edge attribute used as weight.
+      The weight of an edge is treated as the length or distance between the two sides.
+
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with percolation centrality as the value.
+
+    See Also
+    --------
+    betweenness_centrality
+
+    Notes
+    -----
+    The algorithm is from Mahendra Piraveenan, Mikhail Prokopenko, and
+    Liaquat Hossain [1]_
+    Pair dependencies are calculated and accumulated using [2]_
+
+    For weighted graphs the edge weights must be greater than zero.
+    Zero edge weights can produce an infinite number of equal length
+    paths between pairs of nodes.
+
+    References
+    ----------
+    .. [1] Mahendra Piraveenan, Mikhail Prokopenko, Liaquat Hossain
+       Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes
+       during Percolation in Networks
+       http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0053095
+    .. [2] Ulrik Brandes:
+       A Faster Algorithm for Betweenness Centrality.
+       Journal of Mathematical Sociology 25(2):163-177, 2001.
+       https://doi.org/10.1080/0022250X.2001.9990249
+    """
+    percolation = dict.fromkeys(G, 0.0)  # b[v]=0 for v in G
+
+    nodes = G
+
+    if states is None:
+        states = nx.get_node_attributes(nodes, attribute, default=1)
+
+    # sum of all percolation states
+    p_sigma_x_t = 0.0
+    for v in states.values():
+        p_sigma_x_t += v
+
+    for s in nodes:
+        # single source shortest paths
+        if weight is None:  # use BFS
+            S, P, sigma, _ = shortest_path(G, s)
+        else:  # use Dijkstra's algorithm
+            S, P, sigma, _ = dijkstra(G, s, weight)
+        # accumulation
+        percolation = _accumulate_percolation(
+            percolation, S, P, sigma, s, states, p_sigma_x_t
+        )
+
+    n = len(G)
+
+    for v in percolation:
+        percolation[v] *= 1 / (n - 2)
+
+    return percolation
+
+
+def _accumulate_percolation(percolation, S, P, sigma, s, states, p_sigma_x_t):
+    delta = dict.fromkeys(S, 0)
+    while S:
+        w = S.pop()
+        coeff = (1 + delta[w]) / sigma[w]
+        for v in P[w]:
+            delta[v] += sigma[v] * coeff
+        if w != s:
+            # percolation weight
+            pw_s_w = states[s] / (p_sigma_x_t - states[w])
+            percolation[w] += delta[w] * pw_s_w
+    return percolation

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/second_order.py

@@ -0,0 +1,138 @@
+"""Copyright (c) 2015 – Thomson Licensing, SAS
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted (subject to the limitations in the
+disclaimer below) provided that the following conditions are met:
+
+* Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in the
+documentation and/or other materials provided with the distribution.
+
+* Neither the name of Thomson Licensing, or Technicolor, nor the names
+of its contributors may be used to endorse or promote products derived
+from this software without specific prior written permission.
+
+NO EXPRESS OR IMPLIED LICENSES TO ANY PARTY'S PATENT RIGHTS ARE
+GRANTED BY THIS LICENSE.  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT
+HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED
+WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
+MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
+BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
+WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE
+OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN
+IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+"""
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+# Authors: Erwan Le Merrer (erwan.lemerrer@technicolor.com)
+
+__all__ = ["second_order_centrality"]
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs="weight")
+def second_order_centrality(G, weight="weight"):
+    """Compute the second order centrality for nodes of G.
+
+    The second order centrality of a given node is the standard deviation of
+    the return times to that node of a perpetual random walk on G:
+
+    Parameters
+    ----------
+    G : graph
+      A NetworkX connected and undirected graph.
+
+    weight : string or None, optional (default="weight")
+        The name of an edge attribute that holds the numerical value
+        used as a weight. If None then each edge has weight 1.
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary keyed by node with second order centrality as the value.
+
+    Examples
+    --------
+    >>> G = nx.star_graph(10)
+    >>> soc = nx.second_order_centrality(G)
+    >>> print(sorted(soc.items(), key=lambda x: x[1])[0][0])  # pick first id
+    0
+
+    Raises
+    ------
+    NetworkXException
+        If the graph G is empty, non connected or has negative weights.
+
+    See Also
+    --------
+    betweenness_centrality
+
+    Notes
+    -----
+    Lower values of second order centrality indicate higher centrality.
+
+    The algorithm is from Kermarrec, Le Merrer, Sericola and Trédan [1]_.
+
+    This code implements the analytical version of the algorithm, i.e.,
+    there is no simulation of a random walk process involved. The random walk
+    is here unbiased (corresponding to eq 6 of the paper [1]_), thus the
+    centrality values are the standard deviations for random walk return times
+    on the transformed input graph G (equal in-degree at each nodes by adding
+    self-loops).
+
+    Complexity of this implementation, made to run locally on a single machine,
+    is O(n^3), with n the size of G, which makes it viable only for small
+    graphs.
+
+    References
+    ----------
+    .. [1] Anne-Marie Kermarrec, Erwan Le Merrer, Bruno Sericola, Gilles Trédan
+       "Second order centrality: Distributed assessment of nodes criticity in
+       complex networks", Elsevier Computer Communications 34(5):619-628, 2011.
+    """
+    import numpy as np
+
+    n = len(G)
+
+    if n == 0:
+        raise nx.NetworkXException("Empty graph.")
+    if not nx.is_connected(G):
+        raise nx.NetworkXException("Non connected graph.")
+    if any(d.get(weight, 0) < 0 for u, v, d in G.edges(data=True)):
+        raise nx.NetworkXException("Graph has negative edge weights.")
+
+    # balancing G for Metropolis-Hastings random walks
+    G = nx.DiGraph(G)
+    in_deg = dict(G.in_degree(weight=weight))
+    d_max = max(in_deg.values())
+    for i, deg in in_deg.items():
+        if deg < d_max:
+            G.add_edge(i, i, weight=d_max - deg)
+
+    P = nx.to_numpy_array(G)
+    P /= P.sum(axis=1)[:, np.newaxis]  # to transition probability matrix
+
+    def _Qj(P, j):
+        P = P.copy()
+        P[:, j] = 0
+        return P
+
+    M = np.empty([n, n])
+
+    for i in range(n):
+        M[:, i] = np.linalg.solve(
+            np.identity(n) - _Qj(P, i), np.ones([n, 1])[:, 0]
+        )  # eq 3
+
+    return dict(
+        zip(G.nodes, [np.sqrt(2 * np.sum(M[:, i]) - n * (n + 1)) for i in range(n)])
+    )  # eq 6

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/subgraph_alg.py

@@ -0,0 +1,340 @@
+"""
+Subraph centrality and communicability betweenness.
+"""
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "subgraph_centrality_exp",
+    "subgraph_centrality",
+    "communicability_betweenness_centrality",
+    "estrada_index",
+]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def subgraph_centrality_exp(G):
+    r"""Returns the subgraph centrality for each node of G.
+
+    Subgraph centrality  of a node `n` is the sum of weighted closed
+    walks of all lengths starting and ending at node `n`. The weights
+    decrease with path length. Each closed walk is associated with a
+    connected subgraph ([1]_).
+
+    Parameters
+    ----------
+    G: graph
+
+    Returns
+    -------
+    nodes:dictionary
+        Dictionary of nodes with subgraph centrality as the value.
+
+    Raises
+    ------
+    NetworkXError
+        If the graph is not undirected and simple.
+
+    See Also
+    --------
+    subgraph_centrality:
+        Alternative algorithm of the subgraph centrality for each node of G.
+
+    Notes
+    -----
+    This version of the algorithm exponentiates the adjacency matrix.
+
+    The subgraph centrality of a node `u` in G can be found using
+    the matrix exponential of the adjacency matrix of G [1]_,
+
+    .. math::
+
+        SC(u)=(e^A)_{uu} .
+
+    References
+    ----------
+    .. [1] Ernesto Estrada, Juan A. Rodriguez-Velazquez,
+       "Subgraph centrality in complex networks",
+       Physical Review E 71, 056103 (2005).
+       https://arxiv.org/abs/cond-mat/0504730
+
+    Examples
+    --------
+    (Example from [1]_)
+    >>> G = nx.Graph(
+    ...     [
+    ...         (1, 2),
+    ...         (1, 5),
+    ...         (1, 8),
+    ...         (2, 3),
+    ...         (2, 8),
+    ...         (3, 4),
+    ...         (3, 6),
+    ...         (4, 5),
+    ...         (4, 7),
+    ...         (5, 6),
+    ...         (6, 7),
+    ...         (7, 8),
+    ...     ]
+    ... )
+    >>> sc = nx.subgraph_centrality_exp(G)
+    >>> print([f"{node} {sc[node]:0.2f}" for node in sorted(sc)])
+    ['1 3.90', '2 3.90', '3 3.64', '4 3.71', '5 3.64', '6 3.71', '7 3.64', '8 3.90']
+    """
+    # alternative implementation that calculates the matrix exponential
+    import scipy as sp
+
+    nodelist = list(G)  # ordering of nodes in matrix
+    A = nx.to_numpy_array(G, nodelist)
+    # convert to 0-1 matrix
+    A[A != 0.0] = 1
+    expA = sp.linalg.expm(A)
+    # convert diagonal to dictionary keyed by node
+    sc = dict(zip(nodelist, map(float, expA.diagonal())))
+    return sc
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def subgraph_centrality(G):
+    r"""Returns subgraph centrality for each node in G.
+
+    Subgraph centrality  of a node `n` is the sum of weighted closed
+    walks of all lengths starting and ending at node `n`. The weights
+    decrease with path length. Each closed walk is associated with a
+    connected subgraph ([1]_).
+
+    Parameters
+    ----------
+    G: graph
+
+    Returns
+    -------
+    nodes : dictionary
+       Dictionary of nodes with subgraph centrality as the value.
+
+    Raises
+    ------
+    NetworkXError
+       If the graph is not undirected and simple.
+
+    See Also
+    --------
+    subgraph_centrality_exp:
+        Alternative algorithm of the subgraph centrality for each node of G.
+
+    Notes
+    -----
+    This version of the algorithm computes eigenvalues and eigenvectors
+    of the adjacency matrix.
+
+    Subgraph centrality of a node `u` in G can be found using
+    a spectral decomposition of the adjacency matrix [1]_,
+
+    .. math::
+
+       SC(u)=\sum_{j=1}^{N}(v_{j}^{u})^2 e^{\lambda_{j}},
+
+    where `v_j` is an eigenvector of the adjacency matrix `A` of G
+    corresponding to the eigenvalue `\lambda_j`.
+
+    Examples
+    --------
+    (Example from [1]_)
+    >>> G = nx.Graph(
+    ...     [
+    ...         (1, 2),
+    ...         (1, 5),
+    ...         (1, 8),
+    ...         (2, 3),
+    ...         (2, 8),
+    ...         (3, 4),
+    ...         (3, 6),
+    ...         (4, 5),
+    ...         (4, 7),
+    ...         (5, 6),
+    ...         (6, 7),
+    ...         (7, 8),
+    ...     ]
+    ... )
+    >>> sc = nx.subgraph_centrality(G)
+    >>> print([f"{node} {sc[node]:0.2f}" for node in sorted(sc)])
+    ['1 3.90', '2 3.90', '3 3.64', '4 3.71', '5 3.64', '6 3.71', '7 3.64', '8 3.90']
+
+    References
+    ----------
+    .. [1] Ernesto Estrada, Juan A. Rodriguez-Velazquez,
+       "Subgraph centrality in complex networks",
+       Physical Review E 71, 056103 (2005).
+       https://arxiv.org/abs/cond-mat/0504730
+
+    """
+    import numpy as np
+
+    nodelist = list(G)  # ordering of nodes in matrix
+    A = nx.to_numpy_array(G, nodelist)
+    # convert to 0-1 matrix
+    A[np.nonzero(A)] = 1
+    w, v = np.linalg.eigh(A)
+    vsquare = np.array(v) ** 2
+    expw = np.exp(w)
+    xg = vsquare @ expw
+    # convert vector dictionary keyed by node
+    sc = dict(zip(nodelist, map(float, xg)))
+    return sc
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def communicability_betweenness_centrality(G):
+    r"""Returns subgraph communicability for all pairs of nodes in G.
+
+    Communicability betweenness measure makes use of the number of walks
+    connecting every pair of nodes as the basis of a betweenness centrality
+    measure.
+
+    Parameters
+    ----------
+    G: graph
+
+    Returns
+    -------
+    nodes : dictionary
+        Dictionary of nodes with communicability betweenness as the value.
+
+    Raises
+    ------
+    NetworkXError
+        If the graph is not undirected and simple.
+
+    Notes
+    -----
+    Let `G=(V,E)` be a simple undirected graph with `n` nodes and `m` edges,
+    and `A` denote the adjacency matrix of `G`.
+
+    Let `G(r)=(V,E(r))` be the graph resulting from
+    removing all edges connected to node `r` but not the node itself.
+
+    The adjacency matrix for `G(r)` is `A+E(r)`,  where `E(r)` has nonzeros
+    only in row and column `r`.
+
+    The subraph betweenness of a node `r`  is [1]_
+
+    .. math::
+
+         \omega_{r} = \frac{1}{C}\sum_{p}\sum_{q}\frac{G_{prq}}{G_{pq}},
+         p\neq q, q\neq r,
+
+    where
+    `G_{prq}=(e^{A}_{pq} - (e^{A+E(r)})_{pq}`  is the number of walks
+    involving node r,
+    `G_{pq}=(e^{A})_{pq}` is the number of closed walks starting
+    at node `p` and ending at node `q`,
+    and `C=(n-1)^{2}-(n-1)` is a normalization factor equal to the
+    number of terms in the sum.
+
+    The resulting `\omega_{r}` takes values between zero and one.
+    The lower bound cannot be attained for a connected
+    graph, and the upper bound is attained in the star graph.
+
+    References
+    ----------
+    .. [1] Ernesto Estrada, Desmond J. Higham, Naomichi Hatano,
+       "Communicability Betweenness in Complex Networks"
+       Physica A 388 (2009) 764-774.
+       https://arxiv.org/abs/0905.4102
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (1, 5), (5, 4), (2, 4), (2, 3), (4, 3), (3, 6)])
+    >>> cbc = nx.communicability_betweenness_centrality(G)
+    >>> print([f"{node} {cbc[node]:0.2f}" for node in sorted(cbc)])
+    ['0 0.03', '1 0.45', '2 0.51', '3 0.45', '4 0.40', '5 0.19', '6 0.03']
+    """
+    import numpy as np
+    import scipy as sp
+
+    nodelist = list(G)  # ordering of nodes in matrix
+    n = len(nodelist)
+    A = nx.to_numpy_array(G, nodelist)
+    # convert to 0-1 matrix
+    A[np.nonzero(A)] = 1
+    expA = sp.linalg.expm(A)
+    mapping = dict(zip(nodelist, range(n)))
+    cbc = {}
+    for v in G:
+        # remove row and col of node v
+        i = mapping[v]
+        row = A[i, :].copy()
+        col = A[:, i].copy()
+        A[i, :] = 0
+        A[:, i] = 0
+        B = (expA - sp.linalg.expm(A)) / expA
+        # sum with row/col of node v and diag set to zero
+        B[i, :] = 0
+        B[:, i] = 0
+        B -= np.diag(np.diag(B))
+        cbc[v] = B.sum()
+        # put row and col back
+        A[i, :] = row
+        A[:, i] = col
+    # rescale when more than two nodes
+    order = len(cbc)
+    if order > 2:
+        scale = 1.0 / ((order - 1.0) ** 2 - (order - 1.0))
+        for v in cbc:
+            cbc[v] *= scale
+    return cbc
+
+
+@nx._dispatch
+def estrada_index(G):
+    r"""Returns the Estrada index of a the graph G.
+
+    The Estrada Index is a topological index of folding or 3D "compactness" ([1]_).
+
+    Parameters
+    ----------
+    G: graph
+
+    Returns
+    -------
+    estrada index: float
+
+    Raises
+    ------
+    NetworkXError
+        If the graph is not undirected and simple.
+
+    Notes
+    -----
+    Let `G=(V,E)` be a simple undirected graph with `n` nodes  and let
+    `\lambda_{1}\leq\lambda_{2}\leq\cdots\lambda_{n}`
+    be a non-increasing ordering of the eigenvalues of its adjacency
+    matrix `A`. The Estrada index is ([1]_, [2]_)
+
+    .. math::
+        EE(G)=\sum_{j=1}^n e^{\lambda _j}.
+
+    References
+    ----------
+    .. [1] E. Estrada, "Characterization of 3D molecular structure",
+       Chem. Phys. Lett. 319, 713 (2000).
+       https://doi.org/10.1016/S0009-2614(00)00158-5
+    .. [2] José Antonio de la Peñaa, Ivan Gutman, Juan Rada,
+       "Estimating the Estrada index",
+       Linear Algebra and its Applications. 427, 1 (2007).
+       https://doi.org/10.1016/j.laa.2007.06.020
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (1, 5), (5, 4), (2, 4), (2, 3), (4, 3), (3, 6)])
+    >>> ei = nx.estrada_index(G)
+    >>> print(f"{ei:0.5}")
+    20.55
+    """
+    return sum(subgraph_centrality(G).values())

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_betweenness_centrality.py

@@ -0,0 +1,780 @@
+import pytest
+
+import networkx as nx
+
+
+def weighted_G():
+    G = nx.Graph()
+    G.add_edge(0, 1, weight=3)
+    G.add_edge(0, 2, weight=2)
+    G.add_edge(0, 3, weight=6)
+    G.add_edge(0, 4, weight=4)
+    G.add_edge(1, 3, weight=5)
+    G.add_edge(1, 5, weight=5)
+    G.add_edge(2, 4, weight=1)
+    G.add_edge(3, 4, weight=2)
+    G.add_edge(3, 5, weight=1)
+    G.add_edge(4, 5, weight=4)
+    return G
+
+
+class TestBetweennessCentrality:
+    def test_K5(self):
+        """Betweenness centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.betweenness_centrality(G, weight=None, normalized=False)
+        b_answer = {0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_K5_endpoints(self):
+        """Betweenness centrality: K5 endpoints"""
+        G = nx.complete_graph(5)
+        b = nx.betweenness_centrality(G, weight=None, normalized=False, endpoints=True)
+        b_answer = {0: 4.0, 1: 4.0, 2: 4.0, 3: 4.0, 4: 4.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        # normalized = True case
+        b = nx.betweenness_centrality(G, weight=None, normalized=True, endpoints=True)
+        b_answer = {0: 0.4, 1: 0.4, 2: 0.4, 3: 0.4, 4: 0.4}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P3_normalized(self):
+        """Betweenness centrality: P3 normalized"""
+        G = nx.path_graph(3)
+        b = nx.betweenness_centrality(G, weight=None, normalized=True)
+        b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P3(self):
+        """Betweenness centrality: P3"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
+        b = nx.betweenness_centrality(G, weight=None, normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_sample_from_P3(self):
+        """Betweenness centrality: P3 sample"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
+        b = nx.betweenness_centrality(G, k=3, weight=None, normalized=False, seed=1)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        b = nx.betweenness_centrality(G, k=2, weight=None, normalized=False, seed=1)
+        # python versions give different results with same seed
+        b_approx1 = {0: 0.0, 1: 1.5, 2: 0.0}
+        b_approx2 = {0: 0.0, 1: 0.75, 2: 0.0}
+        for n in sorted(G):
+            assert b[n] in (b_approx1[n], b_approx2[n])
+
+    def test_P3_endpoints(self):
+        """Betweenness centrality: P3 endpoints"""
+        G = nx.path_graph(3)
+        b_answer = {0: 2.0, 1: 3.0, 2: 2.0}
+        b = nx.betweenness_centrality(G, weight=None, normalized=False, endpoints=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        # normalized = True case
+        b_answer = {0: 2 / 3, 1: 1.0, 2: 2 / 3}
+        b = nx.betweenness_centrality(G, weight=None, normalized=True, endpoints=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_krackhardt_kite_graph(self):
+        """Betweenness centrality: Krackhardt kite graph"""
+        G = nx.krackhardt_kite_graph()
+        b_answer = {
+            0: 1.667,
+            1: 1.667,
+            2: 0.000,
+            3: 7.333,
+            4: 0.000,
+            5: 16.667,
+            6: 16.667,
+            7: 28.000,
+            8: 16.000,
+            9: 0.000,
+        }
+        for b in b_answer:
+            b_answer[b] /= 2
+        b = nx.betweenness_centrality(G, weight=None, normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_krackhardt_kite_graph_normalized(self):
+        """Betweenness centrality: Krackhardt kite graph normalized"""
+        G = nx.krackhardt_kite_graph()
+        b_answer = {
+            0: 0.023,
+            1: 0.023,
+            2: 0.000,
+            3: 0.102,
+            4: 0.000,
+            5: 0.231,
+            6: 0.231,
+            7: 0.389,
+            8: 0.222,
+            9: 0.000,
+        }
+        b = nx.betweenness_centrality(G, weight=None, normalized=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_florentine_families_graph(self):
+        """Betweenness centrality: Florentine families graph"""
+        G = nx.florentine_families_graph()
+        b_answer = {
+            "Acciaiuoli": 0.000,
+            "Albizzi": 0.212,
+            "Barbadori": 0.093,
+            "Bischeri": 0.104,
+            "Castellani": 0.055,
+            "Ginori": 0.000,
+            "Guadagni": 0.255,
+            "Lamberteschi": 0.000,
+            "Medici": 0.522,
+            "Pazzi": 0.000,
+            "Peruzzi": 0.022,
+            "Ridolfi": 0.114,
+            "Salviati": 0.143,
+            "Strozzi": 0.103,
+            "Tornabuoni": 0.092,
+        }
+
+        b = nx.betweenness_centrality(G, weight=None, normalized=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_les_miserables_graph(self):
+        """Betweenness centrality: Les Miserables graph"""
+        G = nx.les_miserables_graph()
+        b_answer = {
+            "Napoleon": 0.000,
+            "Myriel": 0.177,
+            "MlleBaptistine": 0.000,
+            "MmeMagloire": 0.000,
+            "CountessDeLo": 0.000,
+            "Geborand": 0.000,
+            "Champtercier": 0.000,
+            "Cravatte": 0.000,
+            "Count": 0.000,
+            "OldMan": 0.000,
+            "Valjean": 0.570,
+            "Labarre": 0.000,
+            "Marguerite": 0.000,
+            "MmeDeR": 0.000,
+            "Isabeau": 0.000,
+            "Gervais": 0.000,
+            "Listolier": 0.000,
+            "Tholomyes": 0.041,
+            "Fameuil": 0.000,
+            "Blacheville": 0.000,
+            "Favourite": 0.000,
+            "Dahlia": 0.000,
+            "Zephine": 0.000,
+            "Fantine": 0.130,
+            "MmeThenardier": 0.029,
+            "Thenardier": 0.075,
+            "Cosette": 0.024,
+            "Javert": 0.054,
+            "Fauchelevent": 0.026,
+            "Bamatabois": 0.008,
+            "Perpetue": 0.000,
+            "Simplice": 0.009,
+            "Scaufflaire": 0.000,
+            "Woman1": 0.000,
+            "Judge": 0.000,
+            "Champmathieu": 0.000,
+            "Brevet": 0.000,
+            "Chenildieu": 0.000,
+            "Cochepaille": 0.000,
+            "Pontmercy": 0.007,
+            "Boulatruelle": 0.000,
+            "Eponine": 0.011,
+            "Anzelma": 0.000,
+            "Woman2": 0.000,
+            "MotherInnocent": 0.000,
+            "Gribier": 0.000,
+            "MmeBurgon": 0.026,
+            "Jondrette": 0.000,
+            "Gavroche": 0.165,
+            "Gillenormand": 0.020,
+            "Magnon": 0.000,
+            "MlleGillenormand": 0.048,
+            "MmePontmercy": 0.000,
+            "MlleVaubois": 0.000,
+            "LtGillenormand": 0.000,
+            "Marius": 0.132,
+            "BaronessT": 0.000,
+            "Mabeuf": 0.028,
+            "Enjolras": 0.043,
+            "Combeferre": 0.001,
+            "Prouvaire": 0.000,
+            "Feuilly": 0.001,
+            "Courfeyrac": 0.005,
+            "Bahorel": 0.002,
+            "Bossuet": 0.031,
+            "Joly": 0.002,
+            "Grantaire": 0.000,
+            "MotherPlutarch": 0.000,
+            "Gueulemer": 0.005,
+            "Babet": 0.005,
+            "Claquesous": 0.005,
+            "Montparnasse": 0.004,
+            "Toussaint": 0.000,
+            "Child1": 0.000,
+            "Child2": 0.000,
+            "Brujon": 0.000,
+            "MmeHucheloup": 0.000,
+        }
+
+        b = nx.betweenness_centrality(G, weight=None, normalized=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_ladder_graph(self):
+        """Betweenness centrality: Ladder graph"""
+        G = nx.Graph()  # ladder_graph(3)
+        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
+        b_answer = {0: 1.667, 1: 1.667, 2: 6.667, 3: 6.667, 4: 1.667, 5: 1.667}
+        for b in b_answer:
+            b_answer[b] /= 2
+        b = nx.betweenness_centrality(G, weight=None, normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_disconnected_path(self):
+        """Betweenness centrality: disconnected path"""
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2])
+        nx.add_path(G, [3, 4, 5, 6])
+        b_answer = {0: 0, 1: 1, 2: 0, 3: 0, 4: 2, 5: 2, 6: 0}
+        b = nx.betweenness_centrality(G, weight=None, normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_disconnected_path_endpoints(self):
+        """Betweenness centrality: disconnected path endpoints"""
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2])
+        nx.add_path(G, [3, 4, 5, 6])
+        b_answer = {0: 2, 1: 3, 2: 2, 3: 3, 4: 5, 5: 5, 6: 3}
+        b = nx.betweenness_centrality(G, weight=None, normalized=False, endpoints=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        # normalized = True case
+        b = nx.betweenness_centrality(G, weight=None, normalized=True, endpoints=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n] / 21, abs=1e-7)
+
+    def test_directed_path(self):
+        """Betweenness centrality: directed path"""
+        G = nx.DiGraph()
+        nx.add_path(G, [0, 1, 2])
+        b = nx.betweenness_centrality(G, weight=None, normalized=False)
+        b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_directed_path_normalized(self):
+        """Betweenness centrality: directed path normalized"""
+        G = nx.DiGraph()
+        nx.add_path(G, [0, 1, 2])
+        b = nx.betweenness_centrality(G, weight=None, normalized=True)
+        b_answer = {0: 0.0, 1: 0.5, 2: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+
+class TestWeightedBetweennessCentrality:
+    def test_K5(self):
+        """Weighted betweenness centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = {0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P3_normalized(self):
+        """Weighted betweenness centrality: P3 normalized"""
+        G = nx.path_graph(3)
+        b = nx.betweenness_centrality(G, weight="weight", normalized=True)
+        b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P3(self):
+        """Weighted betweenness centrality: P3"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.0, 1: 1.0, 2: 0.0}
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_krackhardt_kite_graph(self):
+        """Weighted betweenness centrality: Krackhardt kite graph"""
+        G = nx.krackhardt_kite_graph()
+        b_answer = {
+            0: 1.667,
+            1: 1.667,
+            2: 0.000,
+            3: 7.333,
+            4: 0.000,
+            5: 16.667,
+            6: 16.667,
+            7: 28.000,
+            8: 16.000,
+            9: 0.000,
+        }
+        for b in b_answer:
+            b_answer[b] /= 2
+
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_krackhardt_kite_graph_normalized(self):
+        """Weighted betweenness centrality:
+        Krackhardt kite graph normalized
+        """
+        G = nx.krackhardt_kite_graph()
+        b_answer = {
+            0: 0.023,
+            1: 0.023,
+            2: 0.000,
+            3: 0.102,
+            4: 0.000,
+            5: 0.231,
+            6: 0.231,
+            7: 0.389,
+            8: 0.222,
+            9: 0.000,
+        }
+        b = nx.betweenness_centrality(G, weight="weight", normalized=True)
+
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_florentine_families_graph(self):
+        """Weighted betweenness centrality:
+        Florentine families graph"""
+        G = nx.florentine_families_graph()
+        b_answer = {
+            "Acciaiuoli": 0.000,
+            "Albizzi": 0.212,
+            "Barbadori": 0.093,
+            "Bischeri": 0.104,
+            "Castellani": 0.055,
+            "Ginori": 0.000,
+            "Guadagni": 0.255,
+            "Lamberteschi": 0.000,
+            "Medici": 0.522,
+            "Pazzi": 0.000,
+            "Peruzzi": 0.022,
+            "Ridolfi": 0.114,
+            "Salviati": 0.143,
+            "Strozzi": 0.103,
+            "Tornabuoni": 0.092,
+        }
+
+        b = nx.betweenness_centrality(G, weight="weight", normalized=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_les_miserables_graph(self):
+        """Weighted betweenness centrality: Les Miserables graph"""
+        G = nx.les_miserables_graph()
+        b_answer = {
+            "Napoleon": 0.000,
+            "Myriel": 0.177,
+            "MlleBaptistine": 0.000,
+            "MmeMagloire": 0.000,
+            "CountessDeLo": 0.000,
+            "Geborand": 0.000,
+            "Champtercier": 0.000,
+            "Cravatte": 0.000,
+            "Count": 0.000,
+            "OldMan": 0.000,
+            "Valjean": 0.454,
+            "Labarre": 0.000,
+            "Marguerite": 0.009,
+            "MmeDeR": 0.000,
+            "Isabeau": 0.000,
+            "Gervais": 0.000,
+            "Listolier": 0.000,
+            "Tholomyes": 0.066,
+            "Fameuil": 0.000,
+            "Blacheville": 0.000,
+            "Favourite": 0.000,
+            "Dahlia": 0.000,
+            "Zephine": 0.000,
+            "Fantine": 0.114,
+            "MmeThenardier": 0.046,
+            "Thenardier": 0.129,
+            "Cosette": 0.075,
+            "Javert": 0.193,
+            "Fauchelevent": 0.026,
+            "Bamatabois": 0.080,
+            "Perpetue": 0.000,
+            "Simplice": 0.001,
+            "Scaufflaire": 0.000,
+            "Woman1": 0.000,
+            "Judge": 0.000,
+            "Champmathieu": 0.000,
+            "Brevet": 0.000,
+            "Chenildieu": 0.000,
+            "Cochepaille": 0.000,
+            "Pontmercy": 0.023,
+            "Boulatruelle": 0.000,
+            "Eponine": 0.023,
+            "Anzelma": 0.000,
+            "Woman2": 0.000,
+            "MotherInnocent": 0.000,
+            "Gribier": 0.000,
+            "MmeBurgon": 0.026,
+            "Jondrette": 0.000,
+            "Gavroche": 0.285,
+            "Gillenormand": 0.024,
+            "Magnon": 0.005,
+            "MlleGillenormand": 0.036,
+            "MmePontmercy": 0.005,
+            "MlleVaubois": 0.000,
+            "LtGillenormand": 0.015,
+            "Marius": 0.072,
+            "BaronessT": 0.004,
+            "Mabeuf": 0.089,
+            "Enjolras": 0.003,
+            "Combeferre": 0.000,
+            "Prouvaire": 0.000,
+            "Feuilly": 0.004,
+            "Courfeyrac": 0.001,
+            "Bahorel": 0.007,
+            "Bossuet": 0.028,
+            "Joly": 0.000,
+            "Grantaire": 0.036,
+            "MotherPlutarch": 0.000,
+            "Gueulemer": 0.025,
+            "Babet": 0.015,
+            "Claquesous": 0.042,
+            "Montparnasse": 0.050,
+            "Toussaint": 0.011,
+            "Child1": 0.000,
+            "Child2": 0.000,
+            "Brujon": 0.002,
+            "MmeHucheloup": 0.034,
+        }
+
+        b = nx.betweenness_centrality(G, weight="weight", normalized=True)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_ladder_graph(self):
+        """Weighted betweenness centrality: Ladder graph"""
+        G = nx.Graph()  # ladder_graph(3)
+        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
+        b_answer = {0: 1.667, 1: 1.667, 2: 6.667, 3: 6.667, 4: 1.667, 5: 1.667}
+        for b in b_answer:
+            b_answer[b] /= 2
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_G(self):
+        """Weighted betweenness centrality: G"""
+        G = weighted_G()
+        b_answer = {0: 2.0, 1: 0.0, 2: 4.0, 3: 3.0, 4: 4.0, 5: 0.0}
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_G2(self):
+        """Weighted betweenness centrality: G2"""
+        G = nx.DiGraph()
+        G.add_weighted_edges_from(
+            [
+                ("s", "u", 10),
+                ("s", "x", 5),
+                ("u", "v", 1),
+                ("u", "x", 2),
+                ("v", "y", 1),
+                ("x", "u", 3),
+                ("x", "v", 5),
+                ("x", "y", 2),
+                ("y", "s", 7),
+                ("y", "v", 6),
+            ]
+        )
+
+        b_answer = {"y": 5.0, "x": 5.0, "s": 4.0, "u": 2.0, "v": 2.0}
+
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_G3(self):
+        """Weighted betweenness centrality: G3"""
+        G = nx.MultiGraph(weighted_G())
+        es = list(G.edges(data=True))[::2]  # duplicate every other edge
+        G.add_edges_from(es)
+        b_answer = {0: 2.0, 1: 0.0, 2: 4.0, 3: 3.0, 4: 4.0, 5: 0.0}
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_G4(self):
+        """Weighted betweenness centrality: G4"""
+        G = nx.MultiDiGraph()
+        G.add_weighted_edges_from(
+            [
+                ("s", "u", 10),
+                ("s", "x", 5),
+                ("s", "x", 6),
+                ("u", "v", 1),
+                ("u", "x", 2),
+                ("v", "y", 1),
+                ("v", "y", 1),
+                ("x", "u", 3),
+                ("x", "v", 5),
+                ("x", "y", 2),
+                ("x", "y", 3),
+                ("y", "s", 7),
+                ("y", "v", 6),
+                ("y", "v", 6),
+            ]
+        )
+
+        b_answer = {"y": 5.0, "x": 5.0, "s": 4.0, "u": 2.0, "v": 2.0}
+
+        b = nx.betweenness_centrality(G, weight="weight", normalized=False)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+
+class TestEdgeBetweennessCentrality:
+    def test_K5(self):
+        """Edge betweenness centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.edge_betweenness_centrality(G, weight=None, normalized=False)
+        b_answer = dict.fromkeys(G.edges(), 1)
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_normalized_K5(self):
+        """Edge betweenness centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
+        b_answer = dict.fromkeys(G.edges(), 1 / 10)
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_C4(self):
+        """Edge betweenness centrality: C4"""
+        G = nx.cycle_graph(4)
+        b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
+        b_answer = {(0, 1): 2, (0, 3): 2, (1, 2): 2, (2, 3): 2}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n] / 6, abs=1e-7)
+
+    def test_P4(self):
+        """Edge betweenness centrality: P4"""
+        G = nx.path_graph(4)
+        b = nx.edge_betweenness_centrality(G, weight=None, normalized=False)
+        b_answer = {(0, 1): 3, (1, 2): 4, (2, 3): 3}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_normalized_P4(self):
+        """Edge betweenness centrality: P4"""
+        G = nx.path_graph(4)
+        b = nx.edge_betweenness_centrality(G, weight=None, normalized=True)
+        b_answer = {(0, 1): 3, (1, 2): 4, (2, 3): 3}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n] / 6, abs=1e-7)
+
+    def test_balanced_tree(self):
+        """Edge betweenness centrality: balanced tree"""
+        G = nx.balanced_tree(r=2, h=2)
+        b = nx.edge_betweenness_centrality(G, weight=None, normalized=False)
+        b_answer = {(0, 1): 12, (0, 2): 12, (1, 3): 6, (1, 4): 6, (2, 5): 6, (2, 6): 6}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+
+class TestWeightedEdgeBetweennessCentrality:
+    def test_K5(self):
+        """Edge betweenness centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = dict.fromkeys(G.edges(), 1)
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_C4(self):
+        """Edge betweenness centrality: C4"""
+        G = nx.cycle_graph(4)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = {(0, 1): 2, (0, 3): 2, (1, 2): 2, (2, 3): 2}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P4(self):
+        """Edge betweenness centrality: P4"""
+        G = nx.path_graph(4)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = {(0, 1): 3, (1, 2): 4, (2, 3): 3}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_balanced_tree(self):
+        """Edge betweenness centrality: balanced tree"""
+        G = nx.balanced_tree(r=2, h=2)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = {(0, 1): 12, (0, 2): 12, (1, 3): 6, (1, 4): 6, (2, 5): 6, (2, 6): 6}
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_weighted_graph(self):
+        """Edge betweenness centrality: weighted"""
+        eList = [
+            (0, 1, 5),
+            (0, 2, 4),
+            (0, 3, 3),
+            (0, 4, 2),
+            (1, 2, 4),
+            (1, 3, 1),
+            (1, 4, 3),
+            (2, 4, 5),
+            (3, 4, 4),
+        ]
+        G = nx.Graph()
+        G.add_weighted_edges_from(eList)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = {
+            (0, 1): 0.0,
+            (0, 2): 1.0,
+            (0, 3): 2.0,
+            (0, 4): 1.0,
+            (1, 2): 2.0,
+            (1, 3): 3.5,
+            (1, 4): 1.5,
+            (2, 4): 1.0,
+            (3, 4): 0.5,
+        }
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_normalized_weighted_graph(self):
+        """Edge betweenness centrality: normalized weighted"""
+        eList = [
+            (0, 1, 5),
+            (0, 2, 4),
+            (0, 3, 3),
+            (0, 4, 2),
+            (1, 2, 4),
+            (1, 3, 1),
+            (1, 4, 3),
+            (2, 4, 5),
+            (3, 4, 4),
+        ]
+        G = nx.Graph()
+        G.add_weighted_edges_from(eList)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=True)
+        b_answer = {
+            (0, 1): 0.0,
+            (0, 2): 1.0,
+            (0, 3): 2.0,
+            (0, 4): 1.0,
+            (1, 2): 2.0,
+            (1, 3): 3.5,
+            (1, 4): 1.5,
+            (2, 4): 1.0,
+            (3, 4): 0.5,
+        }
+        norm = len(G) * (len(G) - 1) / 2
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n] / norm, abs=1e-7)
+
+    def test_weighted_multigraph(self):
+        """Edge betweenness centrality: weighted multigraph"""
+        eList = [
+            (0, 1, 5),
+            (0, 1, 4),
+            (0, 2, 4),
+            (0, 3, 3),
+            (0, 3, 3),
+            (0, 4, 2),
+            (1, 2, 4),
+            (1, 3, 1),
+            (1, 3, 2),
+            (1, 4, 3),
+            (1, 4, 4),
+            (2, 4, 5),
+            (3, 4, 4),
+            (3, 4, 4),
+        ]
+        G = nx.MultiGraph()
+        G.add_weighted_edges_from(eList)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=False)
+        b_answer = {
+            (0, 1, 0): 0.0,
+            (0, 1, 1): 0.5,
+            (0, 2, 0): 1.0,
+            (0, 3, 0): 0.75,
+            (0, 3, 1): 0.75,
+            (0, 4, 0): 1.0,
+            (1, 2, 0): 2.0,
+            (1, 3, 0): 3.0,
+            (1, 3, 1): 0.0,
+            (1, 4, 0): 1.5,
+            (1, 4, 1): 0.0,
+            (2, 4, 0): 1.0,
+            (3, 4, 0): 0.25,
+            (3, 4, 1): 0.25,
+        }
+        for n in sorted(G.edges(keys=True)):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_normalized_weighted_multigraph(self):
+        """Edge betweenness centrality: normalized weighted multigraph"""
+        eList = [
+            (0, 1, 5),
+            (0, 1, 4),
+            (0, 2, 4),
+            (0, 3, 3),
+            (0, 3, 3),
+            (0, 4, 2),
+            (1, 2, 4),
+            (1, 3, 1),
+            (1, 3, 2),
+            (1, 4, 3),
+            (1, 4, 4),
+            (2, 4, 5),
+            (3, 4, 4),
+            (3, 4, 4),
+        ]
+        G = nx.MultiGraph()
+        G.add_weighted_edges_from(eList)
+        b = nx.edge_betweenness_centrality(G, weight="weight", normalized=True)
+        b_answer = {
+            (0, 1, 0): 0.0,
+            (0, 1, 1): 0.5,
+            (0, 2, 0): 1.0,
+            (0, 3, 0): 0.75,
+            (0, 3, 1): 0.75,
+            (0, 4, 0): 1.0,
+            (1, 2, 0): 2.0,
+            (1, 3, 0): 3.0,
+            (1, 3, 1): 0.0,
+            (1, 4, 0): 1.5,
+            (1, 4, 1): 0.0,
+            (2, 4, 0): 1.0,
+            (3, 4, 0): 0.25,
+            (3, 4, 1): 0.25,
+        }
+        norm = len(G) * (len(G) - 1) / 2
+        for n in sorted(G.edges(keys=True)):
+            assert b[n] == pytest.approx(b_answer[n] / norm, abs=1e-7)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_betweenness_centrality_subset.py

@@ -0,0 +1,340 @@
+import pytest
+
+import networkx as nx
+
+
+class TestSubsetBetweennessCentrality:
+    def test_K5(self):
+        """Betweenness Centrality Subset: K5"""
+        G = nx.complete_graph(5)
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[1, 3], weight=None
+        )
+        b_answer = {0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P5_directed(self):
+        """Betweenness Centrality Subset: P5 directed"""
+        G = nx.DiGraph()
+        nx.add_path(G, range(5))
+        b_answer = {0: 0, 1: 1, 2: 1, 3: 0, 4: 0, 5: 0}
+        b = nx.betweenness_centrality_subset(G, sources=[0], targets=[3], weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P5(self):
+        """Betweenness Centrality Subset: P5"""
+        G = nx.Graph()
+        nx.add_path(G, range(5))
+        b_answer = {0: 0, 1: 0.5, 2: 0.5, 3: 0, 4: 0, 5: 0}
+        b = nx.betweenness_centrality_subset(G, sources=[0], targets=[3], weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P5_multiple_target(self):
+        """Betweenness Centrality Subset: P5 multiple target"""
+        G = nx.Graph()
+        nx.add_path(G, range(5))
+        b_answer = {0: 0, 1: 1, 2: 1, 3: 0.5, 4: 0, 5: 0}
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[3, 4], weight=None
+        )
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_box(self):
+        """Betweenness Centrality Subset: box"""
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
+        b_answer = {0: 0, 1: 0.25, 2: 0.25, 3: 0}
+        b = nx.betweenness_centrality_subset(G, sources=[0], targets=[3], weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_box_and_path(self):
+        """Betweenness Centrality Subset: box and path"""
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (3, 4), (4, 5)])
+        b_answer = {0: 0, 1: 0.5, 2: 0.5, 3: 0.5, 4: 0, 5: 0}
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[3, 4], weight=None
+        )
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_box_and_path2(self):
+        """Betweenness Centrality Subset: box and path multiple target"""
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (1, 2), (2, 3), (1, 20), (20, 3), (3, 4)])
+        b_answer = {0: 0, 1: 1.0, 2: 0.5, 20: 0.5, 3: 0.5, 4: 0}
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[3, 4], weight=None
+        )
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_diamond_multi_path(self):
+        """Betweenness Centrality Subset: Diamond Multi Path"""
+        G = nx.Graph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (1, 3),
+                (1, 4),
+                (1, 5),
+                (1, 10),
+                (10, 11),
+                (11, 12),
+                (12, 9),
+                (2, 6),
+                (3, 6),
+                (4, 6),
+                (5, 7),
+                (7, 8),
+                (6, 8),
+                (8, 9),
+            ]
+        )
+        b = nx.betweenness_centrality_subset(G, sources=[1], targets=[9], weight=None)
+
+        expected_b = {
+            1: 0,
+            2: 1.0 / 10,
+            3: 1.0 / 10,
+            4: 1.0 / 10,
+            5: 1.0 / 10,
+            6: 3.0 / 10,
+            7: 1.0 / 10,
+            8: 4.0 / 10,
+            9: 0,
+            10: 1.0 / 10,
+            11: 1.0 / 10,
+            12: 1.0 / 10,
+        }
+
+        for n in sorted(G):
+            assert b[n] == pytest.approx(expected_b[n], abs=1e-7)
+
+    def test_normalized_p2(self):
+        """
+        Betweenness Centrality Subset: Normalized P2
+        if n <= 2:  no normalization, betweenness centrality should be 0 for all nodes.
+        """
+        G = nx.Graph()
+        nx.add_path(G, range(2))
+        b_answer = {0: 0, 1: 0.0}
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[1], normalized=True, weight=None
+        )
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_normalized_P5_directed(self):
+        """Betweenness Centrality Subset: Normalized Directed P5"""
+        G = nx.DiGraph()
+        nx.add_path(G, range(5))
+        b_answer = {0: 0, 1: 1.0 / 12.0, 2: 1.0 / 12.0, 3: 0, 4: 0, 5: 0}
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[3], normalized=True, weight=None
+        )
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_weighted_graph(self):
+        """Betweenness Centrality Subset: Weighted Graph"""
+        G = nx.DiGraph()
+        G.add_edge(0, 1, weight=3)
+        G.add_edge(0, 2, weight=2)
+        G.add_edge(0, 3, weight=6)
+        G.add_edge(0, 4, weight=4)
+        G.add_edge(1, 3, weight=5)
+        G.add_edge(1, 5, weight=5)
+        G.add_edge(2, 4, weight=1)
+        G.add_edge(3, 4, weight=2)
+        G.add_edge(3, 5, weight=1)
+        G.add_edge(4, 5, weight=4)
+        b_answer = {0: 0.0, 1: 0.0, 2: 0.5, 3: 0.5, 4: 0.5, 5: 0.0}
+        b = nx.betweenness_centrality_subset(
+            G, sources=[0], targets=[5], normalized=False, weight="weight"
+        )
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+
+class TestEdgeSubsetBetweennessCentrality:
+    def test_K5(self):
+        """Edge betweenness subset centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[1, 3], weight=None
+        )
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 3)] = b_answer[(0, 1)] = 0.5
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P5_directed(self):
+        """Edge betweenness subset centrality: P5 directed"""
+        G = nx.DiGraph()
+        nx.add_path(G, range(5))
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = b_answer[(1, 2)] = b_answer[(2, 3)] = 1
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3], weight=None
+        )
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P5(self):
+        """Edge betweenness subset centrality: P5"""
+        G = nx.Graph()
+        nx.add_path(G, range(5))
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = b_answer[(1, 2)] = b_answer[(2, 3)] = 0.5
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3], weight=None
+        )
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P5_multiple_target(self):
+        """Edge betweenness subset centrality: P5 multiple target"""
+        G = nx.Graph()
+        nx.add_path(G, range(5))
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = b_answer[(1, 2)] = b_answer[(2, 3)] = 1
+        b_answer[(3, 4)] = 0.5
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3, 4], weight=None
+        )
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_box(self):
+        """Edge betweenness subset centrality: box"""
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3)])
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = b_answer[(0, 2)] = 0.25
+        b_answer[(1, 3)] = b_answer[(2, 3)] = 0.25
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3], weight=None
+        )
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_box_and_path(self):
+        """Edge betweenness subset centrality: box and path"""
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (3, 4), (4, 5)])
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = b_answer[(0, 2)] = 0.5
+        b_answer[(1, 3)] = b_answer[(2, 3)] = 0.5
+        b_answer[(3, 4)] = 0.5
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3, 4], weight=None
+        )
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_box_and_path2(self):
+        """Edge betweenness subset centrality: box and path multiple target"""
+        G = nx.Graph()
+        G.add_edges_from([(0, 1), (1, 2), (2, 3), (1, 20), (20, 3), (3, 4)])
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = 1.0
+        b_answer[(1, 20)] = b_answer[(3, 20)] = 0.5
+        b_answer[(1, 2)] = b_answer[(2, 3)] = 0.5
+        b_answer[(3, 4)] = 0.5
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3, 4], weight=None
+        )
+        for n in sorted(G.edges()):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_diamond_multi_path(self):
+        """Edge betweenness subset centrality: Diamond Multi Path"""
+        G = nx.Graph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (1, 3),
+                (1, 4),
+                (1, 5),
+                (1, 10),
+                (10, 11),
+                (11, 12),
+                (12, 9),
+                (2, 6),
+                (3, 6),
+                (4, 6),
+                (5, 7),
+                (7, 8),
+                (6, 8),
+                (8, 9),
+            ]
+        )
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(8, 9)] = 0.4
+        b_answer[(6, 8)] = b_answer[(7, 8)] = 0.2
+        b_answer[(2, 6)] = b_answer[(3, 6)] = b_answer[(4, 6)] = 0.2 / 3.0
+        b_answer[(1, 2)] = b_answer[(1, 3)] = b_answer[(1, 4)] = 0.2 / 3.0
+        b_answer[(5, 7)] = 0.2
+        b_answer[(1, 5)] = 0.2
+        b_answer[(9, 12)] = 0.1
+        b_answer[(11, 12)] = b_answer[(10, 11)] = b_answer[(1, 10)] = 0.1
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[1], targets=[9], weight=None
+        )
+        for n in G.edges():
+            sort_n = tuple(sorted(n))
+            assert b[n] == pytest.approx(b_answer[sort_n], abs=1e-7)
+
+    def test_normalized_p1(self):
+        """
+        Edge betweenness subset centrality: P1
+        if n <= 1: no normalization b=0 for all nodes
+        """
+        G = nx.Graph()
+        nx.add_path(G, range(1))
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[0], normalized=True, weight=None
+        )
+        for n in G.edges():
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_normalized_P5_directed(self):
+        """Edge betweenness subset centrality: Normalized Directed P5"""
+        G = nx.DiGraph()
+        nx.add_path(G, range(5))
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 1)] = b_answer[(1, 2)] = b_answer[(2, 3)] = 0.05
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[3], normalized=True, weight=None
+        )
+        for n in G.edges():
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_weighted_graph(self):
+        """Edge betweenness subset centrality: Weighted Graph"""
+        G = nx.DiGraph()
+        G.add_edge(0, 1, weight=3)
+        G.add_edge(0, 2, weight=2)
+        G.add_edge(0, 3, weight=6)
+        G.add_edge(0, 4, weight=4)
+        G.add_edge(1, 3, weight=5)
+        G.add_edge(1, 5, weight=5)
+        G.add_edge(2, 4, weight=1)
+        G.add_edge(3, 4, weight=2)
+        G.add_edge(3, 5, weight=1)
+        G.add_edge(4, 5, weight=4)
+        b_answer = dict.fromkeys(G.edges(), 0)
+        b_answer[(0, 2)] = b_answer[(2, 4)] = b_answer[(4, 5)] = 0.5
+        b_answer[(0, 3)] = b_answer[(3, 5)] = 0.5
+        b = nx.edge_betweenness_centrality_subset(
+            G, sources=[0], targets=[5], normalized=False, weight="weight"
+        )
+        for n in G.edges():
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_closeness_centrality.py

@@ -0,0 +1,306 @@
+"""
+Tests for closeness centrality.
+"""
+import pytest
+
+import networkx as nx
+
+
+class TestClosenessCentrality:
+    @classmethod
+    def setup_class(cls):
+        cls.K = nx.krackhardt_kite_graph()
+        cls.P3 = nx.path_graph(3)
+        cls.P4 = nx.path_graph(4)
+        cls.K5 = nx.complete_graph(5)
+
+        cls.C4 = nx.cycle_graph(4)
+        cls.T = nx.balanced_tree(r=2, h=2)
+        cls.Gb = nx.Graph()
+        cls.Gb.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
+
+        F = nx.florentine_families_graph()
+        cls.F = F
+
+        cls.LM = nx.les_miserables_graph()
+
+        # Create random undirected, unweighted graph for testing incremental version
+        cls.undirected_G = nx.fast_gnp_random_graph(n=100, p=0.6, seed=123)
+        cls.undirected_G_cc = nx.closeness_centrality(cls.undirected_G)
+
+    def test_wf_improved(self):
+        G = nx.union(self.P4, nx.path_graph([4, 5, 6]))
+        c = nx.closeness_centrality(G)
+        cwf = nx.closeness_centrality(G, wf_improved=False)
+        res = {0: 0.25, 1: 0.375, 2: 0.375, 3: 0.25, 4: 0.222, 5: 0.333, 6: 0.222}
+        wf_res = {0: 0.5, 1: 0.75, 2: 0.75, 3: 0.5, 4: 0.667, 5: 1.0, 6: 0.667}
+        for n in G:
+            assert c[n] == pytest.approx(res[n], abs=1e-3)
+            assert cwf[n] == pytest.approx(wf_res[n], abs=1e-3)
+
+    def test_digraph(self):
+        G = nx.path_graph(3, create_using=nx.DiGraph())
+        c = nx.closeness_centrality(G)
+        cr = nx.closeness_centrality(G.reverse())
+        d = {0: 0.0, 1: 0.500, 2: 0.667}
+        dr = {0: 0.667, 1: 0.500, 2: 0.0}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+            assert cr[n] == pytest.approx(dr[n], abs=1e-3)
+
+    def test_k5_closeness(self):
+        c = nx.closeness_centrality(self.K5)
+        d = {0: 1.000, 1: 1.000, 2: 1.000, 3: 1.000, 4: 1.000}
+        for n in sorted(self.K5):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p3_closeness(self):
+        c = nx.closeness_centrality(self.P3)
+        d = {0: 0.667, 1: 1.000, 2: 0.667}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_krackhardt_closeness(self):
+        c = nx.closeness_centrality(self.K)
+        d = {
+            0: 0.529,
+            1: 0.529,
+            2: 0.500,
+            3: 0.600,
+            4: 0.500,
+            5: 0.643,
+            6: 0.643,
+            7: 0.600,
+            8: 0.429,
+            9: 0.310,
+        }
+        for n in sorted(self.K):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_florentine_families_closeness(self):
+        c = nx.closeness_centrality(self.F)
+        d = {
+            "Acciaiuoli": 0.368,
+            "Albizzi": 0.483,
+            "Barbadori": 0.4375,
+            "Bischeri": 0.400,
+            "Castellani": 0.389,
+            "Ginori": 0.333,
+            "Guadagni": 0.467,
+            "Lamberteschi": 0.326,
+            "Medici": 0.560,
+            "Pazzi": 0.286,
+            "Peruzzi": 0.368,
+            "Ridolfi": 0.500,
+            "Salviati": 0.389,
+            "Strozzi": 0.4375,
+            "Tornabuoni": 0.483,
+        }
+        for n in sorted(self.F):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_les_miserables_closeness(self):
+        c = nx.closeness_centrality(self.LM)
+        d = {
+            "Napoleon": 0.302,
+            "Myriel": 0.429,
+            "MlleBaptistine": 0.413,
+            "MmeMagloire": 0.413,
+            "CountessDeLo": 0.302,
+            "Geborand": 0.302,
+            "Champtercier": 0.302,
+            "Cravatte": 0.302,
+            "Count": 0.302,
+            "OldMan": 0.302,
+            "Valjean": 0.644,
+            "Labarre": 0.394,
+            "Marguerite": 0.413,
+            "MmeDeR": 0.394,
+            "Isabeau": 0.394,
+            "Gervais": 0.394,
+            "Listolier": 0.341,
+            "Tholomyes": 0.392,
+            "Fameuil": 0.341,
+            "Blacheville": 0.341,
+            "Favourite": 0.341,
+            "Dahlia": 0.341,
+            "Zephine": 0.341,
+            "Fantine": 0.461,
+            "MmeThenardier": 0.461,
+            "Thenardier": 0.517,
+            "Cosette": 0.478,
+            "Javert": 0.517,
+            "Fauchelevent": 0.402,
+            "Bamatabois": 0.427,
+            "Perpetue": 0.318,
+            "Simplice": 0.418,
+            "Scaufflaire": 0.394,
+            "Woman1": 0.396,
+            "Judge": 0.404,
+            "Champmathieu": 0.404,
+            "Brevet": 0.404,
+            "Chenildieu": 0.404,
+            "Cochepaille": 0.404,
+            "Pontmercy": 0.373,
+            "Boulatruelle": 0.342,
+            "Eponine": 0.396,
+            "Anzelma": 0.352,
+            "Woman2": 0.402,
+            "MotherInnocent": 0.398,
+            "Gribier": 0.288,
+            "MmeBurgon": 0.344,
+            "Jondrette": 0.257,
+            "Gavroche": 0.514,
+            "Gillenormand": 0.442,
+            "Magnon": 0.335,
+            "MlleGillenormand": 0.442,
+            "MmePontmercy": 0.315,
+            "MlleVaubois": 0.308,
+            "LtGillenormand": 0.365,
+            "Marius": 0.531,
+            "BaronessT": 0.352,
+            "Mabeuf": 0.396,
+            "Enjolras": 0.481,
+            "Combeferre": 0.392,
+            "Prouvaire": 0.357,
+            "Feuilly": 0.392,
+            "Courfeyrac": 0.400,
+            "Bahorel": 0.394,
+            "Bossuet": 0.475,
+            "Joly": 0.394,
+            "Grantaire": 0.358,
+            "MotherPlutarch": 0.285,
+            "Gueulemer": 0.463,
+            "Babet": 0.463,
+            "Claquesous": 0.452,
+            "Montparnasse": 0.458,
+            "Toussaint": 0.402,
+            "Child1": 0.342,
+            "Child2": 0.342,
+            "Brujon": 0.380,
+            "MmeHucheloup": 0.353,
+        }
+        for n in sorted(self.LM):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_weighted_closeness(self):
+        edges = [
+            ("s", "u", 10),
+            ("s", "x", 5),
+            ("u", "v", 1),
+            ("u", "x", 2),
+            ("v", "y", 1),
+            ("x", "u", 3),
+            ("x", "v", 5),
+            ("x", "y", 2),
+            ("y", "s", 7),
+            ("y", "v", 6),
+        ]
+        XG = nx.Graph()
+        XG.add_weighted_edges_from(edges)
+        c = nx.closeness_centrality(XG, distance="weight")
+        d = {"y": 0.200, "x": 0.286, "s": 0.138, "u": 0.235, "v": 0.200}
+        for n in sorted(XG):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    #
+    # Tests for incremental closeness centrality.
+    #
+    @staticmethod
+    def pick_add_edge(g):
+        u = nx.utils.arbitrary_element(g)
+        possible_nodes = set(g.nodes())
+        neighbors = list(g.neighbors(u)) + [u]
+        possible_nodes.difference_update(neighbors)
+        v = nx.utils.arbitrary_element(possible_nodes)
+        return (u, v)
+
+    @staticmethod
+    def pick_remove_edge(g):
+        u = nx.utils.arbitrary_element(g)
+        possible_nodes = list(g.neighbors(u))
+        v = nx.utils.arbitrary_element(possible_nodes)
+        return (u, v)
+
+    def test_directed_raises(self):
+        with pytest.raises(nx.NetworkXNotImplemented):
+            dir_G = nx.gn_graph(n=5)
+            prev_cc = None
+            edge = self.pick_add_edge(dir_G)
+            insert = True
+            nx.incremental_closeness_centrality(dir_G, edge, prev_cc, insert)
+
+    def test_wrong_size_prev_cc_raises(self):
+        with pytest.raises(nx.NetworkXError):
+            G = self.undirected_G.copy()
+            edge = self.pick_add_edge(G)
+            insert = True
+            prev_cc = self.undirected_G_cc.copy()
+            prev_cc.pop(0)
+            nx.incremental_closeness_centrality(G, edge, prev_cc, insert)
+
+    def test_wrong_nodes_prev_cc_raises(self):
+        with pytest.raises(nx.NetworkXError):
+            G = self.undirected_G.copy()
+            edge = self.pick_add_edge(G)
+            insert = True
+            prev_cc = self.undirected_G_cc.copy()
+            num_nodes = len(prev_cc)
+            prev_cc.pop(0)
+            prev_cc[num_nodes] = 0.5
+            nx.incremental_closeness_centrality(G, edge, prev_cc, insert)
+
+    def test_zero_centrality(self):
+        G = nx.path_graph(3)
+        prev_cc = nx.closeness_centrality(G)
+        edge = self.pick_remove_edge(G)
+        test_cc = nx.incremental_closeness_centrality(G, edge, prev_cc, insertion=False)
+        G.remove_edges_from([edge])
+        real_cc = nx.closeness_centrality(G)
+        shared_items = set(test_cc.items()) & set(real_cc.items())
+        assert len(shared_items) == len(real_cc)
+        assert 0 in test_cc.values()
+
+    def test_incremental(self):
+        # Check that incremental and regular give same output
+        G = self.undirected_G.copy()
+        prev_cc = None
+        for i in range(5):
+            if i % 2 == 0:
+                # Remove an edge
+                insert = False
+                edge = self.pick_remove_edge(G)
+            else:
+                # Add an edge
+                insert = True
+                edge = self.pick_add_edge(G)
+
+            # start = timeit.default_timer()
+            test_cc = nx.incremental_closeness_centrality(G, edge, prev_cc, insert)
+            # inc_elapsed = (timeit.default_timer() - start)
+            # print(f"incremental time: {inc_elapsed}")
+
+            if insert:
+                G.add_edges_from([edge])
+            else:
+                G.remove_edges_from([edge])
+
+            # start = timeit.default_timer()
+            real_cc = nx.closeness_centrality(G)
+            # reg_elapsed = (timeit.default_timer() - start)
+            # print(f"regular time: {reg_elapsed}")
+            # Example output:
+            # incremental time: 0.208
+            # regular time: 0.276
+            # incremental time: 0.00683
+            # regular time: 0.260
+            # incremental time: 0.0224
+            # regular time: 0.278
+            # incremental time: 0.00804
+            # regular time: 0.208
+            # incremental time: 0.00947
+            # regular time: 0.188
+
+            assert set(test_cc.items()) == set(real_cc.items())
+
+            prev_cc = test_cc

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_current_flow_closeness.py

@@ -0,0 +1,43 @@
+import pytest
+
+pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+
+
+class TestFlowClosenessCentrality:
+    def test_K4(self):
+        """Closeness centrality: K4"""
+        G = nx.complete_graph(4)
+        b = nx.current_flow_closeness_centrality(G)
+        b_answer = {0: 2.0 / 3, 1: 2.0 / 3, 2: 2.0 / 3, 3: 2.0 / 3}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_P4(self):
+        """Closeness centrality: P4"""
+        G = nx.path_graph(4)
+        b = nx.current_flow_closeness_centrality(G)
+        b_answer = {0: 1.0 / 6, 1: 1.0 / 4, 2: 1.0 / 4, 3: 1.0 / 6}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_star(self):
+        """Closeness centrality: star"""
+        G = nx.Graph()
+        nx.add_star(G, ["a", "b", "c", "d"])
+        b = nx.current_flow_closeness_centrality(G)
+        b_answer = {"a": 1.0 / 3, "b": 0.6 / 3, "c": 0.6 / 3, "d": 0.6 / 3}
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+    def test_current_flow_closeness_centrality_not_connected(self):
+        G = nx.Graph()
+        G.add_nodes_from([1, 2, 3])
+        with pytest.raises(nx.NetworkXError):
+            nx.current_flow_closeness_centrality(G)
+
+
+class TestWeightedFlowClosenessCentrality:
+    pass

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_dispersion.py

@@ -0,0 +1,73 @@
+import networkx as nx
+
+
+def small_ego_G():
+    """The sample network from https://arxiv.org/pdf/1310.6753v1.pdf"""
+    edges = [
+        ("a", "b"),
+        ("a", "c"),
+        ("b", "c"),
+        ("b", "d"),
+        ("b", "e"),
+        ("b", "f"),
+        ("c", "d"),
+        ("c", "f"),
+        ("c", "h"),
+        ("d", "f"),
+        ("e", "f"),
+        ("f", "h"),
+        ("h", "j"),
+        ("h", "k"),
+        ("i", "j"),
+        ("i", "k"),
+        ("j", "k"),
+        ("u", "a"),
+        ("u", "b"),
+        ("u", "c"),
+        ("u", "d"),
+        ("u", "e"),
+        ("u", "f"),
+        ("u", "g"),
+        ("u", "h"),
+        ("u", "i"),
+        ("u", "j"),
+        ("u", "k"),
+    ]
+    G = nx.Graph()
+    G.add_edges_from(edges)
+
+    return G
+
+
+class TestDispersion:
+    def test_article(self):
+        """our algorithm matches article's"""
+        G = small_ego_G()
+        disp_uh = nx.dispersion(G, "u", "h", normalized=False)
+        disp_ub = nx.dispersion(G, "u", "b", normalized=False)
+        assert disp_uh == 4
+        assert disp_ub == 1
+
+    def test_results_length(self):
+        """there is a result for every node"""
+        G = small_ego_G()
+        disp = nx.dispersion(G)
+        disp_Gu = nx.dispersion(G, "u")
+        disp_uv = nx.dispersion(G, "u", "h")
+        assert len(disp) == len(G)
+        assert len(disp_Gu) == len(G) - 1
+        assert isinstance(disp_uv, float)
+
+    def test_dispersion_v_only(self):
+        G = small_ego_G()
+        disp_G_h = nx.dispersion(G, v="h", normalized=False)
+        disp_G_h_normalized = nx.dispersion(G, v="h", normalized=True)
+        assert disp_G_h == {"c": 0, "f": 0, "j": 0, "k": 0, "u": 4}
+        assert disp_G_h_normalized == {"c": 0.0, "f": 0.0, "j": 0.0, "k": 0.0, "u": 1.0}
+
+    def test_impossible_things(self):
+        G = nx.karate_club_graph()
+        disp = nx.dispersion(G)
+        for u in disp:
+            for v in disp[u]:
+                assert disp[u][v] >= 0

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_eigenvector_centrality.py

@@ -0,0 +1,175 @@
+import math
+
+import pytest
+
+np = pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+
+import networkx as nx
+
+
+class TestEigenvectorCentrality:
+    def test_K5(self):
+        """Eigenvector centrality: K5"""
+        G = nx.complete_graph(5)
+        b = nx.eigenvector_centrality(G)
+        v = math.sqrt(1 / 5.0)
+        b_answer = dict.fromkeys(G, v)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+        nstart = {n: 1 for n in G}
+        b = nx.eigenvector_centrality(G, nstart=nstart)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-7)
+
+        b = nx.eigenvector_centrality_numpy(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-3)
+
+    def test_P3(self):
+        """Eigenvector centrality: P3"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5, 1: 0.7071, 2: 0.5}
+        b = nx.eigenvector_centrality_numpy(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+        b = nx.eigenvector_centrality(G)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_P3_unweighted(self):
+        """Eigenvector centrality: P3"""
+        G = nx.path_graph(3)
+        b_answer = {0: 0.5, 1: 0.7071, 2: 0.5}
+        b = nx.eigenvector_centrality_numpy(G, weight=None)
+        for n in sorted(G):
+            assert b[n] == pytest.approx(b_answer[n], abs=1e-4)
+
+    def test_maxiter(self):
+        with pytest.raises(nx.PowerIterationFailedConvergence):
+            G = nx.path_graph(3)
+            nx.eigenvector_centrality(G, max_iter=0)
+
+
+class TestEigenvectorCentralityDirected:
+    @classmethod
+    def setup_class(cls):
+        G = nx.DiGraph()
+
+        edges = [
+            (1, 2),
+            (1, 3),
+            (2, 4),
+            (3, 2),
+            (3, 5),
+            (4, 2),
+            (4, 5),
+            (4, 6),
+            (5, 6),
+            (5, 7),
+            (5, 8),
+            (6, 8),
+            (7, 1),
+            (7, 5),
+            (7, 8),
+            (8, 6),
+            (8, 7),
+        ]
+
+        G.add_edges_from(edges, weight=2.0)
+        cls.G = G.reverse()
+        cls.G.evc = [
+            0.25368793,
+            0.19576478,
+            0.32817092,
+            0.40430835,
+            0.48199885,
+            0.15724483,
+            0.51346196,
+            0.32475403,
+        ]
+
+        H = nx.DiGraph()
+
+        edges = [
+            (1, 2),
+            (1, 3),
+            (2, 4),
+            (3, 2),
+            (3, 5),
+            (4, 2),
+            (4, 5),
+            (4, 6),
+            (5, 6),
+            (5, 7),
+            (5, 8),
+            (6, 8),
+            (7, 1),
+            (7, 5),
+            (7, 8),
+            (8, 6),
+            (8, 7),
+        ]
+
+        G.add_edges_from(edges)
+        cls.H = G.reverse()
+        cls.H.evc = [
+            0.25368793,
+            0.19576478,
+            0.32817092,
+            0.40430835,
+            0.48199885,
+            0.15724483,
+            0.51346196,
+            0.32475403,
+        ]
+
+    def test_eigenvector_centrality_weighted(self):
+        G = self.G
+        p = nx.eigenvector_centrality(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-4)
+
+    def test_eigenvector_centrality_weighted_numpy(self):
+        G = self.G
+        p = nx.eigenvector_centrality_numpy(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+    def test_eigenvector_centrality_unweighted(self):
+        G = self.H
+        p = nx.eigenvector_centrality(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-4)
+
+    def test_eigenvector_centrality_unweighted_numpy(self):
+        G = self.H
+        p = nx.eigenvector_centrality_numpy(G)
+        for a, b in zip(list(p.values()), self.G.evc):
+            assert a == pytest.approx(b, abs=1e-7)
+
+
+class TestEigenvectorCentralityExceptions:
+    def test_multigraph(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality(nx.MultiGraph())
+
+    def test_multigraph_numpy(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality_numpy(nx.MultiGraph())
+
+    def test_empty(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality(nx.Graph())
+
+    def test_empty_numpy(self):
+        with pytest.raises(nx.NetworkXException):
+            nx.eigenvector_centrality_numpy(nx.Graph())
+
+    def test_zero_nstart(self):
+        G = nx.Graph([(1, 2), (1, 3), (2, 3)])
+        with pytest.raises(
+            nx.NetworkXException, match="initial vector cannot have all zero values"
+        ):
+            nx.eigenvector_centrality(G, nstart={v: 0 for v in G})

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_harmonic_centrality.py

@@ -0,0 +1,115 @@
+"""
+Tests for degree centrality.
+"""
+import pytest
+
+import networkx as nx
+from networkx.algorithms.centrality import harmonic_centrality
+
+
+class TestClosenessCentrality:
+    @classmethod
+    def setup_class(cls):
+        cls.P3 = nx.path_graph(3)
+        cls.P4 = nx.path_graph(4)
+        cls.K5 = nx.complete_graph(5)
+
+        cls.C4 = nx.cycle_graph(4)
+        cls.C4_directed = nx.cycle_graph(4, create_using=nx.DiGraph)
+
+        cls.C5 = nx.cycle_graph(5)
+
+        cls.T = nx.balanced_tree(r=2, h=2)
+
+        cls.Gb = nx.DiGraph()
+        cls.Gb.add_edges_from([(0, 1), (0, 2), (0, 4), (2, 1), (2, 3), (4, 3)])
+
+    def test_p3_harmonic(self):
+        c = harmonic_centrality(self.P3)
+        d = {0: 1.5, 1: 2, 2: 1.5}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p4_harmonic(self):
+        c = harmonic_centrality(self.P4)
+        d = {0: 1.8333333, 1: 2.5, 2: 2.5, 3: 1.8333333}
+        for n in sorted(self.P4):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_clique_complete(self):
+        c = harmonic_centrality(self.K5)
+        d = {0: 4, 1: 4, 2: 4, 3: 4, 4: 4}
+        for n in sorted(self.P3):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_cycle_C4(self):
+        c = harmonic_centrality(self.C4)
+        d = {0: 2.5, 1: 2.5, 2: 2.5, 3: 2.5}
+        for n in sorted(self.C4):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_cycle_C5(self):
+        c = harmonic_centrality(self.C5)
+        d = {0: 3, 1: 3, 2: 3, 3: 3, 4: 3, 5: 4}
+        for n in sorted(self.C5):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_bal_tree(self):
+        c = harmonic_centrality(self.T)
+        d = {0: 4.0, 1: 4.1666, 2: 4.1666, 3: 2.8333, 4: 2.8333, 5: 2.8333, 6: 2.8333}
+        for n in sorted(self.T):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_exampleGraph(self):
+        c = harmonic_centrality(self.Gb)
+        d = {0: 0, 1: 2, 2: 1, 3: 2.5, 4: 1}
+        for n in sorted(self.Gb):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_weighted_harmonic(self):
+        XG = nx.DiGraph()
+        XG.add_weighted_edges_from(
+            [
+                ("a", "b", 10),
+                ("d", "c", 5),
+                ("a", "c", 1),
+                ("e", "f", 2),
+                ("f", "c", 1),
+                ("a", "f", 3),
+            ]
+        )
+        c = harmonic_centrality(XG, distance="weight")
+        d = {"a": 0, "b": 0.1, "c": 2.533, "d": 0, "e": 0, "f": 0.83333}
+        for n in sorted(XG):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_empty(self):
+        G = nx.DiGraph()
+        c = harmonic_centrality(G, distance="weight")
+        d = {}
+        assert c == d
+
+    def test_singleton(self):
+        G = nx.DiGraph()
+        G.add_node(0)
+        c = harmonic_centrality(G, distance="weight")
+        d = {0: 0}
+        assert c == d
+
+    def test_cycle_c4_directed(self):
+        c = harmonic_centrality(self.C4_directed, nbunch=[0, 1], sources=[1, 2])
+        d = {0: 0.833, 1: 0.333}
+        for n in [0, 1]:
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p3_harmonic_subset(self):
+        c = harmonic_centrality(self.P3, sources=[0, 1])
+        d = {0: 1, 1: 1, 2: 1.5}
+        for n in self.P3:
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p4_harmonic_subset(self):
+        c = harmonic_centrality(self.P4, nbunch=[2, 3], sources=[0, 1])
+        d = {2: 1.5, 3: 0.8333333}
+        for n in [2, 3]:
+            assert c[n] == pytest.approx(d[n], abs=1e-3)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_laplacian_centrality.py

@@ -0,0 +1,221 @@
+import pytest
+
+import networkx as nx
+
+np = pytest.importorskip("numpy")
+sp = pytest.importorskip("scipy")
+
+
+def test_laplacian_centrality_null_graph():
+    G = nx.Graph()
+    with pytest.raises(nx.NetworkXPointlessConcept):
+        d = nx.laplacian_centrality(G, normalized=False)
+
+
+def test_laplacian_centrality_single_node():
+    """See gh-6571"""
+    G = nx.empty_graph(1)
+    assert nx.laplacian_centrality(G, normalized=False) == {0: 0}
+    with pytest.raises(ZeroDivisionError):
+        nx.laplacian_centrality(G, normalized=True)
+
+
+def test_laplacian_centrality_unconnected_nodes():
+    """laplacian_centrality on a unconnected node graph should return 0
+
+    For graphs without edges, the Laplacian energy is 0 and is unchanged with
+    node removal, so::
+
+        LC(v) = LE(G) - LE(G - v) = 0 - 0 = 0
+    """
+    G = nx.empty_graph(3)
+    assert nx.laplacian_centrality(G, normalized=False) == {0: 0, 1: 0, 2: 0}
+
+
+def test_laplacian_centrality_empty_graph():
+    G = nx.empty_graph(3)
+    with pytest.raises(ZeroDivisionError):
+        d = nx.laplacian_centrality(G, normalized=True)
+
+
+def test_laplacian_centrality_E():
+    E = nx.Graph()
+    E.add_weighted_edges_from(
+        [(0, 1, 4), (4, 5, 1), (0, 2, 2), (2, 1, 1), (1, 3, 2), (1, 4, 2)]
+    )
+    d = nx.laplacian_centrality(E)
+    exact = {
+        0: 0.700000,
+        1: 0.900000,
+        2: 0.280000,
+        3: 0.220000,
+        4: 0.260000,
+        5: 0.040000,
+    }
+
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 200
+    dnn = nx.laplacian_centrality(E, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-7)
+
+    # Check unweighted not-normalized version
+    duw_nn = nx.laplacian_centrality(E, normalized=False, weight=None)
+    print(duw_nn)
+    exact_uw_nn = {
+        0: 18,
+        1: 34,
+        2: 18,
+        3: 10,
+        4: 16,
+        5: 6,
+    }
+    for n, dc in duw_nn.items():
+        assert exact_uw_nn[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check unweighted version
+    duw = nx.laplacian_centrality(E, weight=None)
+    full_energy = 42
+    for n, dc in duw.items():
+        assert exact_uw_nn[n] / full_energy == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_KC():
+    KC = nx.karate_club_graph()
+    d = nx.laplacian_centrality(KC)
+    exact = {
+        0: 0.2543593,
+        1: 0.1724524,
+        2: 0.2166053,
+        3: 0.0964646,
+        4: 0.0350344,
+        5: 0.0571109,
+        6: 0.0540713,
+        7: 0.0788674,
+        8: 0.1222204,
+        9: 0.0217565,
+        10: 0.0308751,
+        11: 0.0215965,
+        12: 0.0174372,
+        13: 0.118861,
+        14: 0.0366341,
+        15: 0.0548712,
+        16: 0.0172772,
+        17: 0.0191969,
+        18: 0.0225564,
+        19: 0.0331147,
+        20: 0.0279955,
+        21: 0.0246361,
+        22: 0.0382339,
+        23: 0.1294193,
+        24: 0.0227164,
+        25: 0.0644697,
+        26: 0.0281555,
+        27: 0.075188,
+        28: 0.0364742,
+        29: 0.0707087,
+        30: 0.0708687,
+        31: 0.131019,
+        32: 0.2370821,
+        33: 0.3066709,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 12502
+    dnn = nx.laplacian_centrality(KC, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3)
+
+
+def test_laplacian_centrality_K():
+    K = nx.krackhardt_kite_graph()
+    d = nx.laplacian_centrality(K)
+    exact = {
+        0: 0.3010753,
+        1: 0.3010753,
+        2: 0.2258065,
+        3: 0.483871,
+        4: 0.2258065,
+        5: 0.3870968,
+        6: 0.3870968,
+        7: 0.1935484,
+        8: 0.0752688,
+        9: 0.0322581,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 186
+    dnn = nx.laplacian_centrality(K, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-3)
+
+
+def test_laplacian_centrality_P3():
+    P3 = nx.path_graph(3)
+    d = nx.laplacian_centrality(P3)
+    exact = {0: 0.6, 1: 1.0, 2: 0.6}
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_K5():
+    K5 = nx.complete_graph(5)
+    d = nx.laplacian_centrality(K5)
+    exact = {0: 0.52, 1: 0.52, 2: 0.52, 3: 0.52, 4: 0.52}
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_FF():
+    FF = nx.florentine_families_graph()
+    d = nx.laplacian_centrality(FF)
+    exact = {
+        "Acciaiuoli": 0.0804598,
+        "Medici": 0.4022989,
+        "Castellani": 0.1724138,
+        "Peruzzi": 0.183908,
+        "Strozzi": 0.2528736,
+        "Barbadori": 0.137931,
+        "Ridolfi": 0.2183908,
+        "Tornabuoni": 0.2183908,
+        "Albizzi": 0.1954023,
+        "Salviati": 0.1149425,
+        "Pazzi": 0.0344828,
+        "Bischeri": 0.1954023,
+        "Guadagni": 0.2298851,
+        "Ginori": 0.045977,
+        "Lamberteschi": 0.0574713,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+
+def test_laplacian_centrality_DG():
+    DG = nx.DiGraph([(0, 5), (1, 5), (2, 5), (3, 5), (4, 5), (5, 6), (5, 7), (5, 8)])
+    d = nx.laplacian_centrality(DG)
+    exact = {
+        0: 0.2123352,
+        5: 0.515391,
+        1: 0.2123352,
+        2: 0.2123352,
+        3: 0.2123352,
+        4: 0.2123352,
+        6: 0.2952031,
+        7: 0.2952031,
+        8: 0.2952031,
+    }
+    for n, dc in d.items():
+        assert exact[n] == pytest.approx(dc, abs=1e-7)
+
+    # Check not normalized
+    full_energy = 9.50704
+    dnn = nx.laplacian_centrality(DG, normalized=False)
+    for n, dc in dnn.items():
+        assert exact[n] * full_energy == pytest.approx(dc, abs=1e-4)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_load_centrality.py

@@ -0,0 +1,344 @@
+import pytest
+
+import networkx as nx
+
+
+class TestLoadCentrality:
+    @classmethod
+    def setup_class(cls):
+        G = nx.Graph()
+        G.add_edge(0, 1, weight=3)
+        G.add_edge(0, 2, weight=2)
+        G.add_edge(0, 3, weight=6)
+        G.add_edge(0, 4, weight=4)
+        G.add_edge(1, 3, weight=5)
+        G.add_edge(1, 5, weight=5)
+        G.add_edge(2, 4, weight=1)
+        G.add_edge(3, 4, weight=2)
+        G.add_edge(3, 5, weight=1)
+        G.add_edge(4, 5, weight=4)
+        cls.G = G
+        cls.exact_weighted = {0: 4.0, 1: 0.0, 2: 8.0, 3: 6.0, 4: 8.0, 5: 0.0}
+        cls.K = nx.krackhardt_kite_graph()
+        cls.P3 = nx.path_graph(3)
+        cls.P4 = nx.path_graph(4)
+        cls.K5 = nx.complete_graph(5)
+        cls.P2 = nx.path_graph(2)
+
+        cls.C4 = nx.cycle_graph(4)
+        cls.T = nx.balanced_tree(r=2, h=2)
+        cls.Gb = nx.Graph()
+        cls.Gb.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
+        cls.F = nx.florentine_families_graph()
+        cls.LM = nx.les_miserables_graph()
+        cls.D = nx.cycle_graph(3, create_using=nx.DiGraph())
+        cls.D.add_edges_from([(3, 0), (4, 3)])
+
+    def test_not_strongly_connected(self):
+        b = nx.load_centrality(self.D)
+        result = {0: 5.0 / 12, 1: 1.0 / 4, 2: 1.0 / 12, 3: 1.0 / 4, 4: 0.000}
+        for n in sorted(self.D):
+            assert result[n] == pytest.approx(b[n], abs=1e-3)
+            assert result[n] == pytest.approx(nx.load_centrality(self.D, n), abs=1e-3)
+
+    def test_P2_normalized_load(self):
+        G = self.P2
+        c = nx.load_centrality(G, normalized=True)
+        d = {0: 0.000, 1: 0.000}
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_weighted_load(self):
+        b = nx.load_centrality(self.G, weight="weight", normalized=False)
+        for n in sorted(self.G):
+            assert b[n] == self.exact_weighted[n]
+
+    def test_k5_load(self):
+        G = self.K5
+        c = nx.load_centrality(G)
+        d = {0: 0.000, 1: 0.000, 2: 0.000, 3: 0.000, 4: 0.000}
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p3_load(self):
+        G = self.P3
+        c = nx.load_centrality(G)
+        d = {0: 0.000, 1: 1.000, 2: 0.000}
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+        c = nx.load_centrality(G, v=1)
+        assert c == pytest.approx(1.0, abs=1e-7)
+        c = nx.load_centrality(G, v=1, normalized=True)
+        assert c == pytest.approx(1.0, abs=1e-7)
+
+    def test_p2_load(self):
+        G = nx.path_graph(2)
+        c = nx.load_centrality(G)
+        d = {0: 0.000, 1: 0.000}
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_krackhardt_load(self):
+        G = self.K
+        c = nx.load_centrality(G)
+        d = {
+            0: 0.023,
+            1: 0.023,
+            2: 0.000,
+            3: 0.102,
+            4: 0.000,
+            5: 0.231,
+            6: 0.231,
+            7: 0.389,
+            8: 0.222,
+            9: 0.000,
+        }
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_florentine_families_load(self):
+        G = self.F
+        c = nx.load_centrality(G)
+        d = {
+            "Acciaiuoli": 0.000,
+            "Albizzi": 0.211,
+            "Barbadori": 0.093,
+            "Bischeri": 0.104,
+            "Castellani": 0.055,
+            "Ginori": 0.000,
+            "Guadagni": 0.251,
+            "Lamberteschi": 0.000,
+            "Medici": 0.522,
+            "Pazzi": 0.000,
+            "Peruzzi": 0.022,
+            "Ridolfi": 0.117,
+            "Salviati": 0.143,
+            "Strozzi": 0.106,
+            "Tornabuoni": 0.090,
+        }
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_les_miserables_load(self):
+        G = self.LM
+        c = nx.load_centrality(G)
+        d = {
+            "Napoleon": 0.000,
+            "Myriel": 0.177,
+            "MlleBaptistine": 0.000,
+            "MmeMagloire": 0.000,
+            "CountessDeLo": 0.000,
+            "Geborand": 0.000,
+            "Champtercier": 0.000,
+            "Cravatte": 0.000,
+            "Count": 0.000,
+            "OldMan": 0.000,
+            "Valjean": 0.567,
+            "Labarre": 0.000,
+            "Marguerite": 0.000,
+            "MmeDeR": 0.000,
+            "Isabeau": 0.000,
+            "Gervais": 0.000,
+            "Listolier": 0.000,
+            "Tholomyes": 0.043,
+            "Fameuil": 0.000,
+            "Blacheville": 0.000,
+            "Favourite": 0.000,
+            "Dahlia": 0.000,
+            "Zephine": 0.000,
+            "Fantine": 0.128,
+            "MmeThenardier": 0.029,
+            "Thenardier": 0.075,
+            "Cosette": 0.024,
+            "Javert": 0.054,
+            "Fauchelevent": 0.026,
+            "Bamatabois": 0.008,
+            "Perpetue": 0.000,
+            "Simplice": 0.009,
+            "Scaufflaire": 0.000,
+            "Woman1": 0.000,
+            "Judge": 0.000,
+            "Champmathieu": 0.000,
+            "Brevet": 0.000,
+            "Chenildieu": 0.000,
+            "Cochepaille": 0.000,
+            "Pontmercy": 0.007,
+            "Boulatruelle": 0.000,
+            "Eponine": 0.012,
+            "Anzelma": 0.000,
+            "Woman2": 0.000,
+            "MotherInnocent": 0.000,
+            "Gribier": 0.000,
+            "MmeBurgon": 0.026,
+            "Jondrette": 0.000,
+            "Gavroche": 0.164,
+            "Gillenormand": 0.021,
+            "Magnon": 0.000,
+            "MlleGillenormand": 0.047,
+            "MmePontmercy": 0.000,
+            "MlleVaubois": 0.000,
+            "LtGillenormand": 0.000,
+            "Marius": 0.133,
+            "BaronessT": 0.000,
+            "Mabeuf": 0.028,
+            "Enjolras": 0.041,
+            "Combeferre": 0.001,
+            "Prouvaire": 0.000,
+            "Feuilly": 0.001,
+            "Courfeyrac": 0.006,
+            "Bahorel": 0.002,
+            "Bossuet": 0.032,
+            "Joly": 0.002,
+            "Grantaire": 0.000,
+            "MotherPlutarch": 0.000,
+            "Gueulemer": 0.005,
+            "Babet": 0.005,
+            "Claquesous": 0.005,
+            "Montparnasse": 0.004,
+            "Toussaint": 0.000,
+            "Child1": 0.000,
+            "Child2": 0.000,
+            "Brujon": 0.000,
+            "MmeHucheloup": 0.000,
+        }
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_unnormalized_k5_load(self):
+        G = self.K5
+        c = nx.load_centrality(G, normalized=False)
+        d = {0: 0.000, 1: 0.000, 2: 0.000, 3: 0.000, 4: 0.000}
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_unnormalized_p3_load(self):
+        G = self.P3
+        c = nx.load_centrality(G, normalized=False)
+        d = {0: 0.000, 1: 2.000, 2: 0.000}
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_unnormalized_krackhardt_load(self):
+        G = self.K
+        c = nx.load_centrality(G, normalized=False)
+        d = {
+            0: 1.667,
+            1: 1.667,
+            2: 0.000,
+            3: 7.333,
+            4: 0.000,
+            5: 16.667,
+            6: 16.667,
+            7: 28.000,
+            8: 16.000,
+            9: 0.000,
+        }
+
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_unnormalized_florentine_families_load(self):
+        G = self.F
+        c = nx.load_centrality(G, normalized=False)
+
+        d = {
+            "Acciaiuoli": 0.000,
+            "Albizzi": 38.333,
+            "Barbadori": 17.000,
+            "Bischeri": 19.000,
+            "Castellani": 10.000,
+            "Ginori": 0.000,
+            "Guadagni": 45.667,
+            "Lamberteschi": 0.000,
+            "Medici": 95.000,
+            "Pazzi": 0.000,
+            "Peruzzi": 4.000,
+            "Ridolfi": 21.333,
+            "Salviati": 26.000,
+            "Strozzi": 19.333,
+            "Tornabuoni": 16.333,
+        }
+        for n in sorted(G):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_load_betweenness_difference(self):
+        # Difference Between Load and Betweenness
+        # --------------------------------------- The smallest graph
+        # that shows the difference between load and betweenness is
+        # G=ladder_graph(3) (Graph B below)
+
+        # Graph A and B are from Tao Zhou, Jian-Guo Liu, Bing-Hong
+        # Wang: Comment on "Scientific collaboration
+        # networks. II. Shortest paths, weighted networks, and
+        # centrality". https://arxiv.org/pdf/physics/0511084
+
+        # Notice that unlike here, their calculation adds to 1 to the
+        # betweenness of every node i for every path from i to every
+        # other node.  This is exactly what it should be, based on
+        # Eqn. (1) in their paper: the eqn is B(v) = \sum_{s\neq t,
+        # s\neq v}{\frac{\sigma_{st}(v)}{\sigma_{st}}}, therefore,
+        # they allow v to be the target node.
+
+        # We follow Brandes 2001, who follows Freeman 1977 that make
+        # the sum for betweenness of v exclude paths where v is either
+        # the source or target node.  To agree with their numbers, we
+        # must additionally, remove edge (4,8) from the graph, see AC
+        # example following (there is a mistake in the figure in their
+        # paper - personal communication).
+
+        # A = nx.Graph()
+        # A.add_edges_from([(0,1), (1,2), (1,3), (2,4),
+        #                  (3,5), (4,6), (4,7), (4,8),
+        #                  (5,8), (6,9), (7,9), (8,9)])
+        B = nx.Graph()  # ladder_graph(3)
+        B.add_edges_from([(0, 1), (0, 2), (1, 3), (2, 3), (2, 4), (4, 5), (3, 5)])
+        c = nx.load_centrality(B, normalized=False)
+        d = {0: 1.750, 1: 1.750, 2: 6.500, 3: 6.500, 4: 1.750, 5: 1.750}
+        for n in sorted(B):
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_c4_edge_load(self):
+        G = self.C4
+        c = nx.edge_load_centrality(G)
+        d = {(0, 1): 6.000, (0, 3): 6.000, (1, 2): 6.000, (2, 3): 6.000}
+        for n in G.edges():
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_p4_edge_load(self):
+        G = self.P4
+        c = nx.edge_load_centrality(G)
+        d = {(0, 1): 6.000, (1, 2): 8.000, (2, 3): 6.000}
+        for n in G.edges():
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_k5_edge_load(self):
+        G = self.K5
+        c = nx.edge_load_centrality(G)
+        d = {
+            (0, 1): 5.000,
+            (0, 2): 5.000,
+            (0, 3): 5.000,
+            (0, 4): 5.000,
+            (1, 2): 5.000,
+            (1, 3): 5.000,
+            (1, 4): 5.000,
+            (2, 3): 5.000,
+            (2, 4): 5.000,
+            (3, 4): 5.000,
+        }
+        for n in G.edges():
+            assert c[n] == pytest.approx(d[n], abs=1e-3)
+
+    def test_tree_edge_load(self):
+        G = self.T
+        c = nx.edge_load_centrality(G)
+        d = {
+            (0, 1): 24.000,
+            (0, 2): 24.000,
+            (1, 3): 12.000,
+            (1, 4): 12.000,
+            (2, 5): 12.000,
+            (2, 6): 12.000,
+        }
+        for n in G.edges():
+            assert c[n] == pytest.approx(d[n], abs=1e-3)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_percolation_centrality.py

@@ -0,0 +1,87 @@
+import pytest
+
+import networkx as nx
+
+
+def example1a_G():
+    G = nx.Graph()
+    G.add_node(1, percolation=0.1)
+    G.add_node(2, percolation=0.2)
+    G.add_node(3, percolation=0.2)
+    G.add_node(4, percolation=0.2)
+    G.add_node(5, percolation=0.3)
+    G.add_node(6, percolation=0.2)
+    G.add_node(7, percolation=0.5)
+    G.add_node(8, percolation=0.5)
+    G.add_edges_from([(1, 4), (2, 4), (3, 4), (4, 5), (5, 6), (6, 7), (6, 8)])
+    return G
+
+
+def example1b_G():
+    G = nx.Graph()
+    G.add_node(1, percolation=0.3)
+    G.add_node(2, percolation=0.5)
+    G.add_node(3, percolation=0.5)
+    G.add_node(4, percolation=0.2)
+    G.add_node(5, percolation=0.3)
+    G.add_node(6, percolation=0.2)
+    G.add_node(7, percolation=0.1)
+    G.add_node(8, percolation=0.1)
+    G.add_edges_from([(1, 4), (2, 4), (3, 4), (4, 5), (5, 6), (6, 7), (6, 8)])
+    return G
+
+
+def test_percolation_example1a():
+    """percolation centrality: example 1a"""
+    G = example1a_G()
+    p = nx.percolation_centrality(G)
+    p_answer = {4: 0.625, 6: 0.667}
+    for n, k in p_answer.items():
+        assert p[n] == pytest.approx(k, abs=1e-3)
+
+
+def test_percolation_example1b():
+    """percolation centrality: example 1a"""
+    G = example1b_G()
+    p = nx.percolation_centrality(G)
+    p_answer = {4: 0.825, 6: 0.4}
+    for n, k in p_answer.items():
+        assert p[n] == pytest.approx(k, abs=1e-3)
+
+
+def test_converge_to_betweenness():
+    """percolation centrality: should converge to betweenness
+    centrality when all nodes are percolated the same"""
+    # taken from betweenness test test_florentine_families_graph
+    G = nx.florentine_families_graph()
+    b_answer = {
+        "Acciaiuoli": 0.000,
+        "Albizzi": 0.212,
+        "Barbadori": 0.093,
+        "Bischeri": 0.104,
+        "Castellani": 0.055,
+        "Ginori": 0.000,
+        "Guadagni": 0.255,
+        "Lamberteschi": 0.000,
+        "Medici": 0.522,
+        "Pazzi": 0.000,
+        "Peruzzi": 0.022,
+        "Ridolfi": 0.114,
+        "Salviati": 0.143,
+        "Strozzi": 0.103,
+        "Tornabuoni": 0.092,
+    }
+
+    # If no initial state is provided, state for
+    # every node defaults to 1
+    p_answer = nx.percolation_centrality(G)
+    assert p_answer == pytest.approx(b_answer, abs=1e-3)
+
+    p_states = {k: 0.3 for k, v in b_answer.items()}
+    p_answer = nx.percolation_centrality(G, states=p_states)
+    assert p_answer == pytest.approx(b_answer, abs=1e-3)
+
+
+def test_default_percolation():
+    G = nx.erdos_renyi_graph(42, 0.42, seed=42)
+    assert nx.percolation_centrality(G) == pytest.approx(nx.betweenness_centrality(G))

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_reaching.py

@@ -0,0 +1,117 @@
+"""Unit tests for the :mod:`networkx.algorithms.centrality.reaching` module."""
+import pytest
+
+import networkx as nx
+
+
+class TestGlobalReachingCentrality:
+    """Unit tests for the global reaching centrality function."""
+
+    def test_non_positive_weights(self):
+        with pytest.raises(nx.NetworkXError):
+            G = nx.DiGraph()
+            nx.global_reaching_centrality(G, weight="weight")
+
+    def test_negatively_weighted(self):
+        with pytest.raises(nx.NetworkXError):
+            G = nx.Graph()
+            G.add_weighted_edges_from([(0, 1, -2), (1, 2, +1)])
+            nx.global_reaching_centrality(G, weight="weight")
+
+    def test_directed_star(self):
+        G = nx.DiGraph()
+        G.add_weighted_edges_from([(1, 2, 0.5), (1, 3, 0.5)])
+        grc = nx.global_reaching_centrality
+        assert grc(G, normalized=False, weight="weight") == 0.5
+        assert grc(G) == 1
+
+    def test_undirected_unweighted_star(self):
+        G = nx.star_graph(2)
+        grc = nx.global_reaching_centrality
+        assert grc(G, normalized=False, weight=None) == 0.25
+
+    def test_undirected_weighted_star(self):
+        G = nx.Graph()
+        G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2)])
+        grc = nx.global_reaching_centrality
+        assert grc(G, normalized=False, weight="weight") == 0.375
+
+    def test_cycle_directed_unweighted(self):
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        assert nx.global_reaching_centrality(G, weight=None) == 0
+
+    def test_cycle_undirected_unweighted(self):
+        G = nx.Graph()
+        G.add_edge(1, 2)
+        assert nx.global_reaching_centrality(G, weight=None) == 0
+
+    def test_cycle_directed_weighted(self):
+        G = nx.DiGraph()
+        G.add_weighted_edges_from([(1, 2, 1), (2, 1, 1)])
+        assert nx.global_reaching_centrality(G) == 0
+
+    def test_cycle_undirected_weighted(self):
+        G = nx.Graph()
+        G.add_edge(1, 2, weight=1)
+        grc = nx.global_reaching_centrality
+        assert grc(G, normalized=False) == 0
+
+    def test_directed_weighted(self):
+        G = nx.DiGraph()
+        G.add_edge("A", "B", weight=5)
+        G.add_edge("B", "C", weight=1)
+        G.add_edge("B", "D", weight=0.25)
+        G.add_edge("D", "E", weight=1)
+
+        denom = len(G) - 1
+        A_local = sum([5, 3, 2.625, 2.0833333333333]) / denom
+        B_local = sum([1, 0.25, 0.625]) / denom
+        C_local = 0
+        D_local = sum([1]) / denom
+        E_local = 0
+
+        local_reach_ctrs = [A_local, C_local, B_local, D_local, E_local]
+        max_local = max(local_reach_ctrs)
+        expected = sum(max_local - lrc for lrc in local_reach_ctrs) / denom
+        grc = nx.global_reaching_centrality
+        actual = grc(G, normalized=False, weight="weight")
+        assert expected == pytest.approx(actual, abs=1e-7)
+
+
+class TestLocalReachingCentrality:
+    """Unit tests for the local reaching centrality function."""
+
+    def test_non_positive_weights(self):
+        with pytest.raises(nx.NetworkXError):
+            G = nx.DiGraph()
+            G.add_weighted_edges_from([(0, 1, 0)])
+            nx.local_reaching_centrality(G, 0, weight="weight")
+
+    def test_negatively_weighted(self):
+        with pytest.raises(nx.NetworkXError):
+            G = nx.Graph()
+            G.add_weighted_edges_from([(0, 1, -2), (1, 2, +1)])
+            nx.local_reaching_centrality(G, 0, weight="weight")
+
+    def test_undirected_unweighted_star(self):
+        G = nx.star_graph(2)
+        grc = nx.local_reaching_centrality
+        assert grc(G, 1, weight=None, normalized=False) == 0.75
+
+    def test_undirected_weighted_star(self):
+        G = nx.Graph()
+        G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2)])
+        centrality = nx.local_reaching_centrality(
+            G, 1, normalized=False, weight="weight"
+        )
+        assert centrality == 1.5
+
+    def test_undirected_weighted_normalized(self):
+        G = nx.Graph()
+        G.add_weighted_edges_from([(1, 2, 1), (1, 3, 2)])
+        centrality = nx.local_reaching_centrality(
+            G, 1, normalized=True, weight="weight"
+        )
+        assert centrality == 1.0

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_second_order_centrality.py

@@ -0,0 +1,82 @@
+"""
+Tests for second order centrality.
+"""
+
+import pytest
+
+pytest.importorskip("numpy")
+pytest.importorskip("scipy")
+
+import networkx as nx
+
+
+def test_empty():
+    with pytest.raises(nx.NetworkXException):
+        G = nx.empty_graph()
+        nx.second_order_centrality(G)
+
+
+def test_non_connected():
+    with pytest.raises(nx.NetworkXException):
+        G = nx.Graph()
+        G.add_node(0)
+        G.add_node(1)
+        nx.second_order_centrality(G)
+
+
+def test_non_negative_edge_weights():
+    with pytest.raises(nx.NetworkXException):
+        G = nx.path_graph(2)
+        G.add_edge(0, 1, weight=-1)
+        nx.second_order_centrality(G)
+
+
+def test_weight_attribute():
+    G = nx.Graph()
+    G.add_weighted_edges_from([(0, 1, 1.0), (1, 2, 3.5)], weight="w")
+    expected = {0: 3.431, 1: 3.082, 2: 5.612}
+    b = nx.second_order_centrality(G, weight="w")
+
+    for n in sorted(G):
+        assert b[n] == pytest.approx(expected[n], abs=1e-2)
+
+
+def test_one_node_graph():
+    """Second order centrality: single node"""
+    G = nx.Graph()
+    G.add_node(0)
+    G.add_edge(0, 0)
+    assert nx.second_order_centrality(G)[0] == 0
+
+
+def test_P3():
+    """Second order centrality: line graph, as defined in paper"""
+    G = nx.path_graph(3)
+    b_answer = {0: 3.741, 1: 1.414, 2: 3.741}
+
+    b = nx.second_order_centrality(G)
+
+    for n in sorted(G):
+        assert b[n] == pytest.approx(b_answer[n], abs=1e-2)
+
+
+def test_K3():
+    """Second order centrality: complete graph, as defined in paper"""
+    G = nx.complete_graph(3)
+    b_answer = {0: 1.414, 1: 1.414, 2: 1.414}
+
+    b = nx.second_order_centrality(G)
+
+    for n in sorted(G):
+        assert b[n] == pytest.approx(b_answer[n], abs=1e-2)
+
+
+def test_ring_graph():
+    """Second order centrality: ring graph, as defined in paper"""
+    G = nx.cycle_graph(5)
+    b_answer = {0: 4.472, 1: 4.472, 2: 4.472, 3: 4.472, 4: 4.472}
+
+    b = nx.second_order_centrality(G)
+
+    for n in sorted(G):
+        assert b[n] == pytest.approx(b_answer[n], abs=1e-2)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/tests/test_voterank.py

@@ -0,0 +1,65 @@
+"""
+    Unit tests for VoteRank.
+"""
+
+
+import networkx as nx
+
+
+class TestVoteRankCentrality:
+    # Example Graph present in reference paper
+    def test_voterank_centrality_1(self):
+        G = nx.Graph()
+        G.add_edges_from(
+            [
+                (7, 8),
+                (7, 5),
+                (7, 9),
+                (5, 0),
+                (0, 1),
+                (0, 2),
+                (0, 3),
+                (0, 4),
+                (1, 6),
+                (2, 6),
+                (3, 6),
+                (4, 6),
+            ]
+        )
+        assert [0, 7, 6] == nx.voterank(G)
+
+    def test_voterank_emptygraph(self):
+        G = nx.Graph()
+        assert [] == nx.voterank(G)
+
+    # Graph unit test
+    def test_voterank_centrality_2(self):
+        G = nx.florentine_families_graph()
+        d = nx.voterank(G, 4)
+        exact = ["Medici", "Strozzi", "Guadagni", "Castellani"]
+        assert exact == d
+
+    # DiGraph unit test
+    def test_voterank_centrality_3(self):
+        G = nx.gnc_graph(10, seed=7)
+        d = nx.voterank(G, 4)
+        exact = [3, 6, 8]
+        assert exact == d
+
+    # MultiGraph unit test
+    def test_voterank_centrality_4(self):
+        G = nx.MultiGraph()
+        G.add_edges_from(
+            [(0, 1), (0, 1), (1, 2), (2, 5), (2, 5), (5, 6), (5, 6), (2, 4), (4, 3)]
+        )
+        exact = [2, 1, 5, 4]
+        assert exact == nx.voterank(G)
+
+    # MultiDiGraph unit test
+    def test_voterank_centrality_5(self):
+        G = nx.MultiDiGraph()
+        G.add_edges_from(
+            [(0, 1), (0, 1), (1, 2), (2, 5), (2, 5), (5, 6), (5, 6), (2, 4), (4, 3)]
+        )
+        exact = [2, 0, 5, 4]
+        assert exact == nx.voterank(G)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/trophic.py

@@ -0,0 +1,162 @@
+"""Trophic levels"""
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["trophic_levels", "trophic_differences", "trophic_incoherence_parameter"]
+
+
+@not_implemented_for("undirected")
+@nx._dispatch(edge_attrs="weight")
+def trophic_levels(G, weight="weight"):
+    r"""Compute the trophic levels of nodes.
+
+    The trophic level of a node $i$ is
+
+    .. math::
+
+        s_i = 1 + \frac{1}{k^{in}_i} \sum_{j} a_{ij} s_j
+
+    where $k^{in}_i$ is the in-degree of i
+
+    .. math::
+
+        k^{in}_i = \sum_{j} a_{ij}
+
+    and nodes with $k^{in}_i = 0$ have $s_i = 1$ by convention.
+
+    These are calculated using the method outlined in Levine [1]_.
+
+    Parameters
+    ----------
+    G : DiGraph
+        A directed networkx graph
+
+    Returns
+    -------
+    nodes : dict
+        Dictionary of nodes with trophic level as the value.
+
+    References
+    ----------
+    .. [1] Stephen Levine (1980) J. theor. Biol. 83, 195-207
+    """
+    import numpy as np
+
+    # find adjacency matrix
+    a = nx.adjacency_matrix(G, weight=weight).T.toarray()
+
+    # drop rows/columns where in-degree is zero
+    rowsum = np.sum(a, axis=1)
+    p = a[rowsum != 0][:, rowsum != 0]
+    # normalise so sum of in-degree weights is 1 along each row
+    p = p / rowsum[rowsum != 0][:, np.newaxis]
+
+    # calculate trophic levels
+    nn = p.shape[0]
+    i = np.eye(nn)
+    try:
+        n = np.linalg.inv(i - p)
+    except np.linalg.LinAlgError as err:
+        # LinAlgError is raised when there is a non-basal node
+        msg = (
+            "Trophic levels are only defined for graphs where every "
+            + "node has a path from a basal node (basal nodes are nodes "
+            + "with no incoming edges)."
+        )
+        raise nx.NetworkXError(msg) from err
+    y = n.sum(axis=1) + 1
+
+    levels = {}
+
+    # all nodes with in-degree zero have trophic level == 1
+    zero_node_ids = (node_id for node_id, degree in G.in_degree if degree == 0)
+    for node_id in zero_node_ids:
+        levels[node_id] = 1
+
+    # all other nodes have levels as calculated
+    nonzero_node_ids = (node_id for node_id, degree in G.in_degree if degree != 0)
+    for i, node_id in enumerate(nonzero_node_ids):
+        levels[node_id] = y[i]
+
+    return levels
+
+
+@not_implemented_for("undirected")
+@nx._dispatch(edge_attrs="weight")
+def trophic_differences(G, weight="weight"):
+    r"""Compute the trophic differences of the edges of a directed graph.
+
+    The trophic difference $x_ij$ for each edge is defined in Johnson et al.
+    [1]_ as:
+
+    .. math::
+        x_ij = s_j - s_i
+
+    Where $s_i$ is the trophic level of node $i$.
+
+    Parameters
+    ----------
+    G : DiGraph
+        A directed networkx graph
+
+    Returns
+    -------
+    diffs : dict
+        Dictionary of edges with trophic differences as the value.
+
+    References
+    ----------
+    .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A.
+        Munoz (2014) PNAS "Trophic coherence determines food-web stability"
+    """
+    levels = trophic_levels(G, weight=weight)
+    diffs = {}
+    for u, v in G.edges:
+        diffs[(u, v)] = levels[v] - levels[u]
+    return diffs
+
+
+@not_implemented_for("undirected")
+@nx._dispatch(edge_attrs="weight")
+def trophic_incoherence_parameter(G, weight="weight", cannibalism=False):
+    r"""Compute the trophic incoherence parameter of a graph.
+
+    Trophic coherence is defined as the homogeneity of the distribution of
+    trophic distances: the more similar, the more coherent. This is measured by
+    the standard deviation of the trophic differences and referred to as the
+    trophic incoherence parameter $q$ by [1].
+
+    Parameters
+    ----------
+    G : DiGraph
+        A directed networkx graph
+
+    cannibalism: Boolean
+        If set to False, self edges are not considered in the calculation
+
+    Returns
+    -------
+    trophic_incoherence_parameter : float
+        The trophic coherence of a graph
+
+    References
+    ----------
+    .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A.
+        Munoz (2014) PNAS "Trophic coherence determines food-web stability"
+    """
+    import numpy as np
+
+    if cannibalism:
+        diffs = trophic_differences(G, weight=weight)
+    else:
+        # If no cannibalism, remove self-edges
+        self_loops = list(nx.selfloop_edges(G))
+        if self_loops:
+            # Make a copy so we do not change G's edges in memory
+            G_2 = G.copy()
+            G_2.remove_edges_from(self_loops)
+        else:
+            # Avoid copy otherwise
+            G_2 = G
+        diffs = trophic_differences(G_2, weight=weight)
+    return np.std(list(diffs.values()))

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/centrality/voterank_alg.py

@@ -0,0 +1,94 @@
+"""Algorithm to select influential nodes in a graph using VoteRank."""
+import networkx as nx
+
+__all__ = ["voterank"]
+
+
+@nx._dispatch
+def voterank(G, number_of_nodes=None):
+    """Select a list of influential nodes in a graph using VoteRank algorithm
+
+    VoteRank [1]_ computes a ranking of the nodes in a graph G based on a
+    voting scheme. With VoteRank, all nodes vote for each of its in-neighbours
+    and the node with the highest votes is elected iteratively. The voting
+    ability of out-neighbors of elected nodes is decreased in subsequent turns.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX graph.
+
+    number_of_nodes : integer, optional
+        Number of ranked nodes to extract (default all nodes).
+
+    Returns
+    -------
+    voterank : list
+        Ordered list of computed seeds.
+        Only nodes with positive number of votes are returned.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (0, 3), (1, 4)])
+    >>> nx.voterank(G)
+    [0, 1]
+
+    The algorithm can be used both for undirected and directed graphs.
+    However, the directed version is different in two ways:
+    (i) nodes only vote for their in-neighbors and
+    (ii) only the voting ability of elected node and its out-neighbors are updated:
+
+    >>> G = nx.DiGraph([(0, 1), (2, 1), (2, 3), (3, 4)])
+    >>> nx.voterank(G)
+    [2, 3]
+
+    Notes
+    -----
+    Each edge is treated independently in case of multigraphs.
+
+    References
+    ----------
+    .. [1] Zhang, J.-X. et al. (2016).
+        Identifying a set of influential spreaders in complex networks.
+        Sci. Rep. 6, 27823; doi: 10.1038/srep27823.
+    """
+    influential_nodes = []
+    vote_rank = {}
+    if len(G) == 0:
+        return influential_nodes
+    if number_of_nodes is None or number_of_nodes > len(G):
+        number_of_nodes = len(G)
+    if G.is_directed():
+        # For directed graphs compute average out-degree
+        avgDegree = sum(deg for _, deg in G.out_degree()) / len(G)
+    else:
+        # For undirected graphs compute average degree
+        avgDegree = sum(deg for _, deg in G.degree()) / len(G)
+    # step 1 - initiate all nodes to (0,1) (score, voting ability)
+    for n in G.nodes():
+        vote_rank[n] = [0, 1]
+    # Repeat steps 1b to 4 until num_seeds are elected.
+    for _ in range(number_of_nodes):
+        # step 1b - reset rank
+        for n in G.nodes():
+            vote_rank[n][0] = 0
+        # step 2 - vote
+        for n, nbr in G.edges():
+            # In directed graphs nodes only vote for their in-neighbors
+            vote_rank[n][0] += vote_rank[nbr][1]
+            if not G.is_directed():
+                vote_rank[nbr][0] += vote_rank[n][1]
+        for n in influential_nodes:
+            vote_rank[n][0] = 0
+        # step 3 - select top node
+        n = max(G.nodes, key=lambda x: vote_rank[x][0])
+        if vote_rank[n][0] == 0:
+            return influential_nodes
+        influential_nodes.append(n)
+        # weaken the selected node
+        vote_rank[n] = [0, 0]
+        # step 4 - update voterank properties
+        for _, nbr in G.edges(n):
+            vote_rank[nbr][1] -= 1 / avgDegree
+            vote_rank[nbr][1] = max(vote_rank[nbr][1], 0)
+    return influential_nodes

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/cycles.py

@@ -0,0 +1,1230 @@
+"""
+========================
+Cycle finding algorithms
+========================
+"""
+
+from collections import Counter, defaultdict
+from itertools import combinations, product
+from math import inf
+
+import networkx as nx
+from networkx.utils import not_implemented_for, pairwise
+
+__all__ = [
+    "cycle_basis",
+    "simple_cycles",
+    "recursive_simple_cycles",
+    "find_cycle",
+    "minimum_cycle_basis",
+    "chordless_cycles",
+    "girth",
+]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def cycle_basis(G, root=None):
+    """Returns a list of cycles which form a basis for cycles of G.
+
+    A basis for cycles of a network is a minimal collection of
+    cycles such that any cycle in the network can be written
+    as a sum of cycles in the basis.  Here summation of cycles
+    is defined as "exclusive or" of the edges. Cycle bases are
+    useful, e.g. when deriving equations for electric circuits
+    using Kirchhoff's Laws.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    root : node, optional
+       Specify starting node for basis.
+
+    Returns
+    -------
+    A list of cycle lists.  Each cycle list is a list of nodes
+    which forms a cycle (loop) in G.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_cycle(G, [0, 1, 2, 3])
+    >>> nx.add_cycle(G, [0, 3, 4, 5])
+    >>> nx.cycle_basis(G, 0)
+    [[3, 4, 5, 0], [1, 2, 3, 0]]
+
+    Notes
+    -----
+    This is adapted from algorithm CACM 491 [1]_.
+
+    References
+    ----------
+    .. [1] Paton, K. An algorithm for finding a fundamental set of
+       cycles of a graph. Comm. ACM 12, 9 (Sept 1969), 514-518.
+
+    See Also
+    --------
+    simple_cycles
+    """
+    gnodes = dict.fromkeys(G)  # set-like object that maintains node order
+    cycles = []
+    while gnodes:  # loop over connected components
+        if root is None:
+            root = gnodes.popitem()[0]
+        stack = [root]
+        pred = {root: root}
+        used = {root: set()}
+        while stack:  # walk the spanning tree finding cycles
+            z = stack.pop()  # use last-in so cycles easier to find
+            zused = used[z]
+            for nbr in G[z]:
+                if nbr not in used:  # new node
+                    pred[nbr] = z
+                    stack.append(nbr)
+                    used[nbr] = {z}
+                elif nbr == z:  # self loops
+                    cycles.append([z])
+                elif nbr not in zused:  # found a cycle
+                    pn = used[nbr]
+                    cycle = [nbr, z]
+                    p = pred[z]
+                    while p not in pn:
+                        cycle.append(p)
+                        p = pred[p]
+                    cycle.append(p)
+                    cycles.append(cycle)
+                    used[nbr].add(z)
+        for node in pred:
+            gnodes.pop(node, None)
+        root = None
+    return cycles
+
+
+@nx._dispatch
+def simple_cycles(G, length_bound=None):
+    """Find simple cycles (elementary circuits) of a graph.
+
+    A `simple cycle`, or `elementary circuit`, is a closed path where
+    no node appears twice.  In a directed graph, two simple cycles are distinct
+    if they are not cyclic permutations of each other.  In an undirected graph,
+    two simple cycles are distinct if they are not cyclic permutations of each
+    other nor of the other's reversal.
+
+    Optionally, the cycles are bounded in length.  In the unbounded case, we use
+    a nonrecursive, iterator/generator version of Johnson's algorithm [1]_.  In
+    the bounded case, we use a version of the algorithm of Gupta and
+    Suzumura[2]_. There may be better algorithms for some cases [3]_ [4]_ [5]_.
+
+    The algorithms of Johnson, and Gupta and Suzumura, are enhanced by some
+    well-known preprocessing techniques.  When G is directed, we restrict our
+    attention to strongly connected components of G, generate all simple cycles
+    containing a certain node, remove that node, and further decompose the
+    remainder into strongly connected components.  When G is undirected, we
+    restrict our attention to biconnected components, generate all simple cycles
+    containing a particular edge, remove that edge, and further decompose the
+    remainder into biconnected components.
+
+    Note that multigraphs are supported by this function -- and in undirected
+    multigraphs, a pair of parallel edges is considered a cycle of length 2.
+    Likewise, self-loops are considered to be cycles of length 1.  We define
+    cycles as sequences of nodes; so the presence of loops and parallel edges
+    does not change the number of simple cycles in a graph.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    length_bound : int or None, optional (default=None)
+       If length_bound is an int, generate all simple cycles of G with length at
+       most length_bound.  Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    Examples
+    --------
+    >>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
+    >>> G = nx.DiGraph(edges)
+    >>> sorted(nx.simple_cycles(G))
+    [[0], [0, 1, 2], [0, 2], [1, 2], [2]]
+
+    To filter the cycles so that they don't include certain nodes or edges,
+    copy your graph and eliminate those nodes or edges before calling.
+    For example, to exclude self-loops from the above example:
+
+    >>> H = G.copy()
+    >>> H.remove_edges_from(nx.selfloop_edges(G))
+    >>> sorted(nx.simple_cycles(H))
+    [[0, 1, 2], [0, 2], [1, 2]]
+
+    Notes
+    -----
+    When length_bound is None, the time complexity is $O((n+e)(c+1))$ for $n$
+    nodes, $e$ edges and $c$ simple circuits.  Otherwise, when length_bound > 1,
+    the time complexity is $O((c+n)(k-1)d^k)$ where $d$ is the average degree of
+    the nodes of G and $k$ = length_bound.
+
+    Raises
+    ------
+    ValueError
+        when length_bound < 0.
+
+    References
+    ----------
+    .. [1] Finding all the elementary circuits of a directed graph.
+       D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
+       https://doi.org/10.1137/0204007
+    .. [2] Finding All Bounded-Length Simple Cycles in a Directed Graph
+       A. Gupta and T. Suzumura https://arxiv.org/abs/2105.10094
+    .. [3] Enumerating the cycles of a digraph: a new preprocessing strategy.
+       G. Loizou and P. Thanish, Information Sciences, v. 27, 163-182, 1982.
+    .. [4] A search strategy for the elementary cycles of a directed graph.
+       J.L. Szwarcfiter and P.E. Lauer, BIT NUMERICAL MATHEMATICS,
+       v. 16, no. 2, 192-204, 1976.
+    .. [5] Optimal Listing of Cycles and st-Paths in Undirected Graphs
+        R. Ferreira and R. Grossi and A. Marino and N. Pisanti and R. Rizzi and
+        G. Sacomoto https://arxiv.org/abs/1205.2766
+
+    See Also
+    --------
+    cycle_basis
+    chordless_cycles
+    """
+
+    if length_bound is not None:
+        if length_bound == 0:
+            return
+        elif length_bound < 0:
+            raise ValueError("length bound must be non-negative")
+
+    directed = G.is_directed()
+    yield from ([v] for v, Gv in G.adj.items() if v in Gv)
+
+    if length_bound is not None and length_bound == 1:
+        return
+
+    if G.is_multigraph() and not directed:
+        visited = set()
+        for u, Gu in G.adj.items():
+            multiplicity = ((v, len(Guv)) for v, Guv in Gu.items() if v in visited)
+            yield from ([u, v] for v, m in multiplicity if m > 1)
+            visited.add(u)
+
+    # explicitly filter out loops; implicitly filter out parallel edges
+    if directed:
+        G = nx.DiGraph((u, v) for u, Gu in G.adj.items() for v in Gu if v != u)
+    else:
+        G = nx.Graph((u, v) for u, Gu in G.adj.items() for v in Gu if v != u)
+
+    # this case is not strictly necessary but improves performance
+    if length_bound is not None and length_bound == 2:
+        if directed:
+            visited = set()
+            for u, Gu in G.adj.items():
+                yield from (
+                    [v, u] for v in visited.intersection(Gu) if G.has_edge(v, u)
+                )
+                visited.add(u)
+        return
+
+    if directed:
+        yield from _directed_cycle_search(G, length_bound)
+    else:
+        yield from _undirected_cycle_search(G, length_bound)
+
+
+def _directed_cycle_search(G, length_bound):
+    """A dispatch function for `simple_cycles` for directed graphs.
+
+    We generate all cycles of G through binary partition.
+
+        1. Pick a node v in G which belongs to at least one cycle
+            a. Generate all cycles of G which contain the node v.
+            b. Recursively generate all cycles of G \\ v.
+
+    This is accomplished through the following:
+
+        1. Compute the strongly connected components SCC of G.
+        2. Select and remove a biconnected component C from BCC.  Select a
+           non-tree edge (u, v) of a depth-first search of G[C].
+        3. For each simple cycle P containing v in G[C], yield P.
+        4. Add the biconnected components of G[C \\ v] to BCC.
+
+    If the parameter length_bound is not None, then step 3 will be limited to
+    simple cycles of length at most length_bound.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    length_bound : int or None
+       If length_bound is an int, generate all simple cycles of G with length at most length_bound.
+       Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+    """
+
+    scc = nx.strongly_connected_components
+    components = [c for c in scc(G) if len(c) >= 2]
+    while components:
+        c = components.pop()
+        Gc = G.subgraph(c)
+        v = next(iter(c))
+        if length_bound is None:
+            yield from _johnson_cycle_search(Gc, [v])
+        else:
+            yield from _bounded_cycle_search(Gc, [v], length_bound)
+        # delete v after searching G, to make sure we can find v
+        G.remove_node(v)
+        components.extend(c for c in scc(Gc) if len(c) >= 2)
+
+
+def _undirected_cycle_search(G, length_bound):
+    """A dispatch function for `simple_cycles` for undirected graphs.
+
+    We generate all cycles of G through binary partition.
+
+        1. Pick an edge (u, v) in G which belongs to at least one cycle
+            a. Generate all cycles of G which contain the edge (u, v)
+            b. Recursively generate all cycles of G \\ (u, v)
+
+    This is accomplished through the following:
+
+        1. Compute the biconnected components BCC of G.
+        2. Select and remove a biconnected component C from BCC.  Select a
+           non-tree edge (u, v) of a depth-first search of G[C].
+        3. For each (v -> u) path P remaining in G[C] \\ (u, v), yield P.
+        4. Add the biconnected components of G[C] \\ (u, v) to BCC.
+
+    If the parameter length_bound is not None, then step 3 will be limited to simple paths
+    of length at most length_bound.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph
+
+    length_bound : int or None
+       If length_bound is an int, generate all simple cycles of G with length at most length_bound.
+       Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+    """
+
+    bcc = nx.biconnected_components
+    components = [c for c in bcc(G) if len(c) >= 3]
+    while components:
+        c = components.pop()
+        Gc = G.subgraph(c)
+        uv = list(next(iter(Gc.edges)))
+        G.remove_edge(*uv)
+        # delete (u, v) before searching G, to avoid fake 3-cycles [u, v, u]
+        if length_bound is None:
+            yield from _johnson_cycle_search(Gc, uv)
+        else:
+            yield from _bounded_cycle_search(Gc, uv, length_bound)
+        components.extend(c for c in bcc(Gc) if len(c) >= 3)
+
+
+class _NeighborhoodCache(dict):
+    """Very lightweight graph wrapper which caches neighborhoods as list.
+
+    This dict subclass uses the __missing__ functionality to query graphs for
+    their neighborhoods, and store the result as a list.  This is used to avoid
+    the performance penalty incurred by subgraph views.
+    """
+
+    def __init__(self, G):
+        self.G = G
+
+    def __missing__(self, v):
+        Gv = self[v] = list(self.G[v])
+        return Gv
+
+
+def _johnson_cycle_search(G, path):
+    """The main loop of the cycle-enumeration algorithm of Johnson.
+
+    Parameters
+    ----------
+    G : NetworkX Graph or DiGraph
+       A graph
+
+    path : list
+       A cycle prefix.  All cycles generated will begin with this prefix.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    References
+    ----------
+        .. [1] Finding all the elementary circuits of a directed graph.
+       D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
+       https://doi.org/10.1137/0204007
+
+    """
+
+    G = _NeighborhoodCache(G)
+    blocked = set(path)
+    B = defaultdict(set)  # graph portions that yield no elementary circuit
+    start = path[0]
+    stack = [iter(G[path[-1]])]
+    closed = [False]
+    while stack:
+        nbrs = stack[-1]
+        for w in nbrs:
+            if w == start:
+                yield path[:]
+                closed[-1] = True
+            elif w not in blocked:
+                path.append(w)
+                closed.append(False)
+                stack.append(iter(G[w]))
+                blocked.add(w)
+                break
+        else:  # no more nbrs
+            stack.pop()
+            v = path.pop()
+            if closed.pop():
+                if closed:
+                    closed[-1] = True
+                unblock_stack = {v}
+                while unblock_stack:
+                    u = unblock_stack.pop()
+                    if u in blocked:
+                        blocked.remove(u)
+                        unblock_stack.update(B[u])
+                        B[u].clear()
+            else:
+                for w in G[v]:
+                    B[w].add(v)
+
+
+def _bounded_cycle_search(G, path, length_bound):
+    """The main loop of the cycle-enumeration algorithm of Gupta and Suzumura.
+
+    Parameters
+    ----------
+    G : NetworkX Graph or DiGraph
+       A graph
+
+    path : list
+       A cycle prefix.  All cycles generated will begin with this prefix.
+
+    length_bound: int
+        A length bound.  All cycles generated will have length at most length_bound.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    References
+    ----------
+    .. [1] Finding All Bounded-Length Simple Cycles in a Directed Graph
+       A. Gupta and T. Suzumura https://arxiv.org/abs/2105.10094
+
+    """
+    G = _NeighborhoodCache(G)
+    lock = {v: 0 for v in path}
+    B = defaultdict(set)
+    start = path[0]
+    stack = [iter(G[path[-1]])]
+    blen = [length_bound]
+    while stack:
+        nbrs = stack[-1]
+        for w in nbrs:
+            if w == start:
+                yield path[:]
+                blen[-1] = 1
+            elif len(path) < lock.get(w, length_bound):
+                path.append(w)
+                blen.append(length_bound)
+                lock[w] = len(path)
+                stack.append(iter(G[w]))
+                break
+        else:
+            stack.pop()
+            v = path.pop()
+            bl = blen.pop()
+            if blen:
+                blen[-1] = min(blen[-1], bl)
+            if bl < length_bound:
+                relax_stack = [(bl, v)]
+                while relax_stack:
+                    bl, u = relax_stack.pop()
+                    if lock.get(u, length_bound) < length_bound - bl + 1:
+                        lock[u] = length_bound - bl + 1
+                        relax_stack.extend((bl + 1, w) for w in B[u].difference(path))
+            else:
+                for w in G[v]:
+                    B[w].add(v)
+
+
+@nx._dispatch
+def chordless_cycles(G, length_bound=None):
+    """Find simple chordless cycles of a graph.
+
+    A `simple cycle` is a closed path where no node appears twice.  In a simple
+    cycle, a `chord` is an additional edge between two nodes in the cycle.  A
+    `chordless cycle` is a simple cycle without chords.  Said differently, a
+    chordless cycle is a cycle C in a graph G where the number of edges in the
+    induced graph G[C] is equal to the length of `C`.
+
+    Note that some care must be taken in the case that G is not a simple graph
+    nor a simple digraph.  Some authors limit the definition of chordless cycles
+    to have a prescribed minimum length; we do not.
+
+        1. We interpret self-loops to be chordless cycles, except in multigraphs
+           with multiple loops in parallel.  Likewise, in a chordless cycle of
+           length greater than 1, there can be no nodes with self-loops.
+
+        2. We interpret directed two-cycles to be chordless cycles, except in
+           multi-digraphs when any edge in a two-cycle has a parallel copy.
+
+        3. We interpret parallel pairs of undirected edges as two-cycles, except
+           when a third (or more) parallel edge exists between the two nodes.
+
+        4. Generalizing the above, edges with parallel clones may not occur in
+           chordless cycles.
+
+    In a directed graph, two chordless cycles are distinct if they are not
+    cyclic permutations of each other.  In an undirected graph, two chordless
+    cycles are distinct if they are not cyclic permutations of each other nor of
+    the other's reversal.
+
+    Optionally, the cycles are bounded in length.
+
+    We use an algorithm strongly inspired by that of Dias et al [1]_.  It has
+    been modified in the following ways:
+
+        1. Recursion is avoided, per Python's limitations
+
+        2. The labeling function is not necessary, because the starting paths
+            are chosen (and deleted from the host graph) to prevent multiple
+            occurrences of the same path
+
+        3. The search is optionally bounded at a specified length
+
+        4. Support for directed graphs is provided by extending cycles along
+            forward edges, and blocking nodes along forward and reverse edges
+
+        5. Support for multigraphs is provided by omitting digons from the set
+            of forward edges
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    length_bound : int or None, optional (default=None)
+       If length_bound is an int, generate all simple cycles of G with length at
+       most length_bound.  Otherwise, generate all simple cycles of G.
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    Examples
+    --------
+    >>> sorted(list(nx.chordless_cycles(nx.complete_graph(4))))
+    [[1, 0, 2], [1, 0, 3], [2, 0, 3], [2, 1, 3]]
+
+    Notes
+    -----
+    When length_bound is None, and the graph is simple, the time complexity is
+    $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$ chordless cycles.
+
+    Raises
+    ------
+    ValueError
+        when length_bound < 0.
+
+    References
+    ----------
+    .. [1] Efficient enumeration of chordless cycles
+       E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi
+       https://arxiv.org/abs/1309.1051
+
+    See Also
+    --------
+    simple_cycles
+    """
+
+    if length_bound is not None:
+        if length_bound == 0:
+            return
+        elif length_bound < 0:
+            raise ValueError("length bound must be non-negative")
+
+    directed = G.is_directed()
+    multigraph = G.is_multigraph()
+
+    if multigraph:
+        yield from ([v] for v, Gv in G.adj.items() if len(Gv.get(v, ())) == 1)
+    else:
+        yield from ([v] for v, Gv in G.adj.items() if v in Gv)
+
+    if length_bound is not None and length_bound == 1:
+        return
+
+    # Nodes with loops cannot belong to longer cycles.  Let's delete them here.
+    # also, we implicitly reduce the multiplicity of edges down to 1 in the case
+    # of multiedges.
+    if directed:
+        F = nx.DiGraph((u, v) for u, Gu in G.adj.items() if u not in Gu for v in Gu)
+        B = F.to_undirected(as_view=False)
+    else:
+        F = nx.Graph((u, v) for u, Gu in G.adj.items() if u not in Gu for v in Gu)
+        B = None
+
+    # If we're given a multigraph, we have a few cases to consider with parallel
+    # edges.
+    #
+    # 1. If we have 2 or more edges in parallel between the nodes (u, v), we
+    #    must not construct longer cycles along (u, v).
+    # 2. If G is not directed, then a pair of parallel edges between (u, v) is a
+    #    chordless cycle unless there exists a third (or more) parallel edge.
+    # 3. If G is directed, then parallel edges do not form cycles, but do
+    #    preclude back-edges from forming cycles (handled in the next section),
+    #    Thus, if an edge (u, v) is duplicated and the reverse (v, u) is also
+    #    present, then we remove both from F.
+    #
+    # In directed graphs, we need to consider both directions that edges can
+    # take, so iterate over all edges (u, v) and possibly (v, u).  In undirected
+    # graphs, we need to be a little careful to only consider every edge once,
+    # so we use a "visited" set to emulate node-order comparisons.
+
+    if multigraph:
+        if not directed:
+            B = F.copy()
+            visited = set()
+        for u, Gu in G.adj.items():
+            if directed:
+                multiplicity = ((v, len(Guv)) for v, Guv in Gu.items())
+                for v, m in multiplicity:
+                    if m > 1:
+                        F.remove_edges_from(((u, v), (v, u)))
+            else:
+                multiplicity = ((v, len(Guv)) for v, Guv in Gu.items() if v in visited)
+                for v, m in multiplicity:
+                    if m == 2:
+                        yield [u, v]
+                    if m > 1:
+                        F.remove_edge(u, v)
+                visited.add(u)
+
+    # If we're given a directed graphs, we need to think about digons.  If we
+    # have two edges (u, v) and (v, u), then that's a two-cycle.  If either edge
+    # was duplicated above, then we removed both from F.  So, any digons we find
+    # here are chordless.  After finding digons, we remove their edges from F
+    # to avoid traversing them in the search for chordless cycles.
+    if directed:
+        for u, Fu in F.adj.items():
+            digons = [[u, v] for v in Fu if F.has_edge(v, u)]
+            yield from digons
+            F.remove_edges_from(digons)
+            F.remove_edges_from(e[::-1] for e in digons)
+
+    if length_bound is not None and length_bound == 2:
+        return
+
+    # Now, we prepare to search for cycles.  We have removed all cycles of
+    # lengths 1 and 2, so F is a simple graph or simple digraph.  We repeatedly
+    # separate digraphs into their strongly connected components, and undirected
+    # graphs into their biconnected components.  For each component, we pick a
+    # node v, search for chordless cycles based at each "stem" (u, v, w), and
+    # then remove v from that component before separating the graph again.
+    if directed:
+        separate = nx.strongly_connected_components
+
+        # Directed stems look like (u -> v -> w), so we use the product of
+        # predecessors of v with successors of v.
+        def stems(C, v):
+            for u, w in product(C.pred[v], C.succ[v]):
+                if not G.has_edge(u, w):  # omit stems with acyclic chords
+                    yield [u, v, w], F.has_edge(w, u)
+
+    else:
+        separate = nx.biconnected_components
+
+        # Undirected stems look like (u ~ v ~ w), but we must not also search
+        # (w ~ v ~ u), so we use combinations of v's neighbors of length 2.
+        def stems(C, v):
+            yield from (([u, v, w], F.has_edge(w, u)) for u, w in combinations(C[v], 2))
+
+    components = [c for c in separate(F) if len(c) > 2]
+    while components:
+        c = components.pop()
+        v = next(iter(c))
+        Fc = F.subgraph(c)
+        Fcc = Bcc = None
+        for S, is_triangle in stems(Fc, v):
+            if is_triangle:
+                yield S
+            else:
+                if Fcc is None:
+                    Fcc = _NeighborhoodCache(Fc)
+                    Bcc = Fcc if B is None else _NeighborhoodCache(B.subgraph(c))
+                yield from _chordless_cycle_search(Fcc, Bcc, S, length_bound)
+
+        components.extend(c for c in separate(F.subgraph(c - {v})) if len(c) > 2)
+
+
+def _chordless_cycle_search(F, B, path, length_bound):
+    """The main loop for chordless cycle enumeration.
+
+    This algorithm is strongly inspired by that of Dias et al [1]_.  It has been
+    modified in the following ways:
+
+        1. Recursion is avoided, per Python's limitations
+
+        2. The labeling function is not necessary, because the starting paths
+            are chosen (and deleted from the host graph) to prevent multiple
+            occurrences of the same path
+
+        3. The search is optionally bounded at a specified length
+
+        4. Support for directed graphs is provided by extending cycles along
+            forward edges, and blocking nodes along forward and reverse edges
+
+        5. Support for multigraphs is provided by omitting digons from the set
+            of forward edges
+
+    Parameters
+    ----------
+    F : _NeighborhoodCache
+       A graph of forward edges to follow in constructing cycles
+
+    B : _NeighborhoodCache
+       A graph of blocking edges to prevent the production of chordless cycles
+
+    path : list
+       A cycle prefix.  All cycles generated will begin with this prefix.
+
+    length_bound : int
+       A length bound.  All cycles generated will have length at most length_bound.
+
+
+    Yields
+    ------
+    list of nodes
+       Each cycle is represented by a list of nodes along the cycle.
+
+    References
+    ----------
+    .. [1] Efficient enumeration of chordless cycles
+       E. Dias and D. Castonguay and H. Longo and W.A.R. Jradi
+       https://arxiv.org/abs/1309.1051
+
+    """
+    blocked = defaultdict(int)
+    target = path[0]
+    blocked[path[1]] = 1
+    for w in path[1:]:
+        for v in B[w]:
+            blocked[v] += 1
+
+    stack = [iter(F[path[2]])]
+    while stack:
+        nbrs = stack[-1]
+        for w in nbrs:
+            if blocked[w] == 1 and (length_bound is None or len(path) < length_bound):
+                Fw = F[w]
+                if target in Fw:
+                    yield path + [w]
+                else:
+                    Bw = B[w]
+                    if target in Bw:
+                        continue
+                    for v in Bw:
+                        blocked[v] += 1
+                    path.append(w)
+                    stack.append(iter(Fw))
+                    break
+        else:
+            stack.pop()
+            for v in B[path.pop()]:
+                blocked[v] -= 1
+
+
+@not_implemented_for("undirected")
+@nx._dispatch
+def recursive_simple_cycles(G):
+    """Find simple cycles (elementary circuits) of a directed graph.
+
+    A `simple cycle`, or `elementary circuit`, is a closed path where
+    no node appears twice. Two elementary circuits are distinct if they
+    are not cyclic permutations of each other.
+
+    This version uses a recursive algorithm to build a list of cycles.
+    You should probably use the iterator version called simple_cycles().
+    Warning: This recursive version uses lots of RAM!
+    It appears in NetworkX for pedagogical value.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph
+
+    Returns
+    -------
+    A list of cycles, where each cycle is represented by a list of nodes
+    along the cycle.
+
+    Example:
+
+    >>> edges = [(0, 0), (0, 1), (0, 2), (1, 2), (2, 0), (2, 1), (2, 2)]
+    >>> G = nx.DiGraph(edges)
+    >>> nx.recursive_simple_cycles(G)
+    [[0], [2], [0, 1, 2], [0, 2], [1, 2]]
+
+    Notes
+    -----
+    The implementation follows pp. 79-80 in [1]_.
+
+    The time complexity is $O((n+e)(c+1))$ for $n$ nodes, $e$ edges and $c$
+    elementary circuits.
+
+    References
+    ----------
+    .. [1] Finding all the elementary circuits of a directed graph.
+       D. B. Johnson, SIAM Journal on Computing 4, no. 1, 77-84, 1975.
+       https://doi.org/10.1137/0204007
+
+    See Also
+    --------
+    simple_cycles, cycle_basis
+    """
+
+    # Jon Olav Vik, 2010-08-09
+    def _unblock(thisnode):
+        """Recursively unblock and remove nodes from B[thisnode]."""
+        if blocked[thisnode]:
+            blocked[thisnode] = False
+            while B[thisnode]:
+                _unblock(B[thisnode].pop())
+
+    def circuit(thisnode, startnode, component):
+        closed = False  # set to True if elementary path is closed
+        path.append(thisnode)
+        blocked[thisnode] = True
+        for nextnode in component[thisnode]:  # direct successors of thisnode
+            if nextnode == startnode:
+                result.append(path[:])
+                closed = True
+            elif not blocked[nextnode]:
+                if circuit(nextnode, startnode, component):
+                    closed = True
+        if closed:
+            _unblock(thisnode)
+        else:
+            for nextnode in component[thisnode]:
+                if thisnode not in B[nextnode]:  # TODO: use set for speedup?
+                    B[nextnode].append(thisnode)
+        path.pop()  # remove thisnode from path
+        return closed
+
+    path = []  # stack of nodes in current path
+    blocked = defaultdict(bool)  # vertex: blocked from search?
+    B = defaultdict(list)  # graph portions that yield no elementary circuit
+    result = []  # list to accumulate the circuits found
+
+    # Johnson's algorithm exclude self cycle edges like (v, v)
+    # To be backward compatible, we record those cycles in advance
+    # and then remove from subG
+    for v in G:
+        if G.has_edge(v, v):
+            result.append([v])
+            G.remove_edge(v, v)
+
+    # Johnson's algorithm requires some ordering of the nodes.
+    # They might not be sortable so we assign an arbitrary ordering.
+    ordering = dict(zip(G, range(len(G))))
+    for s in ordering:
+        # Build the subgraph induced by s and following nodes in the ordering
+        subgraph = G.subgraph(node for node in G if ordering[node] >= ordering[s])
+        # Find the strongly connected component in the subgraph
+        # that contains the least node according to the ordering
+        strongcomp = nx.strongly_connected_components(subgraph)
+        mincomp = min(strongcomp, key=lambda ns: min(ordering[n] for n in ns))
+        component = G.subgraph(mincomp)
+        if len(component) > 1:
+            # smallest node in the component according to the ordering
+            startnode = min(component, key=ordering.__getitem__)
+            for node in component:
+                blocked[node] = False
+                B[node][:] = []
+            dummy = circuit(startnode, startnode, component)
+    return result
+
+
+@nx._dispatch
+def find_cycle(G, source=None, orientation=None):
+    """Returns a cycle found via depth-first traversal.
+
+    The cycle is a list of edges indicating the cyclic path.
+    Orientation of directed edges is controlled by `orientation`.
+
+    Parameters
+    ----------
+    G : graph
+        A directed/undirected graph/multigraph.
+
+    source : node, list of nodes
+        The node from which the traversal begins. If None, then a source
+        is chosen arbitrarily and repeatedly until all edges from each node in
+        the graph are searched.
+
+    orientation : None | 'original' | 'reverse' | 'ignore' (default: None)
+        For directed graphs and directed multigraphs, edge traversals need not
+        respect the original orientation of the edges.
+        When set to 'reverse' every edge is traversed in the reverse direction.
+        When set to 'ignore', every edge is treated as undirected.
+        When set to 'original', every edge is treated as directed.
+        In all three cases, the yielded edge tuples add a last entry to
+        indicate the direction in which that edge was traversed.
+        If orientation is None, the yielded edge has no direction indicated.
+        The direction is respected, but not reported.
+
+    Returns
+    -------
+    edges : directed edges
+        A list of directed edges indicating the path taken for the loop.
+        If no cycle is found, then an exception is raised.
+        For graphs, an edge is of the form `(u, v)` where `u` and `v`
+        are the tail and head of the edge as determined by the traversal.
+        For multigraphs, an edge is of the form `(u, v, key)`, where `key` is
+        the key of the edge. When the graph is directed, then `u` and `v`
+        are always in the order of the actual directed edge.
+        If orientation is not None then the edge tuple is extended to include
+        the direction of traversal ('forward' or 'reverse') on that edge.
+
+    Raises
+    ------
+    NetworkXNoCycle
+        If no cycle was found.
+
+    Examples
+    --------
+    In this example, we construct a DAG and find, in the first call, that there
+    are no directed cycles, and so an exception is raised. In the second call,
+    we ignore edge orientations and find that there is an undirected cycle.
+    Note that the second call finds a directed cycle while effectively
+    traversing an undirected graph, and so, we found an "undirected cycle".
+    This means that this DAG structure does not form a directed tree (which
+    is also known as a polytree).
+
+    >>> G = nx.DiGraph([(0, 1), (0, 2), (1, 2)])
+    >>> nx.find_cycle(G, orientation="original")
+    Traceback (most recent call last):
+        ...
+    networkx.exception.NetworkXNoCycle: No cycle found.
+    >>> list(nx.find_cycle(G, orientation="ignore"))
+    [(0, 1, 'forward'), (1, 2, 'forward'), (0, 2, 'reverse')]
+
+    See Also
+    --------
+    simple_cycles
+    """
+    if not G.is_directed() or orientation in (None, "original"):
+
+        def tailhead(edge):
+            return edge[:2]
+
+    elif orientation == "reverse":
+
+        def tailhead(edge):
+            return edge[1], edge[0]
+
+    elif orientation == "ignore":
+
+        def tailhead(edge):
+            if edge[-1] == "reverse":
+                return edge[1], edge[0]
+            return edge[:2]
+
+    explored = set()
+    cycle = []
+    final_node = None
+    for start_node in G.nbunch_iter(source):
+        if start_node in explored:
+            # No loop is possible.
+            continue
+
+        edges = []
+        # All nodes seen in this iteration of edge_dfs
+        seen = {start_node}
+        # Nodes in active path.
+        active_nodes = {start_node}
+        previous_head = None
+
+        for edge in nx.edge_dfs(G, start_node, orientation):
+            # Determine if this edge is a continuation of the active path.
+            tail, head = tailhead(edge)
+            if head in explored:
+                # Then we've already explored it. No loop is possible.
+                continue
+            if previous_head is not None and tail != previous_head:
+                # This edge results from backtracking.
+                # Pop until we get a node whose head equals the current tail.
+                # So for example, we might have:
+                #  (0, 1), (1, 2), (2, 3), (1, 4)
+                # which must become:
+                #  (0, 1), (1, 4)
+                while True:
+                    try:
+                        popped_edge = edges.pop()
+                    except IndexError:
+                        edges = []
+                        active_nodes = {tail}
+                        break
+                    else:
+                        popped_head = tailhead(popped_edge)[1]
+                        active_nodes.remove(popped_head)
+
+                    if edges:
+                        last_head = tailhead(edges[-1])[1]
+                        if tail == last_head:
+                            break
+            edges.append(edge)
+
+            if head in active_nodes:
+                # We have a loop!
+                cycle.extend(edges)
+                final_node = head
+                break
+            else:
+                seen.add(head)
+                active_nodes.add(head)
+                previous_head = head
+
+        if cycle:
+            break
+        else:
+            explored.update(seen)
+
+    else:
+        assert len(cycle) == 0
+        raise nx.exception.NetworkXNoCycle("No cycle found.")
+
+    # We now have a list of edges which ends on a cycle.
+    # So we need to remove from the beginning edges that are not relevant.
+
+    for i, edge in enumerate(cycle):
+        tail, head = tailhead(edge)
+        if tail == final_node:
+            break
+
+    return cycle[i:]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch(edge_attrs="weight")
+def minimum_cycle_basis(G, weight=None):
+    """Returns a minimum weight cycle basis for G
+
+    Minimum weight means a cycle basis for which the total weight
+    (length for unweighted graphs) of all the cycles is minimum.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+    weight: string
+        name of the edge attribute to use for edge weights
+
+    Returns
+    -------
+    A list of cycle lists.  Each cycle list is a list of nodes
+    which forms a cycle (loop) in G. Note that the nodes are not
+    necessarily returned in a order by which they appear in the cycle
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> nx.add_cycle(G, [0, 1, 2, 3])
+    >>> nx.add_cycle(G, [0, 3, 4, 5])
+    >>> nx.minimum_cycle_basis(G)
+    [[5, 4, 3, 0], [3, 2, 1, 0]]
+
+    References:
+        [1] Kavitha, Telikepalli, et al. "An O(m^2n) Algorithm for
+        Minimum Cycle Basis of Graphs."
+        http://link.springer.com/article/10.1007/s00453-007-9064-z
+        [2] de Pina, J. 1995. Applications of shortest path methods.
+        Ph.D. thesis, University of Amsterdam, Netherlands
+
+    See Also
+    --------
+    simple_cycles, cycle_basis
+    """
+    # We first split the graph in connected subgraphs
+    return sum(
+        (_min_cycle_basis(G.subgraph(c), weight) for c in nx.connected_components(G)),
+        [],
+    )
+
+
+def _min_cycle_basis(G, weight):
+    cb = []
+    # We  extract the edges not in a spanning tree. We do not really need a
+    # *minimum* spanning tree. That is why we call the next function with
+    # weight=None. Depending on implementation, it may be faster as well
+    tree_edges = list(nx.minimum_spanning_edges(G, weight=None, data=False))
+    chords = G.edges - tree_edges - {(v, u) for u, v in tree_edges}
+
+    # We maintain a set of vectors orthogonal to sofar found cycles
+    set_orth = [{edge} for edge in chords]
+    while set_orth:
+        base = set_orth.pop()
+        # kth cycle is "parallel" to kth vector in set_orth
+        cycle_edges = _min_cycle(G, base, weight)
+        cb.append([v for u, v in cycle_edges])
+
+        # now update set_orth so that k+1,k+2... th elements are
+        # orthogonal to the newly found cycle, as per [p. 336, 1]
+        set_orth = [
+            (
+                {e for e in orth if e not in base if e[::-1] not in base}
+                | {e for e in base if e not in orth if e[::-1] not in orth}
+            )
+            if sum((e in orth or e[::-1] in orth) for e in cycle_edges) % 2
+            else orth
+            for orth in set_orth
+        ]
+    return cb
+
+
+def _min_cycle(G, orth, weight):
+    """
+    Computes the minimum weight cycle in G,
+    orthogonal to the vector orth as per [p. 338, 1]
+    Use (u, 1) to indicate the lifted copy of u (denoted u' in paper).
+    """
+    Gi = nx.Graph()
+
+    # Add 2 copies of each edge in G to Gi.
+    # If edge is in orth, add cross edge; otherwise in-plane edge
+    for u, v, wt in G.edges(data=weight, default=1):
+        if (u, v) in orth or (v, u) in orth:
+            Gi.add_edges_from([(u, (v, 1)), ((u, 1), v)], Gi_weight=wt)
+        else:
+            Gi.add_edges_from([(u, v), ((u, 1), (v, 1))], Gi_weight=wt)
+
+    # find the shortest length in Gi between n and (n, 1) for each n
+    # Note: Use "Gi_weight" for name of weight attribute
+    spl = nx.shortest_path_length
+    lift = {n: spl(Gi, source=n, target=(n, 1), weight="Gi_weight") for n in G}
+
+    # Now compute that short path in Gi, which translates to a cycle in G
+    start = min(lift, key=lift.get)
+    end = (start, 1)
+    min_path_i = nx.shortest_path(Gi, source=start, target=end, weight="Gi_weight")
+
+    # Now we obtain the actual path, re-map nodes in Gi to those in G
+    min_path = [n if n in G else n[0] for n in min_path_i]
+
+    # Now remove the edges that occur two times
+    # two passes: flag which edges get kept, then build it
+    edgelist = list(pairwise(min_path))
+    edgeset = set()
+    for e in edgelist:
+        if e in edgeset:
+            edgeset.remove(e)
+        elif e[::-1] in edgeset:
+            edgeset.remove(e[::-1])
+        else:
+            edgeset.add(e)
+
+    min_edgelist = []
+    for e in edgelist:
+        if e in edgeset:
+            min_edgelist.append(e)
+            edgeset.remove(e)
+        elif e[::-1] in edgeset:
+            min_edgelist.append(e[::-1])
+            edgeset.remove(e[::-1])
+
+    return min_edgelist
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def girth(G):
+    """Returns the girth of the graph.
+
+    The girth of a graph is the length of its shortest cycle, or infinity if
+    the graph is acyclic. The algorithm follows the description given on the
+    Wikipedia page [1]_, and runs in time O(mn) on a graph with m edges and n
+    nodes.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    Returns
+    -------
+    int or math.inf
+
+    Examples
+    --------
+    All examples below (except P_5) can easily be checked using Wikipedia,
+    which has a page for each of these famous graphs.
+
+    >>> nx.girth(nx.chvatal_graph())
+    4
+    >>> nx.girth(nx.tutte_graph())
+    4
+    >>> nx.girth(nx.petersen_graph())
+    5
+    >>> nx.girth(nx.heawood_graph())
+    6
+    >>> nx.girth(nx.pappus_graph())
+    6
+    >>> nx.girth(nx.path_graph(5))
+    inf
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Girth_(graph_theory)
+
+    """
+    girth = depth_limit = inf
+    tree_edge = nx.algorithms.traversal.breadth_first_search.TREE_EDGE
+    level_edge = nx.algorithms.traversal.breadth_first_search.LEVEL_EDGE
+    for n in G:
+        # run a BFS from source n, keeping track of distances; since we want
+        # the shortest cycle, no need to explore beyond the current minimum length
+        depth = {n: 0}
+        for u, v, label in nx.bfs_labeled_edges(G, n):
+            du = depth[u]
+            if du > depth_limit:
+                break
+            if label is tree_edge:
+                depth[v] = du + 1
+            else:
+                # if (u, v) is a level edge, the length is du + du + 1 (odd)
+                # otherwise, it's a forward edge; length is du + (du + 1) + 1 (even)
+                delta = label is level_edge
+                length = du + du + 2 - delta
+                if length < girth:
+                    girth = length
+                    depth_limit = du - delta
+
+    return girth

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/flow/capacityscaling.py

@@ -0,0 +1,405 @@
+"""
+Capacity scaling minimum cost flow algorithm.
+"""
+
+__all__ = ["capacity_scaling"]
+
+from itertools import chain
+from math import log
+
+import networkx as nx
+
+from ...utils import BinaryHeap, arbitrary_element, not_implemented_for
+
+
+def _detect_unboundedness(R):
+    """Detect infinite-capacity negative cycles."""
+    G = nx.DiGraph()
+    G.add_nodes_from(R)
+
+    # Value simulating infinity.
+    inf = R.graph["inf"]
+    # True infinity.
+    f_inf = float("inf")
+    for u in R:
+        for v, e in R[u].items():
+            # Compute the minimum weight of infinite-capacity (u, v) edges.
+            w = f_inf
+            for k, e in e.items():
+                if e["capacity"] == inf:
+                    w = min(w, e["weight"])
+            if w != f_inf:
+                G.add_edge(u, v, weight=w)
+
+    if nx.negative_edge_cycle(G):
+        raise nx.NetworkXUnbounded(
+            "Negative cost cycle of infinite capacity found. "
+            "Min cost flow may be unbounded below."
+        )
+
+
+@not_implemented_for("undirected")
+def _build_residual_network(G, demand, capacity, weight):
+    """Build a residual network and initialize a zero flow."""
+    if sum(G.nodes[u].get(demand, 0) for u in G) != 0:
+        raise nx.NetworkXUnfeasible("Sum of the demands should be 0.")
+
+    R = nx.MultiDiGraph()
+    R.add_nodes_from(
+        (u, {"excess": -G.nodes[u].get(demand, 0), "potential": 0}) for u in G
+    )
+
+    inf = float("inf")
+    # Detect selfloops with infinite capacities and negative weights.
+    for u, v, e in nx.selfloop_edges(G, data=True):
+        if e.get(weight, 0) < 0 and e.get(capacity, inf) == inf:
+            raise nx.NetworkXUnbounded(
+                "Negative cost cycle of infinite capacity found. "
+                "Min cost flow may be unbounded below."
+            )
+
+    # Extract edges with positive capacities. Self loops excluded.
+    if G.is_multigraph():
+        edge_list = [
+            (u, v, k, e)
+            for u, v, k, e in G.edges(data=True, keys=True)
+            if u != v and e.get(capacity, inf) > 0
+        ]
+    else:
+        edge_list = [
+            (u, v, 0, e)
+            for u, v, e in G.edges(data=True)
+            if u != v and e.get(capacity, inf) > 0
+        ]
+    # Simulate infinity with the larger of the sum of absolute node imbalances
+    # the sum of finite edge capacities or any positive value if both sums are
+    # zero. This allows the infinite-capacity edges to be distinguished for
+    # unboundedness detection and directly participate in residual capacity
+    # calculation.
+    inf = (
+        max(
+            sum(abs(R.nodes[u]["excess"]) for u in R),
+            2
+            * sum(
+                e[capacity]
+                for u, v, k, e in edge_list
+                if capacity in e and e[capacity] != inf
+            ),
+        )
+        or 1
+    )
+    for u, v, k, e in edge_list:
+        r = min(e.get(capacity, inf), inf)
+        w = e.get(weight, 0)
+        # Add both (u, v) and (v, u) into the residual network marked with the
+        # original key. (key[1] == True) indicates the (u, v) is in the
+        # original network.
+        R.add_edge(u, v, key=(k, True), capacity=r, weight=w, flow=0)
+        R.add_edge(v, u, key=(k, False), capacity=0, weight=-w, flow=0)
+
+    # Record the value simulating infinity.
+    R.graph["inf"] = inf
+
+    _detect_unboundedness(R)
+
+    return R
+
+
+def _build_flow_dict(G, R, capacity, weight):
+    """Build a flow dictionary from a residual network."""
+    inf = float("inf")
+    flow_dict = {}
+    if G.is_multigraph():
+        for u in G:
+            flow_dict[u] = {}
+            for v, es in G[u].items():
+                flow_dict[u][v] = {
+                    # Always saturate negative selfloops.
+                    k: (
+                        0
+                        if (
+                            u != v or e.get(capacity, inf) <= 0 or e.get(weight, 0) >= 0
+                        )
+                        else e[capacity]
+                    )
+                    for k, e in es.items()
+                }
+            for v, es in R[u].items():
+                if v in flow_dict[u]:
+                    flow_dict[u][v].update(
+                        (k[0], e["flow"]) for k, e in es.items() if e["flow"] > 0
+                    )
+    else:
+        for u in G:
+            flow_dict[u] = {
+                # Always saturate negative selfloops.
+                v: (
+                    0
+                    if (u != v or e.get(capacity, inf) <= 0 or e.get(weight, 0) >= 0)
+                    else e[capacity]
+                )
+                for v, e in G[u].items()
+            }
+            flow_dict[u].update(
+                (v, e["flow"])
+                for v, es in R[u].items()
+                for e in es.values()
+                if e["flow"] > 0
+            )
+    return flow_dict
+
+
+@nx._dispatch(node_attrs="demand", edge_attrs={"capacity": float("inf"), "weight": 0})
+def capacity_scaling(
+    G, demand="demand", capacity="capacity", weight="weight", heap=BinaryHeap
+):
+    r"""Find a minimum cost flow satisfying all demands in digraph G.
+
+    This is a capacity scaling successive shortest augmenting path algorithm.
+
+    G is a digraph with edge costs and capacities and in which nodes
+    have demand, i.e., they want to send or receive some amount of
+    flow. A negative demand means that the node wants to send flow, a
+    positive demand means that the node want to receive flow. A flow on
+    the digraph G satisfies all demand if the net flow into each node
+    is equal to the demand of that node.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        DiGraph or MultiDiGraph on which a minimum cost flow satisfying all
+        demands is to be found.
+
+    demand : string
+        Nodes of the graph G are expected to have an attribute demand
+        that indicates how much flow a node wants to send (negative
+        demand) or receive (positive demand). Note that the sum of the
+        demands should be 0 otherwise the problem in not feasible. If
+        this attribute is not present, a node is considered to have 0
+        demand. Default value: 'demand'.
+
+    capacity : string
+        Edges of the graph G are expected to have an attribute capacity
+        that indicates how much flow the edge can support. If this
+        attribute is not present, the edge is considered to have
+        infinite capacity. Default value: 'capacity'.
+
+    weight : string
+        Edges of the graph G are expected to have an attribute weight
+        that indicates the cost incurred by sending one unit of flow on
+        that edge. If not present, the weight is considered to be 0.
+        Default value: 'weight'.
+
+    heap : class
+        Type of heap to be used in the algorithm. It should be a subclass of
+        :class:`MinHeap` or implement a compatible interface.
+
+        If a stock heap implementation is to be used, :class:`BinaryHeap` is
+        recommended over :class:`PairingHeap` for Python implementations without
+        optimized attribute accesses (e.g., CPython) despite a slower
+        asymptotic running time. For Python implementations with optimized
+        attribute accesses (e.g., PyPy), :class:`PairingHeap` provides better
+        performance. Default value: :class:`BinaryHeap`.
+
+    Returns
+    -------
+    flowCost : integer
+        Cost of a minimum cost flow satisfying all demands.
+
+    flowDict : dictionary
+        If G is a digraph, a dict-of-dicts keyed by nodes such that
+        flowDict[u][v] is the flow on edge (u, v).
+        If G is a MultiDiGraph, a dict-of-dicts-of-dicts keyed by nodes
+        so that flowDict[u][v][key] is the flow on edge (u, v, key).
+
+    Raises
+    ------
+    NetworkXError
+        This exception is raised if the input graph is not directed,
+        not connected.
+
+    NetworkXUnfeasible
+        This exception is raised in the following situations:
+
+            * The sum of the demands is not zero. Then, there is no
+              flow satisfying all demands.
+            * There is no flow satisfying all demand.
+
+    NetworkXUnbounded
+        This exception is raised if the digraph G has a cycle of
+        negative cost and infinite capacity. Then, the cost of a flow
+        satisfying all demands is unbounded below.
+
+    Notes
+    -----
+    This algorithm does not work if edge weights are floating-point numbers.
+
+    See also
+    --------
+    :meth:`network_simplex`
+
+    Examples
+    --------
+    A simple example of a min cost flow problem.
+
+    >>> G = nx.DiGraph()
+    >>> G.add_node("a", demand=-5)
+    >>> G.add_node("d", demand=5)
+    >>> G.add_edge("a", "b", weight=3, capacity=4)
+    >>> G.add_edge("a", "c", weight=6, capacity=10)
+    >>> G.add_edge("b", "d", weight=1, capacity=9)
+    >>> G.add_edge("c", "d", weight=2, capacity=5)
+    >>> flowCost, flowDict = nx.capacity_scaling(G)
+    >>> flowCost
+    24
+    >>> flowDict
+    {'a': {'b': 4, 'c': 1}, 'd': {}, 'b': {'d': 4}, 'c': {'d': 1}}
+
+    It is possible to change the name of the attributes used for the
+    algorithm.
+
+    >>> G = nx.DiGraph()
+    >>> G.add_node("p", spam=-4)
+    >>> G.add_node("q", spam=2)
+    >>> G.add_node("a", spam=-2)
+    >>> G.add_node("d", spam=-1)
+    >>> G.add_node("t", spam=2)
+    >>> G.add_node("w", spam=3)
+    >>> G.add_edge("p", "q", cost=7, vacancies=5)
+    >>> G.add_edge("p", "a", cost=1, vacancies=4)
+    >>> G.add_edge("q", "d", cost=2, vacancies=3)
+    >>> G.add_edge("t", "q", cost=1, vacancies=2)
+    >>> G.add_edge("a", "t", cost=2, vacancies=4)
+    >>> G.add_edge("d", "w", cost=3, vacancies=4)
+    >>> G.add_edge("t", "w", cost=4, vacancies=1)
+    >>> flowCost, flowDict = nx.capacity_scaling(
+    ...     G, demand="spam", capacity="vacancies", weight="cost"
+    ... )
+    >>> flowCost
+    37
+    >>> flowDict
+    {'p': {'q': 2, 'a': 2}, 'q': {'d': 1}, 'a': {'t': 4}, 'd': {'w': 2}, 't': {'q': 1, 'w': 1}, 'w': {}}
+    """
+    R = _build_residual_network(G, demand, capacity, weight)
+
+    inf = float("inf")
+    # Account cost of negative selfloops.
+    flow_cost = sum(
+        0
+        if e.get(capacity, inf) <= 0 or e.get(weight, 0) >= 0
+        else e[capacity] * e[weight]
+        for u, v, e in nx.selfloop_edges(G, data=True)
+    )
+
+    # Determine the maximum edge capacity.
+    wmax = max(chain([-inf], (e["capacity"] for u, v, e in R.edges(data=True))))
+    if wmax == -inf:
+        # Residual network has no edges.
+        return flow_cost, _build_flow_dict(G, R, capacity, weight)
+
+    R_nodes = R.nodes
+    R_succ = R.succ
+
+    delta = 2 ** int(log(wmax, 2))
+    while delta >= 1:
+        # Saturate Δ-residual edges with negative reduced costs to achieve
+        # Δ-optimality.
+        for u in R:
+            p_u = R_nodes[u]["potential"]
+            for v, es in R_succ[u].items():
+                for k, e in es.items():
+                    flow = e["capacity"] - e["flow"]
+                    if e["weight"] - p_u + R_nodes[v]["potential"] < 0:
+                        flow = e["capacity"] - e["flow"]
+                        if flow >= delta:
+                            e["flow"] += flow
+                            R_succ[v][u][(k[0], not k[1])]["flow"] -= flow
+                            R_nodes[u]["excess"] -= flow
+                            R_nodes[v]["excess"] += flow
+        # Determine the Δ-active nodes.
+        S = set()
+        T = set()
+        S_add = S.add
+        S_remove = S.remove
+        T_add = T.add
+        T_remove = T.remove
+        for u in R:
+            excess = R_nodes[u]["excess"]
+            if excess >= delta:
+                S_add(u)
+            elif excess <= -delta:
+                T_add(u)
+        # Repeatedly augment flow from S to T along shortest paths until
+        # Δ-feasibility is achieved.
+        while S and T:
+            s = arbitrary_element(S)
+            t = None
+            # Search for a shortest path in terms of reduce costs from s to
+            # any t in T in the Δ-residual network.
+            d = {}
+            pred = {s: None}
+            h = heap()
+            h_insert = h.insert
+            h_get = h.get
+            h_insert(s, 0)
+            while h:
+                u, d_u = h.pop()
+                d[u] = d_u
+                if u in T:
+                    # Path found.
+                    t = u
+                    break
+                p_u = R_nodes[u]["potential"]
+                for v, es in R_succ[u].items():
+                    if v in d:
+                        continue
+                    wmin = inf
+                    # Find the minimum-weighted (u, v) Δ-residual edge.
+                    for k, e in es.items():
+                        if e["capacity"] - e["flow"] >= delta:
+                            w = e["weight"]
+                            if w < wmin:
+                                wmin = w
+                                kmin = k
+                                emin = e
+                    if wmin == inf:
+                        continue
+                    # Update the distance label of v.
+                    d_v = d_u + wmin - p_u + R_nodes[v]["potential"]
+                    if h_insert(v, d_v):
+                        pred[v] = (u, kmin, emin)
+            if t is not None:
+                # Augment Δ units of flow from s to t.
+                while u != s:
+                    v = u
+                    u, k, e = pred[v]
+                    e["flow"] += delta
+                    R_succ[v][u][(k[0], not k[1])]["flow"] -= delta
+                # Account node excess and deficit.
+                R_nodes[s]["excess"] -= delta
+                R_nodes[t]["excess"] += delta
+                if R_nodes[s]["excess"] < delta:
+                    S_remove(s)
+                if R_nodes[t]["excess"] > -delta:
+                    T_remove(t)
+                # Update node potentials.
+                d_t = d[t]
+                for u, d_u in d.items():
+                    R_nodes[u]["potential"] -= d_u - d_t
+            else:
+                # Path not found.
+                S_remove(s)
+        delta //= 2
+
+    if any(R.nodes[u]["excess"] != 0 for u in R):
+        raise nx.NetworkXUnfeasible("No flow satisfying all demands.")
+
+    # Calculate the flow cost.
+    for u in R:
+        for v, es in R_succ[u].items():
+            for e in es.values():
+                flow = e["flow"]
+                if flow > 0:
+                    flow_cost += flow * e["weight"]
+
+    return flow_cost, _build_flow_dict(G, R, capacity, weight)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/flow/gomory_hu.py

@@ -0,0 +1,177 @@
+"""
+Gomory-Hu tree of undirected Graphs.
+"""
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+from .edmondskarp import edmonds_karp
+from .utils import build_residual_network
+
+default_flow_func = edmonds_karp
+
+__all__ = ["gomory_hu_tree"]
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs={"capacity": float("inf")})
+def gomory_hu_tree(G, capacity="capacity", flow_func=None):
+    r"""Returns the Gomory-Hu tree of an undirected graph G.
+
+    A Gomory-Hu tree of an undirected graph with capacities is a
+    weighted tree that represents the minimum s-t cuts for all s-t
+    pairs in the graph.
+
+    It only requires `n-1` minimum cut computations instead of the
+    obvious `n(n-1)/2`. The tree represents all s-t cuts as the
+    minimum cut value among any pair of nodes is the minimum edge
+    weight in the shortest path between the two nodes in the
+    Gomory-Hu tree.
+
+    The Gomory-Hu tree also has the property that removing the
+    edge with the minimum weight in the shortest path between
+    any two nodes leaves two connected components that form
+    a partition of the nodes in G that defines the minimum s-t
+    cut.
+
+    See Examples section below for details.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    capacity : string
+        Edges of the graph G are expected to have an attribute capacity
+        that indicates how much flow the edge can support. If this
+        attribute is not present, the edge is considered to have
+        infinite capacity. Default value: 'capacity'.
+
+    flow_func : function
+        Function to perform the underlying flow computations. Default value
+        :func:`edmonds_karp`. This function performs better in sparse graphs
+        with right tailed degree distributions.
+        :func:`shortest_augmenting_path` will perform better in denser
+        graphs.
+
+    Returns
+    -------
+    Tree : NetworkX graph
+        A NetworkX graph representing the Gomory-Hu tree of the input graph.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        Raised if the input graph is directed.
+
+    NetworkXError
+        Raised if the input graph is an empty Graph.
+
+    Examples
+    --------
+    >>> G = nx.karate_club_graph()
+    >>> nx.set_edge_attributes(G, 1, "capacity")
+    >>> T = nx.gomory_hu_tree(G)
+    >>> # The value of the minimum cut between any pair
+    ... # of nodes in G is the minimum edge weight in the
+    ... # shortest path between the two nodes in the
+    ... # Gomory-Hu tree.
+    ... def minimum_edge_weight_in_shortest_path(T, u, v):
+    ...     path = nx.shortest_path(T, u, v, weight="weight")
+    ...     return min((T[u][v]["weight"], (u, v)) for (u, v) in zip(path, path[1:]))
+    >>> u, v = 0, 33
+    >>> cut_value, edge = minimum_edge_weight_in_shortest_path(T, u, v)
+    >>> cut_value
+    10
+    >>> nx.minimum_cut_value(G, u, v)
+    10
+    >>> # The Gomory-Hu tree also has the property that removing the
+    ... # edge with the minimum weight in the shortest path between
+    ... # any two nodes leaves two connected components that form
+    ... # a partition of the nodes in G that defines the minimum s-t
+    ... # cut.
+    ... cut_value, edge = minimum_edge_weight_in_shortest_path(T, u, v)
+    >>> T.remove_edge(*edge)
+    >>> U, V = list(nx.connected_components(T))
+    >>> # Thus U and V form a partition that defines a minimum cut
+    ... # between u and v in G. You can compute the edge cut set,
+    ... # that is, the set of edges that if removed from G will
+    ... # disconnect u from v in G, with this information:
+    ... cutset = set()
+    >>> for x, nbrs in ((n, G[n]) for n in U):
+    ...     cutset.update((x, y) for y in nbrs if y in V)
+    >>> # Because we have set the capacities of all edges to 1
+    ... # the cutset contains ten edges
+    ... len(cutset)
+    10
+    >>> # You can use any maximum flow algorithm for the underlying
+    ... # flow computations using the argument flow_func
+    ... from networkx.algorithms import flow
+    >>> T = nx.gomory_hu_tree(G, flow_func=flow.boykov_kolmogorov)
+    >>> cut_value, edge = minimum_edge_weight_in_shortest_path(T, u, v)
+    >>> cut_value
+    10
+    >>> nx.minimum_cut_value(G, u, v, flow_func=flow.boykov_kolmogorov)
+    10
+
+    Notes
+    -----
+    This implementation is based on Gusfield approach [1]_ to compute
+    Gomory-Hu trees, which does not require node contractions and has
+    the same computational complexity than the original method.
+
+    See also
+    --------
+    :func:`minimum_cut`
+    :func:`maximum_flow`
+
+    References
+    ----------
+    .. [1] Gusfield D: Very simple methods for all pairs network flow analysis.
+           SIAM J Comput 19(1):143-155, 1990.
+
+    """
+    if flow_func is None:
+        flow_func = default_flow_func
+
+    if len(G) == 0:  # empty graph
+        msg = "Empty Graph does not have a Gomory-Hu tree representation"
+        raise nx.NetworkXError(msg)
+
+    # Start the tree as a star graph with an arbitrary node at the center
+    tree = {}
+    labels = {}
+    iter_nodes = iter(G)
+    root = next(iter_nodes)
+    for n in iter_nodes:
+        tree[n] = root
+
+    # Reuse residual network
+    R = build_residual_network(G, capacity)
+
+    # For all the leaves in the star graph tree (that is n-1 nodes).
+    for source in tree:
+        # Find neighbor in the tree
+        target = tree[source]
+        # compute minimum cut
+        cut_value, partition = nx.minimum_cut(
+            G, source, target, capacity=capacity, flow_func=flow_func, residual=R
+        )
+        labels[(source, target)] = cut_value
+        # Update the tree
+        # Source will always be in partition[0] and target in partition[1]
+        for node in partition[0]:
+            if node != source and node in tree and tree[node] == target:
+                tree[node] = source
+                labels[node, source] = labels.get((node, target), cut_value)
+        #
+        if target != root and tree[target] in partition[0]:
+            labels[source, tree[target]] = labels[target, tree[target]]
+            labels[target, source] = cut_value
+            tree[source] = tree[target]
+            tree[target] = source
+
+    # Build the tree
+    T = nx.Graph()
+    T.add_nodes_from(G)
+    T.add_weighted_edges_from(((u, v, labels[u, v]) for u, v in tree.items()))
+    return T

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/flow/maxflow.py

@@ -0,0 +1,607 @@
+"""
+Maximum flow (and minimum cut) algorithms on capacitated graphs.
+"""
+import networkx as nx
+
+from .boykovkolmogorov import boykov_kolmogorov
+from .dinitz_alg import dinitz
+from .edmondskarp import edmonds_karp
+from .preflowpush import preflow_push
+from .shortestaugmentingpath import shortest_augmenting_path
+from .utils import build_flow_dict
+
+# Define the default flow function for computing maximum flow.
+default_flow_func = preflow_push
+
+__all__ = ["maximum_flow", "maximum_flow_value", "minimum_cut", "minimum_cut_value"]
+
+
+@nx._dispatch(graphs="flowG", edge_attrs={"capacity": float("inf")})
+def maximum_flow(flowG, _s, _t, capacity="capacity", flow_func=None, **kwargs):
+    """Find a maximum single-commodity flow.
+
+    Parameters
+    ----------
+    flowG : NetworkX graph
+        Edges of the graph are expected to have an attribute called
+        'capacity'. If this attribute is not present, the edge is
+        considered to have infinite capacity.
+
+    _s : node
+        Source node for the flow.
+
+    _t : node
+        Sink node for the flow.
+
+    capacity : string
+        Edges of the graph G are expected to have an attribute capacity
+        that indicates how much flow the edge can support. If this
+        attribute is not present, the edge is considered to have
+        infinite capacity. Default value: 'capacity'.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes
+        in a capacitated graph. The function has to accept at least three
+        parameters: a Graph or Digraph, a source node, and a target node.
+        And return a residual network that follows NetworkX conventions
+        (see Notes). If flow_func is None, the default maximum
+        flow function (:meth:`preflow_push`) is used. See below for
+        alternative algorithms. The choice of the default function may change
+        from version to version and should not be relied on. Default value:
+        None.
+
+    kwargs : Any other keyword parameter is passed to the function that
+        computes the maximum flow.
+
+    Returns
+    -------
+    flow_value : integer, float
+        Value of the maximum flow, i.e., net outflow from the source.
+
+    flow_dict : dict
+        A dictionary containing the value of the flow that went through
+        each edge.
+
+    Raises
+    ------
+    NetworkXError
+        The algorithm does not support MultiGraph and MultiDiGraph. If
+        the input graph is an instance of one of these two classes, a
+        NetworkXError is raised.
+
+    NetworkXUnbounded
+        If the graph has a path of infinite capacity, the value of a
+        feasible flow on the graph is unbounded above and the function
+        raises a NetworkXUnbounded.
+
+    See also
+    --------
+    :meth:`maximum_flow_value`
+    :meth:`minimum_cut`
+    :meth:`minimum_cut_value`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    Notes
+    -----
+    The function used in the flow_func parameter has to return a residual
+    network that follows NetworkX conventions:
+
+    The residual network :samp:`R` from an input graph :samp:`G` has the
+    same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair
+    of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a
+    self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists
+    in :samp:`G`.
+
+    For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']`
+    is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists
+    in :samp:`G` or zero otherwise. If the capacity is infinite,
+    :samp:`R[u][v]['capacity']` will have a high arbitrary finite value
+    that does not affect the solution of the problem. This value is stored in
+    :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`,
+    :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and
+    satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`.
+
+    The flow value, defined as the total flow into :samp:`t`, the sink, is
+    stored in :samp:`R.graph['flow_value']`. Reachability to :samp:`t` using
+    only edges :samp:`(u, v)` such that
+    :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum
+    :samp:`s`-:samp:`t` cut.
+
+    Specific algorithms may store extra data in :samp:`R`.
+
+    The function should supports an optional boolean parameter value_only. When
+    True, it can optionally terminate the algorithm as soon as the maximum flow
+    value and the minimum cut can be determined.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edge("x", "a", capacity=3.0)
+    >>> G.add_edge("x", "b", capacity=1.0)
+    >>> G.add_edge("a", "c", capacity=3.0)
+    >>> G.add_edge("b", "c", capacity=5.0)
+    >>> G.add_edge("b", "d", capacity=4.0)
+    >>> G.add_edge("d", "e", capacity=2.0)
+    >>> G.add_edge("c", "y", capacity=2.0)
+    >>> G.add_edge("e", "y", capacity=3.0)
+
+    maximum_flow returns both the value of the maximum flow and a
+    dictionary with all flows.
+
+    >>> flow_value, flow_dict = nx.maximum_flow(G, "x", "y")
+    >>> flow_value
+    3.0
+    >>> print(flow_dict["x"]["b"])
+    1.0
+
+    You can also use alternative algorithms for computing the
+    maximum flow by using the flow_func parameter.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> flow_value == nx.maximum_flow(G, "x", "y", flow_func=shortest_augmenting_path)[
+    ...     0
+    ... ]
+    True
+
+    """
+    if flow_func is None:
+        if kwargs:
+            raise nx.NetworkXError(
+                "You have to explicitly set a flow_func if"
+                " you need to pass parameters via kwargs."
+            )
+        flow_func = default_flow_func
+
+    if not callable(flow_func):
+        raise nx.NetworkXError("flow_func has to be callable.")
+
+    R = flow_func(flowG, _s, _t, capacity=capacity, value_only=False, **kwargs)
+    flow_dict = build_flow_dict(flowG, R)
+
+    return (R.graph["flow_value"], flow_dict)
+
+
+@nx._dispatch(graphs="flowG", edge_attrs={"capacity": float("inf")})
+def maximum_flow_value(flowG, _s, _t, capacity="capacity", flow_func=None, **kwargs):
+    """Find the value of maximum single-commodity flow.
+
+    Parameters
+    ----------
+    flowG : NetworkX graph
+        Edges of the graph are expected to have an attribute called
+        'capacity'. If this attribute is not present, the edge is
+        considered to have infinite capacity.
+
+    _s : node
+        Source node for the flow.
+
+    _t : node
+        Sink node for the flow.
+
+    capacity : string
+        Edges of the graph G are expected to have an attribute capacity
+        that indicates how much flow the edge can support. If this
+        attribute is not present, the edge is considered to have
+        infinite capacity. Default value: 'capacity'.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes
+        in a capacitated graph. The function has to accept at least three
+        parameters: a Graph or Digraph, a source node, and a target node.
+        And return a residual network that follows NetworkX conventions
+        (see Notes). If flow_func is None, the default maximum
+        flow function (:meth:`preflow_push`) is used. See below for
+        alternative algorithms. The choice of the default function may change
+        from version to version and should not be relied on. Default value:
+        None.
+
+    kwargs : Any other keyword parameter is passed to the function that
+        computes the maximum flow.
+
+    Returns
+    -------
+    flow_value : integer, float
+        Value of the maximum flow, i.e., net outflow from the source.
+
+    Raises
+    ------
+    NetworkXError
+        The algorithm does not support MultiGraph and MultiDiGraph. If
+        the input graph is an instance of one of these two classes, a
+        NetworkXError is raised.
+
+    NetworkXUnbounded
+        If the graph has a path of infinite capacity, the value of a
+        feasible flow on the graph is unbounded above and the function
+        raises a NetworkXUnbounded.
+
+    See also
+    --------
+    :meth:`maximum_flow`
+    :meth:`minimum_cut`
+    :meth:`minimum_cut_value`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    Notes
+    -----
+    The function used in the flow_func parameter has to return a residual
+    network that follows NetworkX conventions:
+
+    The residual network :samp:`R` from an input graph :samp:`G` has the
+    same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair
+    of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a
+    self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists
+    in :samp:`G`.
+
+    For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']`
+    is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists
+    in :samp:`G` or zero otherwise. If the capacity is infinite,
+    :samp:`R[u][v]['capacity']` will have a high arbitrary finite value
+    that does not affect the solution of the problem. This value is stored in
+    :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`,
+    :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and
+    satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`.
+
+    The flow value, defined as the total flow into :samp:`t`, the sink, is
+    stored in :samp:`R.graph['flow_value']`. Reachability to :samp:`t` using
+    only edges :samp:`(u, v)` such that
+    :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum
+    :samp:`s`-:samp:`t` cut.
+
+    Specific algorithms may store extra data in :samp:`R`.
+
+    The function should supports an optional boolean parameter value_only. When
+    True, it can optionally terminate the algorithm as soon as the maximum flow
+    value and the minimum cut can be determined.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edge("x", "a", capacity=3.0)
+    >>> G.add_edge("x", "b", capacity=1.0)
+    >>> G.add_edge("a", "c", capacity=3.0)
+    >>> G.add_edge("b", "c", capacity=5.0)
+    >>> G.add_edge("b", "d", capacity=4.0)
+    >>> G.add_edge("d", "e", capacity=2.0)
+    >>> G.add_edge("c", "y", capacity=2.0)
+    >>> G.add_edge("e", "y", capacity=3.0)
+
+    maximum_flow_value computes only the value of the
+    maximum flow:
+
+    >>> flow_value = nx.maximum_flow_value(G, "x", "y")
+    >>> flow_value
+    3.0
+
+    You can also use alternative algorithms for computing the
+    maximum flow by using the flow_func parameter.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> flow_value == nx.maximum_flow_value(
+    ...     G, "x", "y", flow_func=shortest_augmenting_path
+    ... )
+    True
+
+    """
+    if flow_func is None:
+        if kwargs:
+            raise nx.NetworkXError(
+                "You have to explicitly set a flow_func if"
+                " you need to pass parameters via kwargs."
+            )
+        flow_func = default_flow_func
+
+    if not callable(flow_func):
+        raise nx.NetworkXError("flow_func has to be callable.")
+
+    R = flow_func(flowG, _s, _t, capacity=capacity, value_only=True, **kwargs)
+
+    return R.graph["flow_value"]
+
+
+@nx._dispatch(graphs="flowG", edge_attrs={"capacity": float("inf")})
+def minimum_cut(flowG, _s, _t, capacity="capacity", flow_func=None, **kwargs):
+    """Compute the value and the node partition of a minimum (s, t)-cut.
+
+    Use the max-flow min-cut theorem, i.e., the capacity of a minimum
+    capacity cut is equal to the flow value of a maximum flow.
+
+    Parameters
+    ----------
+    flowG : NetworkX graph
+        Edges of the graph are expected to have an attribute called
+        'capacity'. If this attribute is not present, the edge is
+        considered to have infinite capacity.
+
+    _s : node
+        Source node for the flow.
+
+    _t : node
+        Sink node for the flow.
+
+    capacity : string
+        Edges of the graph G are expected to have an attribute capacity
+        that indicates how much flow the edge can support. If this
+        attribute is not present, the edge is considered to have
+        infinite capacity. Default value: 'capacity'.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes
+        in a capacitated graph. The function has to accept at least three
+        parameters: a Graph or Digraph, a source node, and a target node.
+        And return a residual network that follows NetworkX conventions
+        (see Notes). If flow_func is None, the default maximum
+        flow function (:meth:`preflow_push`) is used. See below for
+        alternative algorithms. The choice of the default function may change
+        from version to version and should not be relied on. Default value:
+        None.
+
+    kwargs : Any other keyword parameter is passed to the function that
+        computes the maximum flow.
+
+    Returns
+    -------
+    cut_value : integer, float
+        Value of the minimum cut.
+
+    partition : pair of node sets
+        A partitioning of the nodes that defines a minimum cut.
+
+    Raises
+    ------
+    NetworkXUnbounded
+        If the graph has a path of infinite capacity, all cuts have
+        infinite capacity and the function raises a NetworkXError.
+
+    See also
+    --------
+    :meth:`maximum_flow`
+    :meth:`maximum_flow_value`
+    :meth:`minimum_cut_value`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    Notes
+    -----
+    The function used in the flow_func parameter has to return a residual
+    network that follows NetworkX conventions:
+
+    The residual network :samp:`R` from an input graph :samp:`G` has the
+    same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair
+    of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a
+    self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists
+    in :samp:`G`.
+
+    For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']`
+    is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists
+    in :samp:`G` or zero otherwise. If the capacity is infinite,
+    :samp:`R[u][v]['capacity']` will have a high arbitrary finite value
+    that does not affect the solution of the problem. This value is stored in
+    :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`,
+    :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and
+    satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`.
+
+    The flow value, defined as the total flow into :samp:`t`, the sink, is
+    stored in :samp:`R.graph['flow_value']`. Reachability to :samp:`t` using
+    only edges :samp:`(u, v)` such that
+    :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum
+    :samp:`s`-:samp:`t` cut.
+
+    Specific algorithms may store extra data in :samp:`R`.
+
+    The function should supports an optional boolean parameter value_only. When
+    True, it can optionally terminate the algorithm as soon as the maximum flow
+    value and the minimum cut can be determined.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edge("x", "a", capacity=3.0)
+    >>> G.add_edge("x", "b", capacity=1.0)
+    >>> G.add_edge("a", "c", capacity=3.0)
+    >>> G.add_edge("b", "c", capacity=5.0)
+    >>> G.add_edge("b", "d", capacity=4.0)
+    >>> G.add_edge("d", "e", capacity=2.0)
+    >>> G.add_edge("c", "y", capacity=2.0)
+    >>> G.add_edge("e", "y", capacity=3.0)
+
+    minimum_cut computes both the value of the
+    minimum cut and the node partition:
+
+    >>> cut_value, partition = nx.minimum_cut(G, "x", "y")
+    >>> reachable, non_reachable = partition
+
+    'partition' here is a tuple with the two sets of nodes that define
+    the minimum cut. You can compute the cut set of edges that induce
+    the minimum cut as follows:
+
+    >>> cutset = set()
+    >>> for u, nbrs in ((n, G[n]) for n in reachable):
+    ...     cutset.update((u, v) for v in nbrs if v in non_reachable)
+    >>> print(sorted(cutset))
+    [('c', 'y'), ('x', 'b')]
+    >>> cut_value == sum(G.edges[u, v]["capacity"] for (u, v) in cutset)
+    True
+
+    You can also use alternative algorithms for computing the
+    minimum cut by using the flow_func parameter.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> cut_value == nx.minimum_cut(G, "x", "y", flow_func=shortest_augmenting_path)[0]
+    True
+
+    """
+    if flow_func is None:
+        if kwargs:
+            raise nx.NetworkXError(
+                "You have to explicitly set a flow_func if"
+                " you need to pass parameters via kwargs."
+            )
+        flow_func = default_flow_func
+
+    if not callable(flow_func):
+        raise nx.NetworkXError("flow_func has to be callable.")
+
+    if kwargs.get("cutoff") is not None and flow_func is preflow_push:
+        raise nx.NetworkXError("cutoff should not be specified.")
+
+    R = flow_func(flowG, _s, _t, capacity=capacity, value_only=True, **kwargs)
+    # Remove saturated edges from the residual network
+    cutset = [(u, v, d) for u, v, d in R.edges(data=True) if d["flow"] == d["capacity"]]
+    R.remove_edges_from(cutset)
+
+    # Then, reachable and non reachable nodes from source in the
+    # residual network form the node partition that defines
+    # the minimum cut.
+    non_reachable = set(dict(nx.shortest_path_length(R, target=_t)))
+    partition = (set(flowG) - non_reachable, non_reachable)
+    # Finally add again cutset edges to the residual network to make
+    # sure that it is reusable.
+    if cutset is not None:
+        R.add_edges_from(cutset)
+    return (R.graph["flow_value"], partition)
+
+
+@nx._dispatch(graphs="flowG", edge_attrs={"capacity": float("inf")})
+def minimum_cut_value(flowG, _s, _t, capacity="capacity", flow_func=None, **kwargs):
+    """Compute the value of a minimum (s, t)-cut.
+
+    Use the max-flow min-cut theorem, i.e., the capacity of a minimum
+    capacity cut is equal to the flow value of a maximum flow.
+
+    Parameters
+    ----------
+    flowG : NetworkX graph
+        Edges of the graph are expected to have an attribute called
+        'capacity'. If this attribute is not present, the edge is
+        considered to have infinite capacity.
+
+    _s : node
+        Source node for the flow.
+
+    _t : node
+        Sink node for the flow.
+
+    capacity : string
+        Edges of the graph G are expected to have an attribute capacity
+        that indicates how much flow the edge can support. If this
+        attribute is not present, the edge is considered to have
+        infinite capacity. Default value: 'capacity'.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes
+        in a capacitated graph. The function has to accept at least three
+        parameters: a Graph or Digraph, a source node, and a target node.
+        And return a residual network that follows NetworkX conventions
+        (see Notes). If flow_func is None, the default maximum
+        flow function (:meth:`preflow_push`) is used. See below for
+        alternative algorithms. The choice of the default function may change
+        from version to version and should not be relied on. Default value:
+        None.
+
+    kwargs : Any other keyword parameter is passed to the function that
+        computes the maximum flow.
+
+    Returns
+    -------
+    cut_value : integer, float
+        Value of the minimum cut.
+
+    Raises
+    ------
+    NetworkXUnbounded
+        If the graph has a path of infinite capacity, all cuts have
+        infinite capacity and the function raises a NetworkXError.
+
+    See also
+    --------
+    :meth:`maximum_flow`
+    :meth:`maximum_flow_value`
+    :meth:`minimum_cut`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    Notes
+    -----
+    The function used in the flow_func parameter has to return a residual
+    network that follows NetworkX conventions:
+
+    The residual network :samp:`R` from an input graph :samp:`G` has the
+    same nodes as :samp:`G`. :samp:`R` is a DiGraph that contains a pair
+    of edges :samp:`(u, v)` and :samp:`(v, u)` iff :samp:`(u, v)` is not a
+    self-loop, and at least one of :samp:`(u, v)` and :samp:`(v, u)` exists
+    in :samp:`G`.
+
+    For each edge :samp:`(u, v)` in :samp:`R`, :samp:`R[u][v]['capacity']`
+    is equal to the capacity of :samp:`(u, v)` in :samp:`G` if it exists
+    in :samp:`G` or zero otherwise. If the capacity is infinite,
+    :samp:`R[u][v]['capacity']` will have a high arbitrary finite value
+    that does not affect the solution of the problem. This value is stored in
+    :samp:`R.graph['inf']`. For each edge :samp:`(u, v)` in :samp:`R`,
+    :samp:`R[u][v]['flow']` represents the flow function of :samp:`(u, v)` and
+    satisfies :samp:`R[u][v]['flow'] == -R[v][u]['flow']`.
+
+    The flow value, defined as the total flow into :samp:`t`, the sink, is
+    stored in :samp:`R.graph['flow_value']`. Reachability to :samp:`t` using
+    only edges :samp:`(u, v)` such that
+    :samp:`R[u][v]['flow'] < R[u][v]['capacity']` induces a minimum
+    :samp:`s`-:samp:`t` cut.
+
+    Specific algorithms may store extra data in :samp:`R`.
+
+    The function should supports an optional boolean parameter value_only. When
+    True, it can optionally terminate the algorithm as soon as the maximum flow
+    value and the minimum cut can be determined.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph()
+    >>> G.add_edge("x", "a", capacity=3.0)
+    >>> G.add_edge("x", "b", capacity=1.0)
+    >>> G.add_edge("a", "c", capacity=3.0)
+    >>> G.add_edge("b", "c", capacity=5.0)
+    >>> G.add_edge("b", "d", capacity=4.0)
+    >>> G.add_edge("d", "e", capacity=2.0)
+    >>> G.add_edge("c", "y", capacity=2.0)
+    >>> G.add_edge("e", "y", capacity=3.0)
+
+    minimum_cut_value computes only the value of the
+    minimum cut:
+
+    >>> cut_value = nx.minimum_cut_value(G, "x", "y")
+    >>> cut_value
+    3.0
+
+    You can also use alternative algorithms for computing the
+    minimum cut by using the flow_func parameter.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> cut_value == nx.minimum_cut_value(
+    ...     G, "x", "y", flow_func=shortest_augmenting_path
+    ... )
+    True
+
+    """
+    if flow_func is None:
+        if kwargs:
+            raise nx.NetworkXError(
+                "You have to explicitly set a flow_func if"
+                " you need to pass parameters via kwargs."
+            )
+        flow_func = default_flow_func
+
+    if not callable(flow_func):
+        raise nx.NetworkXError("flow_func has to be callable.")
+
+    if kwargs.get("cutoff") is not None and flow_func is preflow_push:
+        raise nx.NetworkXError("cutoff should not be specified.")
+
+    R = flow_func(flowG, _s, _t, capacity=capacity, value_only=True, **kwargs)
+
+    return R.graph["flow_value"]

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/polynomials.py

@@ -0,0 +1,305 @@
+"""Provides algorithms supporting the computation of graph polynomials.
+
+Graph polynomials are polynomial-valued graph invariants that encode a wide
+variety of structural information. Examples include the Tutte polynomial,
+chromatic polynomial, characteristic polynomial, and matching polynomial. An
+extensive treatment is provided in [1]_.
+
+For a simple example, the `~sympy.matrices.matrices.MatrixDeterminant.charpoly`
+method can be used to compute the characteristic polynomial from the adjacency
+matrix of a graph. Consider the complete graph ``K_4``:
+
+>>> import sympy
+>>> x = sympy.Symbol("x")
+>>> G = nx.complete_graph(4)
+>>> A = nx.adjacency_matrix(G)
+>>> M = sympy.SparseMatrix(A.todense())
+>>> M.charpoly(x).as_expr()
+x**4 - 6*x**2 - 8*x - 3
+
+
+.. [1] Y. Shi, M. Dehmer, X. Li, I. Gutman,
+   "Graph Polynomials"
+"""
+from collections import deque
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["tutte_polynomial", "chromatic_polynomial"]
+
+
+@not_implemented_for("directed")
+@nx._dispatch
+def tutte_polynomial(G):
+    r"""Returns the Tutte polynomial of `G`
+
+    This function computes the Tutte polynomial via an iterative version of
+    the deletion-contraction algorithm.
+
+    The Tutte polynomial `T_G(x, y)` is a fundamental graph polynomial invariant in
+    two variables. It encodes a wide array of information related to the
+    edge-connectivity of a graph; "Many problems about graphs can be reduced to
+    problems of finding and evaluating the Tutte polynomial at certain values" [1]_.
+    In fact, every deletion-contraction-expressible feature of a graph is a
+    specialization of the Tutte polynomial [2]_ (see Notes for examples).
+
+    There are several equivalent definitions; here are three:
+
+    Def 1 (rank-nullity expansion): For `G` an undirected graph, `n(G)` the
+    number of vertices of `G`, `E` the edge set of `G`, `V` the vertex set of
+    `G`, and `c(A)` the number of connected components of the graph with vertex
+    set `V` and edge set `A` [3]_:
+
+    .. math::
+
+        T_G(x, y) = \sum_{A \in E} (x-1)^{c(A) - c(E)} (y-1)^{c(A) + |A| - n(G)}
+
+    Def 2 (spanning tree expansion): Let `G` be an undirected graph, `T` a spanning
+    tree of `G`, and `E` the edge set of `G`. Let `E` have an arbitrary strict
+    linear order `L`. Let `B_e` be the unique minimal nonempty edge cut of
+    $E \setminus T \cup {e}$. An edge `e` is internally active with respect to
+    `T` and `L` if `e` is the least edge in `B_e` according to the linear order
+    `L`. The internal activity of `T` (denoted `i(T)`) is the number of edges
+    in $E \setminus T$ that are internally active with respect to `T` and `L`.
+    Let `P_e` be the unique path in $T \cup {e}$ whose source and target vertex
+    are the same. An edge `e` is externally active with respect to `T` and `L`
+    if `e` is the least edge in `P_e` according to the linear order `L`. The
+    external activity of `T` (denoted `e(T)`) is the number of edges in
+    $E \setminus T$ that are externally active with respect to `T` and `L`.
+    Then [4]_ [5]_:
+
+    .. math::
+
+        T_G(x, y) = \sum_{T \text{ a spanning tree of } G} x^{i(T)} y^{e(T)}
+
+    Def 3 (deletion-contraction recurrence): For `G` an undirected graph, `G-e`
+    the graph obtained from `G` by deleting edge `e`, `G/e` the graph obtained
+    from `G` by contracting edge `e`, `k(G)` the number of cut-edges of `G`,
+    and `l(G)` the number of self-loops of `G`:
+
+    .. math::
+        T_G(x, y) = \begin{cases}
+    	   x^{k(G)} y^{l(G)}, & \text{if all edges are cut-edges or self-loops} \\
+           T_{G-e}(x, y) + T_{G/e}(x, y), & \text{otherwise, for an arbitrary edge $e$ not a cut-edge or loop}
+        \end{cases}
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    instance of `sympy.core.add.Add`
+        A Sympy expression representing the Tutte polynomial for `G`.
+
+    Examples
+    --------
+    >>> C = nx.cycle_graph(5)
+    >>> nx.tutte_polynomial(C)
+    x**4 + x**3 + x**2 + x + y
+
+    >>> D = nx.diamond_graph()
+    >>> nx.tutte_polynomial(D)
+    x**3 + 2*x**2 + 2*x*y + x + y**2 + y
+
+    Notes
+    -----
+    Some specializations of the Tutte polynomial:
+
+    - `T_G(1, 1)` counts the number of spanning trees of `G`
+    - `T_G(1, 2)` counts the number of connected spanning subgraphs of `G`
+    - `T_G(2, 1)` counts the number of spanning forests in `G`
+    - `T_G(0, 2)` counts the number of strong orientations of `G`
+    - `T_G(2, 0)` counts the number of acyclic orientations of `G`
+
+    Edge contraction is defined and deletion-contraction is introduced in [6]_.
+    Combinatorial meaning of the coefficients is introduced in [7]_.
+    Universality, properties, and applications are discussed in [8]_.
+
+    Practically, up-front computation of the Tutte polynomial may be useful when
+    users wish to repeatedly calculate edge-connectivity-related information
+    about one or more graphs.
+
+    References
+    ----------
+    .. [1] M. Brandt,
+       "The Tutte Polynomial."
+       Talking About Combinatorial Objects Seminar, 2015
+       https://math.berkeley.edu/~brandtm/talks/tutte.pdf
+    .. [2] A. Björklund, T. Husfeldt, P. Kaski, M. Koivisto,
+       "Computing the Tutte polynomial in vertex-exponential time"
+       49th Annual IEEE Symposium on Foundations of Computer Science, 2008
+       https://ieeexplore.ieee.org/abstract/document/4691000
+    .. [3] Y. Shi, M. Dehmer, X. Li, I. Gutman,
+       "Graph Polynomials," p. 14
+    .. [4] Y. Shi, M. Dehmer, X. Li, I. Gutman,
+       "Graph Polynomials," p. 46
+    .. [5] A. Nešetril, J. Goodall,
+       "Graph invariants, homomorphisms, and the Tutte polynomial"
+       https://iuuk.mff.cuni.cz/~andrew/Tutte.pdf
+    .. [6] D. B. West,
+       "Introduction to Graph Theory," p. 84
+    .. [7] G. Coutinho,
+       "A brief introduction to the Tutte polynomial"
+       Structural Analysis of Complex Networks, 2011
+       https://homepages.dcc.ufmg.br/~gabriel/seminars/coutinho_tuttepolynomial_seminar.pdf
+    .. [8] J. A. Ellis-Monaghan, C. Merino,
+       "Graph polynomials and their applications I: The Tutte polynomial"
+       Structural Analysis of Complex Networks, 2011
+       https://arxiv.org/pdf/0803.3079.pdf
+    """
+    import sympy
+
+    x = sympy.Symbol("x")
+    y = sympy.Symbol("y")
+    stack = deque()
+    stack.append(nx.MultiGraph(G))
+
+    polynomial = 0
+    while stack:
+        G = stack.pop()
+        bridges = set(nx.bridges(G))
+
+        e = None
+        for i in G.edges:
+            if (i[0], i[1]) not in bridges and i[0] != i[1]:
+                e = i
+                break
+        if not e:
+            loops = list(nx.selfloop_edges(G, keys=True))
+            polynomial += x ** len(bridges) * y ** len(loops)
+        else:
+            # deletion-contraction
+            C = nx.contracted_edge(G, e, self_loops=True)
+            C.remove_edge(e[0], e[0])
+            G.remove_edge(*e)
+            stack.append(G)
+            stack.append(C)
+    return sympy.simplify(polynomial)
+
+
+@not_implemented_for("directed")
+@nx._dispatch
+def chromatic_polynomial(G):
+    r"""Returns the chromatic polynomial of `G`
+
+    This function computes the chromatic polynomial via an iterative version of
+    the deletion-contraction algorithm.
+
+    The chromatic polynomial `X_G(x)` is a fundamental graph polynomial
+    invariant in one variable. Evaluating `X_G(k)` for an natural number `k`
+    enumerates the proper k-colorings of `G`.
+
+    There are several equivalent definitions; here are three:
+
+    Def 1 (explicit formula):
+    For `G` an undirected graph, `c(G)` the number of connected components of
+    `G`, `E` the edge set of `G`, and `G(S)` the spanning subgraph of `G` with
+    edge set `S` [1]_:
+
+    .. math::
+
+        X_G(x) = \sum_{S \subseteq E} (-1)^{|S|} x^{c(G(S))}
+
+
+    Def 2 (interpolating polynomial):
+    For `G` an undirected graph, `n(G)` the number of vertices of `G`, `k_0 = 0`,
+    and `k_i` the number of distinct ways to color the vertices of `G` with `i`
+    unique colors (for `i` a natural number at most `n(G)`), `X_G(x)` is the
+    unique Lagrange interpolating polynomial of degree `n(G)` through the points
+    `(0, k_0), (1, k_1), \dots, (n(G), k_{n(G)})` [2]_.
+
+
+    Def 3 (chromatic recurrence):
+    For `G` an undirected graph, `G-e` the graph obtained from `G` by deleting
+    edge `e`, `G/e` the graph obtained from `G` by contracting edge `e`, `n(G)`
+    the number of vertices of `G`, and `e(G)` the number of edges of `G` [3]_:
+
+    .. math::
+        X_G(x) = \begin{cases}
+    	   x^{n(G)}, & \text{if $e(G)=0$} \\
+           X_{G-e}(x) - X_{G/e}(x), & \text{otherwise, for an arbitrary edge $e$}
+        \end{cases}
+
+    This formulation is also known as the Fundamental Reduction Theorem [4]_.
+
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    instance of `sympy.core.add.Add`
+        A Sympy expression representing the chromatic polynomial for `G`.
+
+    Examples
+    --------
+    >>> C = nx.cycle_graph(5)
+    >>> nx.chromatic_polynomial(C)
+    x**5 - 5*x**4 + 10*x**3 - 10*x**2 + 4*x
+
+    >>> G = nx.complete_graph(4)
+    >>> nx.chromatic_polynomial(G)
+    x**4 - 6*x**3 + 11*x**2 - 6*x
+
+    Notes
+    -----
+    Interpretation of the coefficients is discussed in [5]_. Several special
+    cases are listed in [2]_.
+
+    The chromatic polynomial is a specialization of the Tutte polynomial; in
+    particular, ``X_G(x) = T_G(x, 0)`` [6]_.
+
+    The chromatic polynomial may take negative arguments, though evaluations
+    may not have chromatic interpretations. For instance, ``X_G(-1)`` enumerates
+    the acyclic orientations of `G` [7]_.
+
+    References
+    ----------
+    .. [1] D. B. West,
+       "Introduction to Graph Theory," p. 222
+    .. [2] E. W. Weisstein
+       "Chromatic Polynomial"
+       MathWorld--A Wolfram Web Resource
+       https://mathworld.wolfram.com/ChromaticPolynomial.html
+    .. [3] D. B. West,
+       "Introduction to Graph Theory," p. 221
+    .. [4] J. Zhang, J. Goodall,
+       "An Introduction to Chromatic Polynomials"
+       https://math.mit.edu/~apost/courses/18.204_2018/Julie_Zhang_paper.pdf
+    .. [5] R. C. Read,
+       "An Introduction to Chromatic Polynomials"
+       Journal of Combinatorial Theory, 1968
+       https://math.berkeley.edu/~mrklug/ReadChromatic.pdf
+    .. [6] W. T. Tutte,
+       "Graph-polynomials"
+       Advances in Applied Mathematics, 2004
+       https://www.sciencedirect.com/science/article/pii/S0196885803000411
+    .. [7] R. P. Stanley,
+       "Acyclic orientations of graphs"
+       Discrete Mathematics, 2006
+       https://math.mit.edu/~rstan/pubs/pubfiles/18.pdf
+    """
+    import sympy
+
+    x = sympy.Symbol("x")
+    stack = deque()
+    stack.append(nx.MultiGraph(G, contraction_idx=0))
+
+    polynomial = 0
+    while stack:
+        G = stack.pop()
+        edges = list(G.edges)
+        if not edges:
+            polynomial += (-1) ** G.graph["contraction_idx"] * x ** len(G)
+        else:
+            e = edges[0]
+            C = nx.contracted_edge(G, e, self_loops=True)
+            C.graph["contraction_idx"] = G.graph["contraction_idx"] + 1
+            C.remove_edge(e[0], e[0])
+            G.remove_edge(*e)
+            stack.append(G)
+            stack.append(C)
+    return polynomial

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/shortest_paths/tests/test_dense.py

@@ -0,0 +1,212 @@
+import pytest
+
+import networkx as nx
+
+
+class TestFloyd:
+    @classmethod
+    def setup_class(cls):
+        pass
+
+    def test_floyd_warshall_predecessor_and_distance(self):
+        XG = nx.DiGraph()
+        XG.add_weighted_edges_from(
+            [
+                ("s", "u", 10),
+                ("s", "x", 5),
+                ("u", "v", 1),
+                ("u", "x", 2),
+                ("v", "y", 1),
+                ("x", "u", 3),
+                ("x", "v", 5),
+                ("x", "y", 2),
+                ("y", "s", 7),
+                ("y", "v", 6),
+            ]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(XG)
+        assert dist["s"]["v"] == 9
+        assert path["s"]["v"] == "u"
+        assert dist == {
+            "y": {"y": 0, "x": 12, "s": 7, "u": 15, "v": 6},
+            "x": {"y": 2, "x": 0, "s": 9, "u": 3, "v": 4},
+            "s": {"y": 7, "x": 5, "s": 0, "u": 8, "v": 9},
+            "u": {"y": 2, "x": 2, "s": 9, "u": 0, "v": 1},
+            "v": {"y": 1, "x": 13, "s": 8, "u": 16, "v": 0},
+        }
+
+        GG = XG.to_undirected()
+        # make sure we get lower weight
+        # to_undirected might choose either edge with weight 2 or weight 3
+        GG["u"]["x"]["weight"] = 2
+        path, dist = nx.floyd_warshall_predecessor_and_distance(GG)
+        assert dist["s"]["v"] == 8
+        # skip this test, could be alternate path s-u-v
+        #        assert_equal(path['s']['v'],'y')
+
+        G = nx.DiGraph()  # no weights
+        G.add_edges_from(
+            [
+                ("s", "u"),
+                ("s", "x"),
+                ("u", "v"),
+                ("u", "x"),
+                ("v", "y"),
+                ("x", "u"),
+                ("x", "v"),
+                ("x", "y"),
+                ("y", "s"),
+                ("y", "v"),
+            ]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(G)
+        assert dist["s"]["v"] == 2
+        # skip this test, could be alternate path s-u-v
+        # assert_equal(path['s']['v'],'x')
+
+        # alternate interface
+        dist = nx.floyd_warshall(G)
+        assert dist["s"]["v"] == 2
+
+        # floyd_warshall_predecessor_and_distance returns
+        # dicts-of-defautdicts
+        # make sure we don't get empty dictionary
+        XG = nx.DiGraph()
+        XG.add_weighted_edges_from(
+            [("v", "x", 5.0), ("y", "x", 5.0), ("v", "y", 6.0), ("x", "u", 2.0)]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(XG)
+        inf = float("inf")
+        assert dist == {
+            "v": {"v": 0, "x": 5.0, "y": 6.0, "u": 7.0},
+            "x": {"x": 0, "u": 2.0, "v": inf, "y": inf},
+            "y": {"y": 0, "x": 5.0, "v": inf, "u": 7.0},
+            "u": {"u": 0, "v": inf, "x": inf, "y": inf},
+        }
+        assert path == {
+            "v": {"x": "v", "y": "v", "u": "x"},
+            "x": {"u": "x"},
+            "y": {"x": "y", "u": "x"},
+        }
+
+    def test_reconstruct_path(self):
+        with pytest.raises(KeyError):
+            XG = nx.DiGraph()
+            XG.add_weighted_edges_from(
+                [
+                    ("s", "u", 10),
+                    ("s", "x", 5),
+                    ("u", "v", 1),
+                    ("u", "x", 2),
+                    ("v", "y", 1),
+                    ("x", "u", 3),
+                    ("x", "v", 5),
+                    ("x", "y", 2),
+                    ("y", "s", 7),
+                    ("y", "v", 6),
+                ]
+            )
+            predecessors, _ = nx.floyd_warshall_predecessor_and_distance(XG)
+
+            path = nx.reconstruct_path("s", "v", predecessors)
+            assert path == ["s", "x", "u", "v"]
+
+            path = nx.reconstruct_path("s", "s", predecessors)
+            assert path == []
+
+            # this part raises the keyError
+            nx.reconstruct_path("1", "2", predecessors)
+
+    def test_cycle(self):
+        path, dist = nx.floyd_warshall_predecessor_and_distance(nx.cycle_graph(7))
+        assert dist[0][3] == 3
+        assert path[0][3] == 2
+        assert dist[0][4] == 3
+
+    def test_weighted(self):
+        XG3 = nx.Graph()
+        XG3.add_weighted_edges_from(
+            [[0, 1, 2], [1, 2, 12], [2, 3, 1], [3, 4, 5], [4, 5, 1], [5, 0, 10]]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(XG3)
+        assert dist[0][3] == 15
+        assert path[0][3] == 2
+
+    def test_weighted2(self):
+        XG4 = nx.Graph()
+        XG4.add_weighted_edges_from(
+            [
+                [0, 1, 2],
+                [1, 2, 2],
+                [2, 3, 1],
+                [3, 4, 1],
+                [4, 5, 1],
+                [5, 6, 1],
+                [6, 7, 1],
+                [7, 0, 1],
+            ]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(XG4)
+        assert dist[0][2] == 4
+        assert path[0][2] == 1
+
+    def test_weight_parameter(self):
+        XG4 = nx.Graph()
+        XG4.add_edges_from(
+            [
+                (0, 1, {"heavy": 2}),
+                (1, 2, {"heavy": 2}),
+                (2, 3, {"heavy": 1}),
+                (3, 4, {"heavy": 1}),
+                (4, 5, {"heavy": 1}),
+                (5, 6, {"heavy": 1}),
+                (6, 7, {"heavy": 1}),
+                (7, 0, {"heavy": 1}),
+            ]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(XG4, weight="heavy")
+        assert dist[0][2] == 4
+        assert path[0][2] == 1
+
+    def test_zero_distance(self):
+        XG = nx.DiGraph()
+        XG.add_weighted_edges_from(
+            [
+                ("s", "u", 10),
+                ("s", "x", 5),
+                ("u", "v", 1),
+                ("u", "x", 2),
+                ("v", "y", 1),
+                ("x", "u", 3),
+                ("x", "v", 5),
+                ("x", "y", 2),
+                ("y", "s", 7),
+                ("y", "v", 6),
+            ]
+        )
+        path, dist = nx.floyd_warshall_predecessor_and_distance(XG)
+
+        for u in XG:
+            assert dist[u][u] == 0
+
+        GG = XG.to_undirected()
+        # make sure we get lower weight
+        # to_undirected might choose either edge with weight 2 or weight 3
+        GG["u"]["x"]["weight"] = 2
+        path, dist = nx.floyd_warshall_predecessor_and_distance(GG)
+
+        for u in GG:
+            dist[u][u] = 0
+
+    def test_zero_weight(self):
+        G = nx.DiGraph()
+        edges = [(1, 2, -2), (2, 3, -4), (1, 5, 1), (5, 4, 0), (4, 3, -5), (2, 5, -7)]
+        G.add_weighted_edges_from(edges)
+        dist = nx.floyd_warshall(G)
+        assert dist[1][3] == -14
+
+        G = nx.MultiDiGraph()
+        edges.append((2, 5, -7))
+        G.add_weighted_edges_from(edges)
+        dist = nx.floyd_warshall(G)
+        assert dist[1][3] == -14

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/shortest_paths/tests/test_generic.py

@@ -0,0 +1,444 @@
+import pytest
+
+import networkx as nx
+
+
+def validate_grid_path(r, c, s, t, p):
+    assert isinstance(p, list)
+    assert p[0] == s
+    assert p[-1] == t
+    s = ((s - 1) // c, (s - 1) % c)
+    t = ((t - 1) // c, (t - 1) % c)
+    assert len(p) == abs(t[0] - s[0]) + abs(t[1] - s[1]) + 1
+    p = [((u - 1) // c, (u - 1) % c) for u in p]
+    for u in p:
+        assert 0 <= u[0] < r
+        assert 0 <= u[1] < c
+    for u, v in zip(p[:-1], p[1:]):
+        assert (abs(v[0] - u[0]), abs(v[1] - u[1])) in [(0, 1), (1, 0)]
+
+
+class TestGenericPath:
+    @classmethod
+    def setup_class(cls):
+        from networkx import convert_node_labels_to_integers as cnlti
+
+        cls.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
+        cls.cycle = nx.cycle_graph(7)
+        cls.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
+        cls.neg_weights = nx.DiGraph()
+        cls.neg_weights.add_edge(0, 1, weight=1)
+        cls.neg_weights.add_edge(0, 2, weight=3)
+        cls.neg_weights.add_edge(1, 3, weight=1)
+        cls.neg_weights.add_edge(2, 3, weight=-2)
+
+    def test_shortest_path(self):
+        assert nx.shortest_path(self.cycle, 0, 3) == [0, 1, 2, 3]
+        assert nx.shortest_path(self.cycle, 0, 4) == [0, 6, 5, 4]
+        validate_grid_path(4, 4, 1, 12, nx.shortest_path(self.grid, 1, 12))
+        assert nx.shortest_path(self.directed_cycle, 0, 3) == [0, 1, 2, 3]
+        # now with weights
+        assert nx.shortest_path(self.cycle, 0, 3, weight="weight") == [0, 1, 2, 3]
+        assert nx.shortest_path(self.cycle, 0, 4, weight="weight") == [0, 6, 5, 4]
+        validate_grid_path(
+            4, 4, 1, 12, nx.shortest_path(self.grid, 1, 12, weight="weight")
+        )
+        assert nx.shortest_path(self.directed_cycle, 0, 3, weight="weight") == [
+            0,
+            1,
+            2,
+            3,
+        ]
+        # weights and method specified
+        assert nx.shortest_path(
+            self.directed_cycle, 0, 3, weight="weight", method="dijkstra"
+        ) == [0, 1, 2, 3]
+        assert nx.shortest_path(
+            self.directed_cycle, 0, 3, weight="weight", method="bellman-ford"
+        ) == [0, 1, 2, 3]
+        # when Dijkstra's will probably (depending on precise implementation)
+        # incorrectly return [0, 1, 3] instead
+        assert nx.shortest_path(
+            self.neg_weights, 0, 3, weight="weight", method="bellman-ford"
+        ) == [0, 2, 3]
+        # confirm bad method rejection
+        pytest.raises(ValueError, nx.shortest_path, self.cycle, method="SPAM")
+        # confirm absent source rejection
+        pytest.raises(nx.NodeNotFound, nx.shortest_path, self.cycle, 8)
+
+    def test_shortest_path_target(self):
+        answer = {0: [0, 1], 1: [1], 2: [2, 1]}
+        sp = nx.shortest_path(nx.path_graph(3), target=1)
+        assert sp == answer
+        # with weights
+        sp = nx.shortest_path(nx.path_graph(3), target=1, weight="weight")
+        assert sp == answer
+        # weights and method specified
+        sp = nx.shortest_path(
+            nx.path_graph(3), target=1, weight="weight", method="dijkstra"
+        )
+        assert sp == answer
+        sp = nx.shortest_path(
+            nx.path_graph(3), target=1, weight="weight", method="bellman-ford"
+        )
+        assert sp == answer
+
+    def test_shortest_path_length(self):
+        assert nx.shortest_path_length(self.cycle, 0, 3) == 3
+        assert nx.shortest_path_length(self.grid, 1, 12) == 5
+        assert nx.shortest_path_length(self.directed_cycle, 0, 4) == 4
+        # now with weights
+        assert nx.shortest_path_length(self.cycle, 0, 3, weight="weight") == 3
+        assert nx.shortest_path_length(self.grid, 1, 12, weight="weight") == 5
+        assert nx.shortest_path_length(self.directed_cycle, 0, 4, weight="weight") == 4
+        # weights and method specified
+        assert (
+            nx.shortest_path_length(
+                self.cycle, 0, 3, weight="weight", method="dijkstra"
+            )
+            == 3
+        )
+        assert (
+            nx.shortest_path_length(
+                self.cycle, 0, 3, weight="weight", method="bellman-ford"
+            )
+            == 3
+        )
+        # confirm bad method rejection
+        pytest.raises(ValueError, nx.shortest_path_length, self.cycle, method="SPAM")
+        # confirm absent source rejection
+        pytest.raises(nx.NodeNotFound, nx.shortest_path_length, self.cycle, 8)
+
+    def test_shortest_path_length_target(self):
+        answer = {0: 1, 1: 0, 2: 1}
+        sp = dict(nx.shortest_path_length(nx.path_graph(3), target=1))
+        assert sp == answer
+        # with weights
+        sp = nx.shortest_path_length(nx.path_graph(3), target=1, weight="weight")
+        assert sp == answer
+        # weights and method specified
+        sp = nx.shortest_path_length(
+            nx.path_graph(3), target=1, weight="weight", method="dijkstra"
+        )
+        assert sp == answer
+        sp = nx.shortest_path_length(
+            nx.path_graph(3), target=1, weight="weight", method="bellman-ford"
+        )
+        assert sp == answer
+
+    def test_single_source_shortest_path(self):
+        p = nx.shortest_path(self.cycle, 0)
+        assert p[3] == [0, 1, 2, 3]
+        assert p == nx.single_source_shortest_path(self.cycle, 0)
+        p = nx.shortest_path(self.grid, 1)
+        validate_grid_path(4, 4, 1, 12, p[12])
+        # now with weights
+        p = nx.shortest_path(self.cycle, 0, weight="weight")
+        assert p[3] == [0, 1, 2, 3]
+        assert p == nx.single_source_dijkstra_path(self.cycle, 0)
+        p = nx.shortest_path(self.grid, 1, weight="weight")
+        validate_grid_path(4, 4, 1, 12, p[12])
+        # weights and method specified
+        p = nx.shortest_path(self.cycle, 0, method="dijkstra", weight="weight")
+        assert p[3] == [0, 1, 2, 3]
+        assert p == nx.single_source_shortest_path(self.cycle, 0)
+        p = nx.shortest_path(self.cycle, 0, method="bellman-ford", weight="weight")
+        assert p[3] == [0, 1, 2, 3]
+        assert p == nx.single_source_shortest_path(self.cycle, 0)
+
+    def test_single_source_shortest_path_length(self):
+        ans = dict(nx.shortest_path_length(self.cycle, 0))
+        assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.single_source_shortest_path_length(self.cycle, 0))
+        ans = dict(nx.shortest_path_length(self.grid, 1))
+        assert ans[16] == 6
+        # now with weights
+        ans = dict(nx.shortest_path_length(self.cycle, 0, weight="weight"))
+        assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.single_source_dijkstra_path_length(self.cycle, 0))
+        ans = dict(nx.shortest_path_length(self.grid, 1, weight="weight"))
+        assert ans[16] == 6
+        # weights and method specified
+        ans = dict(
+            nx.shortest_path_length(self.cycle, 0, weight="weight", method="dijkstra")
+        )
+        assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.single_source_dijkstra_path_length(self.cycle, 0))
+        ans = dict(
+            nx.shortest_path_length(
+                self.cycle, 0, weight="weight", method="bellman-ford"
+            )
+        )
+        assert ans == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.single_source_bellman_ford_path_length(self.cycle, 0))
+
+    def test_single_source_all_shortest_paths(self):
+        cycle_ans = {0: [[0]], 1: [[0, 1]], 2: [[0, 1, 2], [0, 3, 2]], 3: [[0, 3]]}
+        ans = dict(nx.single_source_all_shortest_paths(nx.cycle_graph(4), 0))
+        assert sorted(ans[2]) == cycle_ans[2]
+        ans = dict(nx.single_source_all_shortest_paths(self.grid, 1))
+        grid_ans = [
+            [1, 2, 3, 7, 11],
+            [1, 2, 6, 7, 11],
+            [1, 2, 6, 10, 11],
+            [1, 5, 6, 7, 11],
+            [1, 5, 6, 10, 11],
+            [1, 5, 9, 10, 11],
+        ]
+        assert sorted(ans[11]) == grid_ans
+        ans = dict(
+            nx.single_source_all_shortest_paths(nx.cycle_graph(4), 0, weight="weight")
+        )
+        assert sorted(ans[2]) == cycle_ans[2]
+        ans = dict(
+            nx.single_source_all_shortest_paths(
+                nx.cycle_graph(4), 0, method="bellman-ford", weight="weight"
+            )
+        )
+        assert sorted(ans[2]) == cycle_ans[2]
+        ans = dict(nx.single_source_all_shortest_paths(self.grid, 1, weight="weight"))
+        assert sorted(ans[11]) == grid_ans
+        ans = dict(
+            nx.single_source_all_shortest_paths(
+                self.grid, 1, method="bellman-ford", weight="weight"
+            )
+        )
+        assert sorted(ans[11]) == grid_ans
+        G = nx.cycle_graph(4)
+        G.add_node(4)
+        ans = dict(nx.single_source_all_shortest_paths(G, 0))
+        assert sorted(ans[2]) == [[0, 1, 2], [0, 3, 2]]
+        ans = dict(nx.single_source_all_shortest_paths(G, 4))
+        assert sorted(ans[4]) == [[4]]
+
+    def test_all_pairs_shortest_path(self):
+        p = nx.shortest_path(self.cycle)
+        assert p[0][3] == [0, 1, 2, 3]
+        assert p == dict(nx.all_pairs_shortest_path(self.cycle))
+        p = nx.shortest_path(self.grid)
+        validate_grid_path(4, 4, 1, 12, p[1][12])
+        # now with weights
+        p = nx.shortest_path(self.cycle, weight="weight")
+        assert p[0][3] == [0, 1, 2, 3]
+        assert p == dict(nx.all_pairs_dijkstra_path(self.cycle))
+        p = nx.shortest_path(self.grid, weight="weight")
+        validate_grid_path(4, 4, 1, 12, p[1][12])
+        # weights and method specified
+        p = nx.shortest_path(self.cycle, weight="weight", method="dijkstra")
+        assert p[0][3] == [0, 1, 2, 3]
+        assert p == dict(nx.all_pairs_dijkstra_path(self.cycle))
+        p = nx.shortest_path(self.cycle, weight="weight", method="bellman-ford")
+        assert p[0][3] == [0, 1, 2, 3]
+        assert p == dict(nx.all_pairs_bellman_ford_path(self.cycle))
+
+    def test_all_pairs_shortest_path_length(self):
+        ans = dict(nx.shortest_path_length(self.cycle))
+        assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.all_pairs_shortest_path_length(self.cycle))
+        ans = dict(nx.shortest_path_length(self.grid))
+        assert ans[1][16] == 6
+        # now with weights
+        ans = dict(nx.shortest_path_length(self.cycle, weight="weight"))
+        assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.all_pairs_dijkstra_path_length(self.cycle))
+        ans = dict(nx.shortest_path_length(self.grid, weight="weight"))
+        assert ans[1][16] == 6
+        # weights and method specified
+        ans = dict(
+            nx.shortest_path_length(self.cycle, weight="weight", method="dijkstra")
+        )
+        assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.all_pairs_dijkstra_path_length(self.cycle))
+        ans = dict(
+            nx.shortest_path_length(self.cycle, weight="weight", method="bellman-ford")
+        )
+        assert ans[0] == {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1}
+        assert ans == dict(nx.all_pairs_bellman_ford_path_length(self.cycle))
+
+    def test_all_pairs_all_shortest_paths(self):
+        ans = dict(nx.all_pairs_all_shortest_paths(nx.cycle_graph(4)))
+        assert sorted(ans[1][3]) == [[1, 0, 3], [1, 2, 3]]
+        ans = dict(nx.all_pairs_all_shortest_paths(nx.cycle_graph(4)), weight="weight")
+        assert sorted(ans[1][3]) == [[1, 0, 3], [1, 2, 3]]
+        ans = dict(
+            nx.all_pairs_all_shortest_paths(nx.cycle_graph(4)),
+            method="bellman-ford",
+            weight="weight",
+        )
+        assert sorted(ans[1][3]) == [[1, 0, 3], [1, 2, 3]]
+        G = nx.cycle_graph(4)
+        G.add_node(4)
+        ans = dict(nx.all_pairs_all_shortest_paths(G))
+        assert sorted(ans[4][4]) == [[4]]
+
+    def test_has_path(self):
+        G = nx.Graph()
+        nx.add_path(G, range(3))
+        nx.add_path(G, range(3, 5))
+        assert nx.has_path(G, 0, 2)
+        assert not nx.has_path(G, 0, 4)
+
+    def test_all_shortest_paths(self):
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2, 3])
+        nx.add_path(G, [0, 10, 20, 3])
+        assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted(nx.all_shortest_paths(G, 0, 3))
+        # with weights
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2, 3])
+        nx.add_path(G, [0, 10, 20, 3])
+        assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted(
+            nx.all_shortest_paths(G, 0, 3, weight="weight")
+        )
+        # weights and method specified
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2, 3])
+        nx.add_path(G, [0, 10, 20, 3])
+        assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted(
+            nx.all_shortest_paths(G, 0, 3, weight="weight", method="dijkstra")
+        )
+        G = nx.Graph()
+        nx.add_path(G, [0, 1, 2, 3])
+        nx.add_path(G, [0, 10, 20, 3])
+        assert [[0, 1, 2, 3], [0, 10, 20, 3]] == sorted(
+            nx.all_shortest_paths(G, 0, 3, weight="weight", method="bellman-ford")
+        )
+
+    def test_all_shortest_paths_raise(self):
+        with pytest.raises(nx.NetworkXNoPath):
+            G = nx.path_graph(4)
+            G.add_node(4)
+            list(nx.all_shortest_paths(G, 0, 4))
+
+    def test_bad_method(self):
+        with pytest.raises(ValueError):
+            G = nx.path_graph(2)
+            list(nx.all_shortest_paths(G, 0, 1, weight="weight", method="SPAM"))
+
+    def test_single_source_all_shortest_paths_bad_method(self):
+        with pytest.raises(ValueError):
+            G = nx.path_graph(2)
+            dict(
+                nx.single_source_all_shortest_paths(
+                    G, 0, weight="weight", method="SPAM"
+                )
+            )
+
+    def test_all_shortest_paths_zero_weight_edge(self):
+        g = nx.Graph()
+        nx.add_path(g, [0, 1, 3])
+        nx.add_path(g, [0, 1, 2, 3])
+        g.edges[1, 2]["weight"] = 0
+        paths30d = list(
+            nx.all_shortest_paths(g, 3, 0, weight="weight", method="dijkstra")
+        )
+        paths03d = list(
+            nx.all_shortest_paths(g, 0, 3, weight="weight", method="dijkstra")
+        )
+        paths30b = list(
+            nx.all_shortest_paths(g, 3, 0, weight="weight", method="bellman-ford")
+        )
+        paths03b = list(
+            nx.all_shortest_paths(g, 0, 3, weight="weight", method="bellman-ford")
+        )
+        assert sorted(paths03d) == sorted(p[::-1] for p in paths30d)
+        assert sorted(paths03d) == sorted(p[::-1] for p in paths30b)
+        assert sorted(paths03b) == sorted(p[::-1] for p in paths30b)
+
+
+class TestAverageShortestPathLength:
+    def test_cycle_graph(self):
+        ans = nx.average_shortest_path_length(nx.cycle_graph(7))
+        assert ans == pytest.approx(2, abs=1e-7)
+
+    def test_path_graph(self):
+        ans = nx.average_shortest_path_length(nx.path_graph(5))
+        assert ans == pytest.approx(2, abs=1e-7)
+
+    def test_weighted(self):
+        G = nx.Graph()
+        nx.add_cycle(G, range(7), weight=2)
+        ans = nx.average_shortest_path_length(G, weight="weight")
+        assert ans == pytest.approx(4, abs=1e-7)
+        G = nx.Graph()
+        nx.add_path(G, range(5), weight=2)
+        ans = nx.average_shortest_path_length(G, weight="weight")
+        assert ans == pytest.approx(4, abs=1e-7)
+
+    def test_specified_methods(self):
+        G = nx.Graph()
+        nx.add_cycle(G, range(7), weight=2)
+        ans = nx.average_shortest_path_length(G, weight="weight", method="dijkstra")
+        assert ans == pytest.approx(4, abs=1e-7)
+        ans = nx.average_shortest_path_length(G, weight="weight", method="bellman-ford")
+        assert ans == pytest.approx(4, abs=1e-7)
+        ans = nx.average_shortest_path_length(
+            G, weight="weight", method="floyd-warshall"
+        )
+        assert ans == pytest.approx(4, abs=1e-7)
+
+        G = nx.Graph()
+        nx.add_path(G, range(5), weight=2)
+        ans = nx.average_shortest_path_length(G, weight="weight", method="dijkstra")
+        assert ans == pytest.approx(4, abs=1e-7)
+        ans = nx.average_shortest_path_length(G, weight="weight", method="bellman-ford")
+        assert ans == pytest.approx(4, abs=1e-7)
+        ans = nx.average_shortest_path_length(
+            G, weight="weight", method="floyd-warshall"
+        )
+        assert ans == pytest.approx(4, abs=1e-7)
+
+    def test_directed_not_strongly_connected(self):
+        G = nx.DiGraph([(0, 1)])
+        with pytest.raises(nx.NetworkXError, match="Graph is not strongly connected"):
+            nx.average_shortest_path_length(G)
+
+    def test_undirected_not_connected(self):
+        g = nx.Graph()
+        g.add_nodes_from(range(3))
+        g.add_edge(0, 1)
+        pytest.raises(nx.NetworkXError, nx.average_shortest_path_length, g)
+
+    def test_trivial_graph(self):
+        """Tests that the trivial graph has average path length zero,
+        since there is exactly one path of length zero in the trivial
+        graph.
+
+        For more information, see issue #1960.
+
+        """
+        G = nx.trivial_graph()
+        assert nx.average_shortest_path_length(G) == 0
+
+    def test_null_graph(self):
+        with pytest.raises(nx.NetworkXPointlessConcept):
+            nx.average_shortest_path_length(nx.null_graph())
+
+    def test_bad_method(self):
+        with pytest.raises(ValueError):
+            G = nx.path_graph(2)
+            nx.average_shortest_path_length(G, weight="weight", method="SPAM")
+
+
+class TestAverageShortestPathLengthNumpy:
+    @classmethod
+    def setup_class(cls):
+        global np
+        import pytest
+
+        np = pytest.importorskip("numpy")
+
+    def test_specified_methods_numpy(self):
+        G = nx.Graph()
+        nx.add_cycle(G, range(7), weight=2)
+        ans = nx.average_shortest_path_length(
+            G, weight="weight", method="floyd-warshall-numpy"
+        )
+        np.testing.assert_almost_equal(ans, 4)
+
+        G = nx.Graph()
+        nx.add_path(G, range(5), weight=2)
+        ans = nx.average_shortest_path_length(
+            G, weight="weight", method="floyd-warshall-numpy"
+        )
+        np.testing.assert_almost_equal(ans, 4)

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/similarity.py

@@ -0,0 +1,1710 @@
+""" Functions measuring similarity using graph edit distance.
+
+The graph edit distance is the number of edge/node changes needed
+to make two graphs isomorphic.
+
+The default algorithm/implementation is sub-optimal for some graphs.
+The problem of finding the exact Graph Edit Distance (GED) is NP-hard
+so it is often slow. If the simple interface `graph_edit_distance`
+takes too long for your graph, try `optimize_graph_edit_distance`
+and/or `optimize_edit_paths`.
+
+At the same time, I encourage capable people to investigate
+alternative GED algorithms, in order to improve the choices available.
+"""
+
+import math
+import time
+import warnings
+from dataclasses import dataclass
+from itertools import product
+
+import networkx as nx
+
+__all__ = [
+    "graph_edit_distance",
+    "optimal_edit_paths",
+    "optimize_graph_edit_distance",
+    "optimize_edit_paths",
+    "simrank_similarity",
+    "panther_similarity",
+    "generate_random_paths",
+]
+
+
+def debug_print(*args, **kwargs):
+    print(*args, **kwargs)
+
+
+@nx._dispatch(
+    graphs={"G1": 0, "G2": 1}, preserve_edge_attrs=True, preserve_node_attrs=True
+)
+def graph_edit_distance(
+    G1,
+    G2,
+    node_match=None,
+    edge_match=None,
+    node_subst_cost=None,
+    node_del_cost=None,
+    node_ins_cost=None,
+    edge_subst_cost=None,
+    edge_del_cost=None,
+    edge_ins_cost=None,
+    roots=None,
+    upper_bound=None,
+    timeout=None,
+):
+    """Returns GED (graph edit distance) between graphs G1 and G2.
+
+    Graph edit distance is a graph similarity measure analogous to
+    Levenshtein distance for strings.  It is defined as minimum cost
+    of edit path (sequence of node and edge edit operations)
+    transforming graph G1 to graph isomorphic to G2.
+
+    Parameters
+    ----------
+    G1, G2: graphs
+        The two graphs G1 and G2 must be of the same type.
+
+    node_match : callable
+        A function that returns True if node n1 in G1 and n2 in G2
+        should be considered equal during matching.
+
+        The function will be called like
+
+           node_match(G1.nodes[n1], G2.nodes[n2]).
+
+        That is, the function will receive the node attribute
+        dictionaries for n1 and n2 as inputs.
+
+        Ignored if node_subst_cost is specified.  If neither
+        node_match nor node_subst_cost are specified then node
+        attributes are not considered.
+
+    edge_match : callable
+        A function that returns True if the edge attribute dictionaries
+        for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
+        be considered equal during matching.
+
+        The function will be called like
+
+           edge_match(G1[u1][v1], G2[u2][v2]).
+
+        That is, the function will receive the edge attribute
+        dictionaries of the edges under consideration.
+
+        Ignored if edge_subst_cost is specified.  If neither
+        edge_match nor edge_subst_cost are specified then edge
+        attributes are not considered.
+
+    node_subst_cost, node_del_cost, node_ins_cost : callable
+        Functions that return the costs of node substitution, node
+        deletion, and node insertion, respectively.
+
+        The functions will be called like
+
+           node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
+           node_del_cost(G1.nodes[n1]),
+           node_ins_cost(G2.nodes[n2]).
+
+        That is, the functions will receive the node attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function node_subst_cost overrides node_match if specified.
+        If neither node_match nor node_subst_cost are specified then
+        default node substitution cost of 0 is used (node attributes
+        are not considered during matching).
+
+        If node_del_cost is not specified then default node deletion
+        cost of 1 is used.  If node_ins_cost is not specified then
+        default node insertion cost of 1 is used.
+
+    edge_subst_cost, edge_del_cost, edge_ins_cost : callable
+        Functions that return the costs of edge substitution, edge
+        deletion, and edge insertion, respectively.
+
+        The functions will be called like
+
+           edge_subst_cost(G1[u1][v1], G2[u2][v2]),
+           edge_del_cost(G1[u1][v1]),
+           edge_ins_cost(G2[u2][v2]).
+
+        That is, the functions will receive the edge attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function edge_subst_cost overrides edge_match if specified.
+        If neither edge_match nor edge_subst_cost are specified then
+        default edge substitution cost of 0 is used (edge attributes
+        are not considered during matching).
+
+        If edge_del_cost is not specified then default edge deletion
+        cost of 1 is used.  If edge_ins_cost is not specified then
+        default edge insertion cost of 1 is used.
+
+    roots : 2-tuple
+        Tuple where first element is a node in G1 and the second
+        is a node in G2.
+        These nodes are forced to be matched in the comparison to
+        allow comparison between rooted graphs.
+
+    upper_bound : numeric
+        Maximum edit distance to consider.  Return None if no edit
+        distance under or equal to upper_bound exists.
+
+    timeout : numeric
+        Maximum number of seconds to execute.
+        After timeout is met, the current best GED is returned.
+
+    Examples
+    --------
+    >>> G1 = nx.cycle_graph(6)
+    >>> G2 = nx.wheel_graph(7)
+    >>> nx.graph_edit_distance(G1, G2)
+    7.0
+
+    >>> G1 = nx.star_graph(5)
+    >>> G2 = nx.star_graph(5)
+    >>> nx.graph_edit_distance(G1, G2, roots=(0, 0))
+    0.0
+    >>> nx.graph_edit_distance(G1, G2, roots=(1, 0))
+    8.0
+
+    See Also
+    --------
+    optimal_edit_paths, optimize_graph_edit_distance,
+
+    is_isomorphic: test for graph edit distance of 0
+
+    References
+    ----------
+    .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
+       Martineau. An Exact Graph Edit Distance Algorithm for Solving
+       Pattern Recognition Problems. 4th International Conference on
+       Pattern Recognition Applications and Methods 2015, Jan 2015,
+       Lisbon, Portugal. 2015,
+       <10.5220/0005209202710278>. <hal-01168816>
+       https://hal.archives-ouvertes.fr/hal-01168816
+
+    """
+    bestcost = None
+    for _, _, cost in optimize_edit_paths(
+        G1,
+        G2,
+        node_match,
+        edge_match,
+        node_subst_cost,
+        node_del_cost,
+        node_ins_cost,
+        edge_subst_cost,
+        edge_del_cost,
+        edge_ins_cost,
+        upper_bound,
+        True,
+        roots,
+        timeout,
+    ):
+        # assert bestcost is None or cost < bestcost
+        bestcost = cost
+    return bestcost
+
+
+@nx._dispatch(graphs={"G1": 0, "G2": 1})
+def optimal_edit_paths(
+    G1,
+    G2,
+    node_match=None,
+    edge_match=None,
+    node_subst_cost=None,
+    node_del_cost=None,
+    node_ins_cost=None,
+    edge_subst_cost=None,
+    edge_del_cost=None,
+    edge_ins_cost=None,
+    upper_bound=None,
+):
+    """Returns all minimum-cost edit paths transforming G1 to G2.
+
+    Graph edit path is a sequence of node and edge edit operations
+    transforming graph G1 to graph isomorphic to G2.  Edit operations
+    include substitutions, deletions, and insertions.
+
+    Parameters
+    ----------
+    G1, G2: graphs
+        The two graphs G1 and G2 must be of the same type.
+
+    node_match : callable
+        A function that returns True if node n1 in G1 and n2 in G2
+        should be considered equal during matching.
+
+        The function will be called like
+
+           node_match(G1.nodes[n1], G2.nodes[n2]).
+
+        That is, the function will receive the node attribute
+        dictionaries for n1 and n2 as inputs.
+
+        Ignored if node_subst_cost is specified.  If neither
+        node_match nor node_subst_cost are specified then node
+        attributes are not considered.
+
+    edge_match : callable
+        A function that returns True if the edge attribute dictionaries
+        for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
+        be considered equal during matching.
+
+        The function will be called like
+
+           edge_match(G1[u1][v1], G2[u2][v2]).
+
+        That is, the function will receive the edge attribute
+        dictionaries of the edges under consideration.
+
+        Ignored if edge_subst_cost is specified.  If neither
+        edge_match nor edge_subst_cost are specified then edge
+        attributes are not considered.
+
+    node_subst_cost, node_del_cost, node_ins_cost : callable
+        Functions that return the costs of node substitution, node
+        deletion, and node insertion, respectively.
+
+        The functions will be called like
+
+           node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
+           node_del_cost(G1.nodes[n1]),
+           node_ins_cost(G2.nodes[n2]).
+
+        That is, the functions will receive the node attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function node_subst_cost overrides node_match if specified.
+        If neither node_match nor node_subst_cost are specified then
+        default node substitution cost of 0 is used (node attributes
+        are not considered during matching).
+
+        If node_del_cost is not specified then default node deletion
+        cost of 1 is used.  If node_ins_cost is not specified then
+        default node insertion cost of 1 is used.
+
+    edge_subst_cost, edge_del_cost, edge_ins_cost : callable
+        Functions that return the costs of edge substitution, edge
+        deletion, and edge insertion, respectively.
+
+        The functions will be called like
+
+           edge_subst_cost(G1[u1][v1], G2[u2][v2]),
+           edge_del_cost(G1[u1][v1]),
+           edge_ins_cost(G2[u2][v2]).
+
+        That is, the functions will receive the edge attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function edge_subst_cost overrides edge_match if specified.
+        If neither edge_match nor edge_subst_cost are specified then
+        default edge substitution cost of 0 is used (edge attributes
+        are not considered during matching).
+
+        If edge_del_cost is not specified then default edge deletion
+        cost of 1 is used.  If edge_ins_cost is not specified then
+        default edge insertion cost of 1 is used.
+
+    upper_bound : numeric
+        Maximum edit distance to consider.
+
+    Returns
+    -------
+    edit_paths : list of tuples (node_edit_path, edge_edit_path)
+        node_edit_path : list of tuples (u, v)
+        edge_edit_path : list of tuples ((u1, v1), (u2, v2))
+
+    cost : numeric
+        Optimal edit path cost (graph edit distance).
+
+    Examples
+    --------
+    >>> G1 = nx.cycle_graph(4)
+    >>> G2 = nx.wheel_graph(5)
+    >>> paths, cost = nx.optimal_edit_paths(G1, G2)
+    >>> len(paths)
+    40
+    >>> cost
+    5.0
+
+    See Also
+    --------
+    graph_edit_distance, optimize_edit_paths
+
+    References
+    ----------
+    .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
+       Martineau. An Exact Graph Edit Distance Algorithm for Solving
+       Pattern Recognition Problems. 4th International Conference on
+       Pattern Recognition Applications and Methods 2015, Jan 2015,
+       Lisbon, Portugal. 2015,
+       <10.5220/0005209202710278>. <hal-01168816>
+       https://hal.archives-ouvertes.fr/hal-01168816
+
+    """
+    paths = []
+    bestcost = None
+    for vertex_path, edge_path, cost in optimize_edit_paths(
+        G1,
+        G2,
+        node_match,
+        edge_match,
+        node_subst_cost,
+        node_del_cost,
+        node_ins_cost,
+        edge_subst_cost,
+        edge_del_cost,
+        edge_ins_cost,
+        upper_bound,
+        False,
+    ):
+        # assert bestcost is None or cost <= bestcost
+        if bestcost is not None and cost < bestcost:
+            paths = []
+        paths.append((vertex_path, edge_path))
+        bestcost = cost
+    return paths, bestcost
+
+
+@nx._dispatch(graphs={"G1": 0, "G2": 1})
+def optimize_graph_edit_distance(
+    G1,
+    G2,
+    node_match=None,
+    edge_match=None,
+    node_subst_cost=None,
+    node_del_cost=None,
+    node_ins_cost=None,
+    edge_subst_cost=None,
+    edge_del_cost=None,
+    edge_ins_cost=None,
+    upper_bound=None,
+):
+    """Returns consecutive approximations of GED (graph edit distance)
+    between graphs G1 and G2.
+
+    Graph edit distance is a graph similarity measure analogous to
+    Levenshtein distance for strings.  It is defined as minimum cost
+    of edit path (sequence of node and edge edit operations)
+    transforming graph G1 to graph isomorphic to G2.
+
+    Parameters
+    ----------
+    G1, G2: graphs
+        The two graphs G1 and G2 must be of the same type.
+
+    node_match : callable
+        A function that returns True if node n1 in G1 and n2 in G2
+        should be considered equal during matching.
+
+        The function will be called like
+
+           node_match(G1.nodes[n1], G2.nodes[n2]).
+
+        That is, the function will receive the node attribute
+        dictionaries for n1 and n2 as inputs.
+
+        Ignored if node_subst_cost is specified.  If neither
+        node_match nor node_subst_cost are specified then node
+        attributes are not considered.
+
+    edge_match : callable
+        A function that returns True if the edge attribute dictionaries
+        for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
+        be considered equal during matching.
+
+        The function will be called like
+
+           edge_match(G1[u1][v1], G2[u2][v2]).
+
+        That is, the function will receive the edge attribute
+        dictionaries of the edges under consideration.
+
+        Ignored if edge_subst_cost is specified.  If neither
+        edge_match nor edge_subst_cost are specified then edge
+        attributes are not considered.
+
+    node_subst_cost, node_del_cost, node_ins_cost : callable
+        Functions that return the costs of node substitution, node
+        deletion, and node insertion, respectively.
+
+        The functions will be called like
+
+           node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
+           node_del_cost(G1.nodes[n1]),
+           node_ins_cost(G2.nodes[n2]).
+
+        That is, the functions will receive the node attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function node_subst_cost overrides node_match if specified.
+        If neither node_match nor node_subst_cost are specified then
+        default node substitution cost of 0 is used (node attributes
+        are not considered during matching).
+
+        If node_del_cost is not specified then default node deletion
+        cost of 1 is used.  If node_ins_cost is not specified then
+        default node insertion cost of 1 is used.
+
+    edge_subst_cost, edge_del_cost, edge_ins_cost : callable
+        Functions that return the costs of edge substitution, edge
+        deletion, and edge insertion, respectively.
+
+        The functions will be called like
+
+           edge_subst_cost(G1[u1][v1], G2[u2][v2]),
+           edge_del_cost(G1[u1][v1]),
+           edge_ins_cost(G2[u2][v2]).
+
+        That is, the functions will receive the edge attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function edge_subst_cost overrides edge_match if specified.
+        If neither edge_match nor edge_subst_cost are specified then
+        default edge substitution cost of 0 is used (edge attributes
+        are not considered during matching).
+
+        If edge_del_cost is not specified then default edge deletion
+        cost of 1 is used.  If edge_ins_cost is not specified then
+        default edge insertion cost of 1 is used.
+
+    upper_bound : numeric
+        Maximum edit distance to consider.
+
+    Returns
+    -------
+    Generator of consecutive approximations of graph edit distance.
+
+    Examples
+    --------
+    >>> G1 = nx.cycle_graph(6)
+    >>> G2 = nx.wheel_graph(7)
+    >>> for v in nx.optimize_graph_edit_distance(G1, G2):
+    ...     minv = v
+    >>> minv
+    7.0
+
+    See Also
+    --------
+    graph_edit_distance, optimize_edit_paths
+
+    References
+    ----------
+    .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
+       Martineau. An Exact Graph Edit Distance Algorithm for Solving
+       Pattern Recognition Problems. 4th International Conference on
+       Pattern Recognition Applications and Methods 2015, Jan 2015,
+       Lisbon, Portugal. 2015,
+       <10.5220/0005209202710278>. <hal-01168816>
+       https://hal.archives-ouvertes.fr/hal-01168816
+    """
+    for _, _, cost in optimize_edit_paths(
+        G1,
+        G2,
+        node_match,
+        edge_match,
+        node_subst_cost,
+        node_del_cost,
+        node_ins_cost,
+        edge_subst_cost,
+        edge_del_cost,
+        edge_ins_cost,
+        upper_bound,
+        True,
+    ):
+        yield cost
+
+
+@nx._dispatch(
+    graphs={"G1": 0, "G2": 1}, preserve_edge_attrs=True, preserve_node_attrs=True
+)
+def optimize_edit_paths(
+    G1,
+    G2,
+    node_match=None,
+    edge_match=None,
+    node_subst_cost=None,
+    node_del_cost=None,
+    node_ins_cost=None,
+    edge_subst_cost=None,
+    edge_del_cost=None,
+    edge_ins_cost=None,
+    upper_bound=None,
+    strictly_decreasing=True,
+    roots=None,
+    timeout=None,
+):
+    """GED (graph edit distance) calculation: advanced interface.
+
+    Graph edit path is a sequence of node and edge edit operations
+    transforming graph G1 to graph isomorphic to G2.  Edit operations
+    include substitutions, deletions, and insertions.
+
+    Graph edit distance is defined as minimum cost of edit path.
+
+    Parameters
+    ----------
+    G1, G2: graphs
+        The two graphs G1 and G2 must be of the same type.
+
+    node_match : callable
+        A function that returns True if node n1 in G1 and n2 in G2
+        should be considered equal during matching.
+
+        The function will be called like
+
+           node_match(G1.nodes[n1], G2.nodes[n2]).
+
+        That is, the function will receive the node attribute
+        dictionaries for n1 and n2 as inputs.
+
+        Ignored if node_subst_cost is specified.  If neither
+        node_match nor node_subst_cost are specified then node
+        attributes are not considered.
+
+    edge_match : callable
+        A function that returns True if the edge attribute dictionaries
+        for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should
+        be considered equal during matching.
+
+        The function will be called like
+
+           edge_match(G1[u1][v1], G2[u2][v2]).
+
+        That is, the function will receive the edge attribute
+        dictionaries of the edges under consideration.
+
+        Ignored if edge_subst_cost is specified.  If neither
+        edge_match nor edge_subst_cost are specified then edge
+        attributes are not considered.
+
+    node_subst_cost, node_del_cost, node_ins_cost : callable
+        Functions that return the costs of node substitution, node
+        deletion, and node insertion, respectively.
+
+        The functions will be called like
+
+           node_subst_cost(G1.nodes[n1], G2.nodes[n2]),
+           node_del_cost(G1.nodes[n1]),
+           node_ins_cost(G2.nodes[n2]).
+
+        That is, the functions will receive the node attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function node_subst_cost overrides node_match if specified.
+        If neither node_match nor node_subst_cost are specified then
+        default node substitution cost of 0 is used (node attributes
+        are not considered during matching).
+
+        If node_del_cost is not specified then default node deletion
+        cost of 1 is used.  If node_ins_cost is not specified then
+        default node insertion cost of 1 is used.
+
+    edge_subst_cost, edge_del_cost, edge_ins_cost : callable
+        Functions that return the costs of edge substitution, edge
+        deletion, and edge insertion, respectively.
+
+        The functions will be called like
+
+           edge_subst_cost(G1[u1][v1], G2[u2][v2]),
+           edge_del_cost(G1[u1][v1]),
+           edge_ins_cost(G2[u2][v2]).
+
+        That is, the functions will receive the edge attribute
+        dictionaries as inputs.  The functions are expected to return
+        positive numeric values.
+
+        Function edge_subst_cost overrides edge_match if specified.
+        If neither edge_match nor edge_subst_cost are specified then
+        default edge substitution cost of 0 is used (edge attributes
+        are not considered during matching).
+
+        If edge_del_cost is not specified then default edge deletion
+        cost of 1 is used.  If edge_ins_cost is not specified then
+        default edge insertion cost of 1 is used.
+
+    upper_bound : numeric
+        Maximum edit distance to consider.
+
+    strictly_decreasing : bool
+        If True, return consecutive approximations of strictly
+        decreasing cost.  Otherwise, return all edit paths of cost
+        less than or equal to the previous minimum cost.
+
+    roots : 2-tuple
+        Tuple where first element is a node in G1 and the second
+        is a node in G2.
+        These nodes are forced to be matched in the comparison to
+        allow comparison between rooted graphs.
+
+    timeout : numeric
+        Maximum number of seconds to execute.
+        After timeout is met, the current best GED is returned.
+
+    Returns
+    -------
+    Generator of tuples (node_edit_path, edge_edit_path, cost)
+        node_edit_path : list of tuples (u, v)
+        edge_edit_path : list of tuples ((u1, v1), (u2, v2))
+        cost : numeric
+
+    See Also
+    --------
+    graph_edit_distance, optimize_graph_edit_distance, optimal_edit_paths
+
+    References
+    ----------
+    .. [1] Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick
+       Martineau. An Exact Graph Edit Distance Algorithm for Solving
+       Pattern Recognition Problems. 4th International Conference on
+       Pattern Recognition Applications and Methods 2015, Jan 2015,
+       Lisbon, Portugal. 2015,
+       <10.5220/0005209202710278>. <hal-01168816>
+       https://hal.archives-ouvertes.fr/hal-01168816
+
+    """
+    # TODO: support DiGraph
+
+    import numpy as np
+    import scipy as sp
+
+    @dataclass
+    class CostMatrix:
+        C: ...
+        lsa_row_ind: ...
+        lsa_col_ind: ...
+        ls: ...
+
+    def make_CostMatrix(C, m, n):
+        # assert(C.shape == (m + n, m + n))
+        lsa_row_ind, lsa_col_ind = sp.optimize.linear_sum_assignment(C)
+
+        # Fixup dummy assignments:
+        # each substitution i<->j should have dummy assignment m+j<->n+i
+        # NOTE: fast reduce of Cv relies on it
+        # assert len(lsa_row_ind) == len(lsa_col_ind)
+        indexes = zip(range(len(lsa_row_ind)), lsa_row_ind, lsa_col_ind)
+        subst_ind = [k for k, i, j in indexes if i < m and j < n]
+        indexes = zip(range(len(lsa_row_ind)), lsa_row_ind, lsa_col_ind)
+        dummy_ind = [k for k, i, j in indexes if i >= m and j >= n]
+        # assert len(subst_ind) == len(dummy_ind)
+        lsa_row_ind[dummy_ind] = lsa_col_ind[subst_ind] + m
+        lsa_col_ind[dummy_ind] = lsa_row_ind[subst_ind] + n
+
+        return CostMatrix(
+            C, lsa_row_ind, lsa_col_ind, C[lsa_row_ind, lsa_col_ind].sum()
+        )
+
+    def extract_C(C, i, j, m, n):
+        # assert(C.shape == (m + n, m + n))
+        row_ind = [k in i or k - m in j for k in range(m + n)]
+        col_ind = [k in j or k - n in i for k in range(m + n)]
+        return C[row_ind, :][:, col_ind]
+
+    def reduce_C(C, i, j, m, n):
+        # assert(C.shape == (m + n, m + n))
+        row_ind = [k not in i and k - m not in j for k in range(m + n)]
+        col_ind = [k not in j and k - n not in i for k in range(m + n)]
+        return C[row_ind, :][:, col_ind]
+
+    def reduce_ind(ind, i):
+        # assert set(ind) == set(range(len(ind)))
+        rind = ind[[k not in i for k in ind]]
+        for k in set(i):
+            rind[rind >= k] -= 1
+        return rind
+
+    def match_edges(u, v, pending_g, pending_h, Ce, matched_uv=None):
+        """
+        Parameters:
+            u, v: matched vertices, u=None or v=None for
+               deletion/insertion
+            pending_g, pending_h: lists of edges not yet mapped
+            Ce: CostMatrix of pending edge mappings
+            matched_uv: partial vertex edit path
+                list of tuples (u, v) of previously matched vertex
+                    mappings u<->v, u=None or v=None for
+                    deletion/insertion
+
+        Returns:
+            list of (i, j): indices of edge mappings g<->h
+            localCe: local CostMatrix of edge mappings
+                (basically submatrix of Ce at cross of rows i, cols j)
+        """
+        M = len(pending_g)
+        N = len(pending_h)
+        # assert Ce.C.shape == (M + N, M + N)
+
+        # only attempt to match edges after one node match has been made
+        # this will stop self-edges on the first node being automatically deleted
+        # even when a substitution is the better option
+        if matched_uv is None or len(matched_uv) == 0:
+            g_ind = []
+            h_ind = []
+        else:
+            g_ind = [
+                i
+                for i in range(M)
+                if pending_g[i][:2] == (u, u)
+                or any(
+                    pending_g[i][:2] in ((p, u), (u, p), (p, p)) for p, q in matched_uv
+                )
+            ]
+            h_ind = [
+                j
+                for j in range(N)
+                if pending_h[j][:2] == (v, v)
+                or any(
+                    pending_h[j][:2] in ((q, v), (v, q), (q, q)) for p, q in matched_uv
+                )
+            ]
+
+        m = len(g_ind)
+        n = len(h_ind)
+
+        if m or n:
+            C = extract_C(Ce.C, g_ind, h_ind, M, N)
+            # assert C.shape == (m + n, m + n)
+
+            # Forbid structurally invalid matches
+            # NOTE: inf remembered from Ce construction
+            for k, i in enumerate(g_ind):
+                g = pending_g[i][:2]
+                for l, j in enumerate(h_ind):
+                    h = pending_h[j][:2]
+                    if nx.is_directed(G1) or nx.is_directed(G2):
+                        if any(
+                            g == (p, u) and h == (q, v) or g == (u, p) and h == (v, q)
+                            for p, q in matched_uv
+                        ):
+                            continue
+                    else:
+                        if any(
+                            g in ((p, u), (u, p)) and h in ((q, v), (v, q))
+                            for p, q in matched_uv
+                        ):
+                            continue
+                    if g == (u, u) or any(g == (p, p) for p, q in matched_uv):
+                        continue
+                    if h == (v, v) or any(h == (q, q) for p, q in matched_uv):
+                        continue
+                    C[k, l] = inf
+
+            localCe = make_CostMatrix(C, m, n)
+            ij = [
+                (
+                    g_ind[k] if k < m else M + h_ind[l],
+                    h_ind[l] if l < n else N + g_ind[k],
+                )
+                for k, l in zip(localCe.lsa_row_ind, localCe.lsa_col_ind)
+                if k < m or l < n
+            ]
+
+        else:
+            ij = []
+            localCe = CostMatrix(np.empty((0, 0)), [], [], 0)
+
+        return ij, localCe
+
+    def reduce_Ce(Ce, ij, m, n):
+        if len(ij):
+            i, j = zip(*ij)
+            m_i = m - sum(1 for t in i if t < m)
+            n_j = n - sum(1 for t in j if t < n)
+            return make_CostMatrix(reduce_C(Ce.C, i, j, m, n), m_i, n_j)
+        return Ce
+
+    def get_edit_ops(
+        matched_uv, pending_u, pending_v, Cv, pending_g, pending_h, Ce, matched_cost
+    ):
+        """
+        Parameters:
+            matched_uv: partial vertex edit path
+                list of tuples (u, v) of vertex mappings u<->v,
+                u=None or v=None for deletion/insertion
+            pending_u, pending_v: lists of vertices not yet mapped
+            Cv: CostMatrix of pending vertex mappings
+            pending_g, pending_h: lists of edges not yet mapped
+            Ce: CostMatrix of pending edge mappings
+            matched_cost: cost of partial edit path
+
+        Returns:
+            sequence of
+                (i, j): indices of vertex mapping u<->v
+                Cv_ij: reduced CostMatrix of pending vertex mappings
+                    (basically Cv with row i, col j removed)
+                list of (x, y): indices of edge mappings g<->h
+                Ce_xy: reduced CostMatrix of pending edge mappings
+                    (basically Ce with rows x, cols y removed)
+                cost: total cost of edit operation
+            NOTE: most promising ops first
+        """
+        m = len(pending_u)
+        n = len(pending_v)
+        # assert Cv.C.shape == (m + n, m + n)
+
+        # 1) a vertex mapping from optimal linear sum assignment
+        i, j = min(
+            (k, l) for k, l in zip(Cv.lsa_row_ind, Cv.lsa_col_ind) if k < m or l < n
+        )
+        xy, localCe = match_edges(
+            pending_u[i] if i < m else None,
+            pending_v[j] if j < n else None,
+            pending_g,
+            pending_h,
+            Ce,
+            matched_uv,
+        )
+        Ce_xy = reduce_Ce(Ce, xy, len(pending_g), len(pending_h))
+        # assert Ce.ls <= localCe.ls + Ce_xy.ls
+        if prune(matched_cost + Cv.ls + localCe.ls + Ce_xy.ls):
+            pass
+        else:
+            # get reduced Cv efficiently
+            Cv_ij = CostMatrix(
+                reduce_C(Cv.C, (i,), (j,), m, n),
+                reduce_ind(Cv.lsa_row_ind, (i, m + j)),
+                reduce_ind(Cv.lsa_col_ind, (j, n + i)),
+                Cv.ls - Cv.C[i, j],
+            )
+            yield (i, j), Cv_ij, xy, Ce_xy, Cv.C[i, j] + localCe.ls
+
+        # 2) other candidates, sorted by lower-bound cost estimate
+        other = []
+        fixed_i, fixed_j = i, j
+        if m <= n:
+            candidates = (
+                (t, fixed_j)
+                for t in range(m + n)
+                if t != fixed_i and (t < m or t == m + fixed_j)
+            )
+        else:
+            candidates = (
+                (fixed_i, t)
+                for t in range(m + n)
+                if t != fixed_j and (t < n or t == n + fixed_i)
+            )
+        for i, j in candidates:
+            if prune(matched_cost + Cv.C[i, j] + Ce.ls):
+                continue
+            Cv_ij = make_CostMatrix(
+                reduce_C(Cv.C, (i,), (j,), m, n),
+                m - 1 if i < m else m,
+                n - 1 if j < n else n,
+            )
+            # assert Cv.ls <= Cv.C[i, j] + Cv_ij.ls
+            if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + Ce.ls):
+                continue
+            xy, localCe = match_edges(
+                pending_u[i] if i < m else None,
+                pending_v[j] if j < n else None,
+                pending_g,
+                pending_h,
+                Ce,
+                matched_uv,
+            )
+            if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + localCe.ls):
+                continue
+            Ce_xy = reduce_Ce(Ce, xy, len(pending_g), len(pending_h))
+            # assert Ce.ls <= localCe.ls + Ce_xy.ls
+            if prune(matched_cost + Cv.C[i, j] + Cv_ij.ls + localCe.ls + Ce_xy.ls):
+                continue
+            other.append(((i, j), Cv_ij, xy, Ce_xy, Cv.C[i, j] + localCe.ls))
+
+        yield from sorted(other, key=lambda t: t[4] + t[1].ls + t[3].ls)
+
+    def get_edit_paths(
+        matched_uv,
+        pending_u,
+        pending_v,
+        Cv,
+        matched_gh,
+        pending_g,
+        pending_h,
+        Ce,
+        matched_cost,
+    ):
+        """
+        Parameters:
+            matched_uv: partial vertex edit path
+                list of tuples (u, v) of vertex mappings u<->v,
+                u=None or v=None for deletion/insertion
+            pending_u, pending_v: lists of vertices not yet mapped
+            Cv: CostMatrix of pending vertex mappings
+            matched_gh: partial edge edit path
+                list of tuples (g, h) of edge mappings g<->h,
+                g=None or h=None for deletion/insertion
+            pending_g, pending_h: lists of edges not yet mapped
+            Ce: CostMatrix of pending edge mappings
+            matched_cost: cost of partial edit path
+
+        Returns:
+            sequence of (vertex_path, edge_path, cost)
+                vertex_path: complete vertex edit path
+                    list of tuples (u, v) of vertex mappings u<->v,
+                    u=None or v=None for deletion/insertion
+                edge_path: complete edge edit path
+                    list of tuples (g, h) of edge mappings g<->h,
+                    g=None or h=None for deletion/insertion
+                cost: total cost of edit path
+            NOTE: path costs are non-increasing
+        """
+        # debug_print('matched-uv:', matched_uv)
+        # debug_print('matched-gh:', matched_gh)
+        # debug_print('matched-cost:', matched_cost)
+        # debug_print('pending-u:', pending_u)
+        # debug_print('pending-v:', pending_v)
+        # debug_print(Cv.C)
+        # assert list(sorted(G1.nodes)) == list(sorted(list(u for u, v in matched_uv if u is not None) + pending_u))
+        # assert list(sorted(G2.nodes)) == list(sorted(list(v for u, v in matched_uv if v is not None) + pending_v))
+        # debug_print('pending-g:', pending_g)
+        # debug_print('pending-h:', pending_h)
+        # debug_print(Ce.C)
+        # assert list(sorted(G1.edges)) == list(sorted(list(g for g, h in matched_gh if g is not None) + pending_g))
+        # assert list(sorted(G2.edges)) == list(sorted(list(h for g, h in matched_gh if h is not None) + pending_h))
+        # debug_print()
+
+        if prune(matched_cost + Cv.ls + Ce.ls):
+            return
+
+        if not max(len(pending_u), len(pending_v)):
+            # assert not len(pending_g)
+            # assert not len(pending_h)
+            # path completed!
+            # assert matched_cost <= maxcost_value
+            nonlocal maxcost_value
+            maxcost_value = min(maxcost_value, matched_cost)
+            yield matched_uv, matched_gh, matched_cost
+
+        else:
+            edit_ops = get_edit_ops(
+                matched_uv,
+                pending_u,
+                pending_v,
+                Cv,
+                pending_g,
+                pending_h,
+                Ce,
+                matched_cost,
+            )
+            for ij, Cv_ij, xy, Ce_xy, edit_cost in edit_ops:
+                i, j = ij
+                # assert Cv.C[i, j] + sum(Ce.C[t] for t in xy) == edit_cost
+                if prune(matched_cost + edit_cost + Cv_ij.ls + Ce_xy.ls):
+                    continue
+
+                # dive deeper
+                u = pending_u.pop(i) if i < len(pending_u) else None
+                v = pending_v.pop(j) if j < len(pending_v) else None
+                matched_uv.append((u, v))
+                for x, y in xy:
+                    len_g = len(pending_g)
+                    len_h = len(pending_h)
+                    matched_gh.append(
+                        (
+                            pending_g[x] if x < len_g else None,
+                            pending_h[y] if y < len_h else None,
+                        )
+                    )
+                sortedx = sorted(x for x, y in xy)
+                sortedy = sorted(y for x, y in xy)
+                G = [
+                    (pending_g.pop(x) if x < len(pending_g) else None)
+                    for x in reversed(sortedx)
+                ]
+                H = [
+                    (pending_h.pop(y) if y < len(pending_h) else None)
+                    for y in reversed(sortedy)
+                ]
+
+                yield from get_edit_paths(
+                    matched_uv,
+                    pending_u,
+                    pending_v,
+                    Cv_ij,
+                    matched_gh,
+                    pending_g,
+                    pending_h,
+                    Ce_xy,
+                    matched_cost + edit_cost,
+                )
+
+                # backtrack
+                if u is not None:
+                    pending_u.insert(i, u)
+                if v is not None:
+                    pending_v.insert(j, v)
+                matched_uv.pop()
+                for x, g in zip(sortedx, reversed(G)):
+                    if g is not None:
+                        pending_g.insert(x, g)
+                for y, h in zip(sortedy, reversed(H)):
+                    if h is not None:
+                        pending_h.insert(y, h)
+                for _ in xy:
+                    matched_gh.pop()
+
+    # Initialization
+
+    pending_u = list(G1.nodes)
+    pending_v = list(G2.nodes)
+
+    initial_cost = 0
+    if roots:
+        root_u, root_v = roots
+        if root_u not in pending_u or root_v not in pending_v:
+            raise nx.NodeNotFound("Root node not in graph.")
+
+        # remove roots from pending
+        pending_u.remove(root_u)
+        pending_v.remove(root_v)
+
+    # cost matrix of vertex mappings
+    m = len(pending_u)
+    n = len(pending_v)
+    C = np.zeros((m + n, m + n))
+    if node_subst_cost:
+        C[0:m, 0:n] = np.array(
+            [
+                node_subst_cost(G1.nodes[u], G2.nodes[v])
+                for u in pending_u
+                for v in pending_v
+            ]
+        ).reshape(m, n)
+        if roots:
+            initial_cost = node_subst_cost(G1.nodes[root_u], G2.nodes[root_v])
+    elif node_match:
+        C[0:m, 0:n] = np.array(
+            [
+                1 - int(node_match(G1.nodes[u], G2.nodes[v]))
+                for u in pending_u
+                for v in pending_v
+            ]
+        ).reshape(m, n)
+        if roots:
+            initial_cost = 1 - node_match(G1.nodes[root_u], G2.nodes[root_v])
+    else:
+        # all zeroes
+        pass
+    # assert not min(m, n) or C[0:m, 0:n].min() >= 0
+    if node_del_cost:
+        del_costs = [node_del_cost(G1.nodes[u]) for u in pending_u]
+    else:
+        del_costs = [1] * len(pending_u)
+    # assert not m or min(del_costs) >= 0
+    if node_ins_cost:
+        ins_costs = [node_ins_cost(G2.nodes[v]) for v in pending_v]
+    else:
+        ins_costs = [1] * len(pending_v)
+    # assert not n or min(ins_costs) >= 0
+    inf = C[0:m, 0:n].sum() + sum(del_costs) + sum(ins_costs) + 1
+    C[0:m, n : n + m] = np.array(
+        [del_costs[i] if i == j else inf for i in range(m) for j in range(m)]
+    ).reshape(m, m)
+    C[m : m + n, 0:n] = np.array(
+        [ins_costs[i] if i == j else inf for i in range(n) for j in range(n)]
+    ).reshape(n, n)
+    Cv = make_CostMatrix(C, m, n)
+    # debug_print(f"Cv: {m} x {n}")
+    # debug_print(Cv.C)
+
+    pending_g = list(G1.edges)
+    pending_h = list(G2.edges)
+
+    # cost matrix of edge mappings
+    m = len(pending_g)
+    n = len(pending_h)
+    C = np.zeros((m + n, m + n))
+    if edge_subst_cost:
+        C[0:m, 0:n] = np.array(
+            [
+                edge_subst_cost(G1.edges[g], G2.edges[h])
+                for g in pending_g
+                for h in pending_h
+            ]
+        ).reshape(m, n)
+    elif edge_match:
+        C[0:m, 0:n] = np.array(
+            [
+                1 - int(edge_match(G1.edges[g], G2.edges[h]))
+                for g in pending_g
+                for h in pending_h
+            ]
+        ).reshape(m, n)
+    else:
+        # all zeroes
+        pass
+    # assert not min(m, n) or C[0:m, 0:n].min() >= 0
+    if edge_del_cost:
+        del_costs = [edge_del_cost(G1.edges[g]) for g in pending_g]
+    else:
+        del_costs = [1] * len(pending_g)
+    # assert not m or min(del_costs) >= 0
+    if edge_ins_cost:
+        ins_costs = [edge_ins_cost(G2.edges[h]) for h in pending_h]
+    else:
+        ins_costs = [1] * len(pending_h)
+    # assert not n or min(ins_costs) >= 0
+    inf = C[0:m, 0:n].sum() + sum(del_costs) + sum(ins_costs) + 1
+    C[0:m, n : n + m] = np.array(
+        [del_costs[i] if i == j else inf for i in range(m) for j in range(m)]
+    ).reshape(m, m)
+    C[m : m + n, 0:n] = np.array(
+        [ins_costs[i] if i == j else inf for i in range(n) for j in range(n)]
+    ).reshape(n, n)
+    Ce = make_CostMatrix(C, m, n)
+    # debug_print(f'Ce: {m} x {n}')
+    # debug_print(Ce.C)
+    # debug_print()
+
+    maxcost_value = Cv.C.sum() + Ce.C.sum() + 1
+
+    if timeout is not None:
+        if timeout <= 0:
+            raise nx.NetworkXError("Timeout value must be greater than 0")
+        start = time.perf_counter()
+
+    def prune(cost):
+        if timeout is not None:
+            if time.perf_counter() - start > timeout:
+                return True
+        if upper_bound is not None:
+            if cost > upper_bound:
+                return True
+        if cost > maxcost_value:
+            return True
+        if strictly_decreasing and cost >= maxcost_value:
+            return True
+        return False
+
+    # Now go!
+
+    done_uv = [] if roots is None else [roots]
+
+    for vertex_path, edge_path, cost in get_edit_paths(
+        done_uv, pending_u, pending_v, Cv, [], pending_g, pending_h, Ce, initial_cost
+    ):
+        # assert sorted(G1.nodes) == sorted(u for u, v in vertex_path if u is not None)
+        # assert sorted(G2.nodes) == sorted(v for u, v in vertex_path if v is not None)
+        # assert sorted(G1.edges) == sorted(g for g, h in edge_path if g is not None)
+        # assert sorted(G2.edges) == sorted(h for g, h in edge_path if h is not None)
+        # print(vertex_path, edge_path, cost, file = sys.stderr)
+        # assert cost == maxcost_value
+        yield list(vertex_path), list(edge_path), cost
+
+
+@nx._dispatch
+def simrank_similarity(
+    G,
+    source=None,
+    target=None,
+    importance_factor=0.9,
+    max_iterations=1000,
+    tolerance=1e-4,
+):
+    """Returns the SimRank similarity of nodes in the graph ``G``.
+
+    SimRank is a similarity metric that says "two objects are considered
+    to be similar if they are referenced by similar objects." [1]_.
+
+    The pseudo-code definition from the paper is::
+
+        def simrank(G, u, v):
+            in_neighbors_u = G.predecessors(u)
+            in_neighbors_v = G.predecessors(v)
+            scale = C / (len(in_neighbors_u) * len(in_neighbors_v))
+            return scale * sum(simrank(G, w, x)
+                               for w, x in product(in_neighbors_u,
+                                                   in_neighbors_v))
+
+    where ``G`` is the graph, ``u`` is the source, ``v`` is the target,
+    and ``C`` is a float decay or importance factor between 0 and 1.
+
+    The SimRank algorithm for determining node similarity is defined in
+    [2]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A NetworkX graph
+
+    source : node
+        If this is specified, the returned dictionary maps each node
+        ``v`` in the graph to the similarity between ``source`` and
+        ``v``.
+
+    target : node
+        If both ``source`` and ``target`` are specified, the similarity
+        value between ``source`` and ``target`` is returned. If
+        ``target`` is specified but ``source`` is not, this argument is
+        ignored.
+
+    importance_factor : float
+        The relative importance of indirect neighbors with respect to
+        direct neighbors.
+
+    max_iterations : integer
+        Maximum number of iterations.
+
+    tolerance : float
+        Error tolerance used to check convergence. When an iteration of
+        the algorithm finds that no similarity value changes more than
+        this amount, the algorithm halts.
+
+    Returns
+    -------
+    similarity : dictionary or float
+        If ``source`` and ``target`` are both ``None``, this returns a
+        dictionary of dictionaries, where keys are node pairs and value
+        are similarity of the pair of nodes.
+
+        If ``source`` is not ``None`` but ``target`` is, this returns a
+        dictionary mapping node to the similarity of ``source`` and that
+        node.
+
+        If neither ``source`` nor ``target`` is ``None``, this returns
+        the similarity value for the given pair of nodes.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(2)
+    >>> nx.simrank_similarity(G)
+    {0: {0: 1.0, 1: 0.0}, 1: {0: 0.0, 1: 1.0}}
+    >>> nx.simrank_similarity(G, source=0)
+    {0: 1.0, 1: 0.0}
+    >>> nx.simrank_similarity(G, source=0, target=0)
+    1.0
+
+    The result of this function can be converted to a numpy array
+    representing the SimRank matrix by using the node order of the
+    graph to determine which row and column represent each node.
+    Other ordering of nodes is also possible.
+
+    >>> import numpy as np
+    >>> sim = nx.simrank_similarity(G)
+    >>> np.array([[sim[u][v] for v in G] for u in G])
+    array([[1., 0.],
+           [0., 1.]])
+    >>> sim_1d = nx.simrank_similarity(G, source=0)
+    >>> np.array([sim[0][v] for v in G])
+    array([1., 0.])
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/SimRank
+    .. [2] G. Jeh and J. Widom.
+           "SimRank: a measure of structural-context similarity",
+           In KDD'02: Proceedings of the Eighth ACM SIGKDD
+           International Conference on Knowledge Discovery and Data Mining,
+           pp. 538--543. ACM Press, 2002.
+    """
+    import numpy as np
+
+    nodelist = list(G)
+    s_indx = None if source is None else nodelist.index(source)
+    t_indx = None if target is None else nodelist.index(target)
+
+    x = _simrank_similarity_numpy(
+        G, s_indx, t_indx, importance_factor, max_iterations, tolerance
+    )
+
+    if isinstance(x, np.ndarray):
+        if x.ndim == 1:
+            return dict(zip(G, x))
+        # else x.ndim == 2
+        return {u: dict(zip(G, row)) for u, row in zip(G, x)}
+    return x
+
+
+def _simrank_similarity_python(
+    G,
+    source=None,
+    target=None,
+    importance_factor=0.9,
+    max_iterations=1000,
+    tolerance=1e-4,
+):
+    """Returns the SimRank similarity of nodes in the graph ``G``.
+
+    This pure Python version is provided for pedagogical purposes.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(2)
+    >>> nx.similarity._simrank_similarity_python(G)
+    {0: {0: 1, 1: 0.0}, 1: {0: 0.0, 1: 1}}
+    >>> nx.similarity._simrank_similarity_python(G, source=0)
+    {0: 1, 1: 0.0}
+    >>> nx.similarity._simrank_similarity_python(G, source=0, target=0)
+    1
+    """
+    # build up our similarity adjacency dictionary output
+    newsim = {u: {v: 1 if u == v else 0 for v in G} for u in G}
+
+    # These functions compute the update to the similarity value of the nodes
+    # `u` and `v` with respect to the previous similarity values.
+    def avg_sim(s):
+        return sum(newsim[w][x] for (w, x) in s) / len(s) if s else 0.0
+
+    Gadj = G.pred if G.is_directed() else G.adj
+
+    def sim(u, v):
+        return importance_factor * avg_sim(list(product(Gadj[u], Gadj[v])))
+
+    for its in range(max_iterations):
+        oldsim = newsim
+        newsim = {u: {v: sim(u, v) if u != v else 1 for v in G} for u in G}
+        is_close = all(
+            all(
+                abs(newsim[u][v] - old) <= tolerance * (1 + abs(old))
+                for v, old in nbrs.items()
+            )
+            for u, nbrs in oldsim.items()
+        )
+        if is_close:
+            break
+
+    if its + 1 == max_iterations:
+        raise nx.ExceededMaxIterations(
+            f"simrank did not converge after {max_iterations} iterations."
+        )
+
+    if source is not None and target is not None:
+        return newsim[source][target]
+    if source is not None:
+        return newsim[source]
+    return newsim
+
+
+def _simrank_similarity_numpy(
+    G,
+    source=None,
+    target=None,
+    importance_factor=0.9,
+    max_iterations=1000,
+    tolerance=1e-4,
+):
+    """Calculate SimRank of nodes in ``G`` using matrices with ``numpy``.
+
+    The SimRank algorithm for determining node similarity is defined in
+    [1]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A NetworkX graph
+
+    source : node
+        If this is specified, the returned dictionary maps each node
+        ``v`` in the graph to the similarity between ``source`` and
+        ``v``.
+
+    target : node
+        If both ``source`` and ``target`` are specified, the similarity
+        value between ``source`` and ``target`` is returned. If
+        ``target`` is specified but ``source`` is not, this argument is
+        ignored.
+
+    importance_factor : float
+        The relative importance of indirect neighbors with respect to
+        direct neighbors.
+
+    max_iterations : integer
+        Maximum number of iterations.
+
+    tolerance : float
+        Error tolerance used to check convergence. When an iteration of
+        the algorithm finds that no similarity value changes more than
+        this amount, the algorithm halts.
+
+    Returns
+    -------
+    similarity : numpy array or float
+        If ``source`` and ``target`` are both ``None``, this returns a
+        2D array containing SimRank scores of the nodes.
+
+        If ``source`` is not ``None`` but ``target`` is, this returns an
+        1D array containing SimRank scores of ``source`` and that
+        node.
+
+        If neither ``source`` nor ``target`` is ``None``, this returns
+        the similarity value for the given pair of nodes.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(2)
+    >>> nx.similarity._simrank_similarity_numpy(G)
+    array([[1., 0.],
+           [0., 1.]])
+    >>> nx.similarity._simrank_similarity_numpy(G, source=0)
+    array([1., 0.])
+    >>> nx.similarity._simrank_similarity_numpy(G, source=0, target=0)
+    1.0
+
+    References
+    ----------
+    .. [1] G. Jeh and J. Widom.
+           "SimRank: a measure of structural-context similarity",
+           In KDD'02: Proceedings of the Eighth ACM SIGKDD
+           International Conference on Knowledge Discovery and Data Mining,
+           pp. 538--543. ACM Press, 2002.
+    """
+    # This algorithm follows roughly
+    #
+    #     S = max{C * (A.T * S * A), I}
+    #
+    # where C is the importance factor, A is the column normalized
+    # adjacency matrix, and I is the identity matrix.
+    import numpy as np
+
+    adjacency_matrix = nx.to_numpy_array(G)
+
+    # column-normalize the ``adjacency_matrix``
+    s = np.array(adjacency_matrix.sum(axis=0))
+    s[s == 0] = 1
+    adjacency_matrix /= s  # adjacency_matrix.sum(axis=0)
+
+    newsim = np.eye(len(G), dtype=np.float64)
+    for its in range(max_iterations):
+        prevsim = newsim.copy()
+        newsim = importance_factor * ((adjacency_matrix.T @ prevsim) @ adjacency_matrix)
+        np.fill_diagonal(newsim, 1.0)
+
+        if np.allclose(prevsim, newsim, atol=tolerance):
+            break
+
+    if its + 1 == max_iterations:
+        raise nx.ExceededMaxIterations(
+            f"simrank did not converge after {max_iterations} iterations."
+        )
+
+    if source is not None and target is not None:
+        return newsim[source, target]
+    if source is not None:
+        return newsim[source]
+    return newsim
+
+
+@nx._dispatch(edge_attrs="weight")
+def panther_similarity(
+    G, source, k=5, path_length=5, c=0.5, delta=0.1, eps=None, weight="weight"
+):
+    r"""Returns the Panther similarity of nodes in the graph `G` to node ``v``.
+
+    Panther is a similarity metric that says "two objects are considered
+    to be similar if they frequently appear on the same paths." [1]_.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A NetworkX graph
+    source : node
+        Source node for which to find the top `k` similar other nodes
+    k : int (default = 5)
+        The number of most similar nodes to return
+    path_length : int (default = 5)
+        How long the randomly generated paths should be (``T`` in [1]_)
+    c : float (default = 0.5)
+        A universal positive constant used to scale the number
+        of sample random paths to generate.
+    delta : float (default = 0.1)
+        The probability that the similarity $S$ is not an epsilon-approximation to (R, phi),
+        where $R$ is the number of random paths and $\phi$ is the probability
+        that an element sampled from a set $A \subseteq D$, where $D$ is the domain.
+    eps : float or None (default = None)
+        The error bound. Per [1]_, a good value is ``sqrt(1/|E|)``. Therefore,
+        if no value is provided, the recommended computed value will be used.
+    weight : string or None, optional (default="weight")
+        The name of an edge attribute that holds the numerical value
+        used as a weight. If None then each edge has weight 1.
+
+    Returns
+    -------
+    similarity : dictionary
+        Dictionary of nodes to similarity scores (as floats). Note:
+        the self-similarity (i.e., ``v``) will not be included in
+        the returned dictionary.
+
+    Examples
+    --------
+    >>> G = nx.star_graph(10)
+    >>> sim = nx.panther_similarity(G, 0)
+
+    References
+    ----------
+    .. [1] Zhang, J., Tang, J., Ma, C., Tong, H., Jing, Y., & Li, J.
+           Panther: Fast top-k similarity search on large networks.
+           In Proceedings of the ACM SIGKDD International Conference
+           on Knowledge Discovery and Data Mining (Vol. 2015-August, pp. 1445–1454).
+           Association for Computing Machinery. https://doi.org/10.1145/2783258.2783267.
+    """
+    import numpy as np
+
+    num_nodes = G.number_of_nodes()
+    if num_nodes < k:
+        warnings.warn(
+            f"Number of nodes is {num_nodes}, but requested k is {k}. "
+            "Setting k to number of nodes."
+        )
+        k = num_nodes
+    # According to [1], they empirically determined
+    # a good value for ``eps`` to be sqrt( 1 / |E| )
+    if eps is None:
+        eps = np.sqrt(1.0 / G.number_of_edges())
+
+    inv_node_map = {name: index for index, name in enumerate(G.nodes)}
+    node_map = np.array(G)
+
+    # Calculate the sample size ``R`` for how many paths
+    # to randomly generate
+    t_choose_2 = math.comb(path_length, 2)
+    sample_size = int((c / eps**2) * (np.log2(t_choose_2) + 1 + np.log(1 / delta)))
+    index_map = {}
+    _ = list(
+        generate_random_paths(
+            G, sample_size, path_length=path_length, index_map=index_map, weight=weight
+        )
+    )
+    S = np.zeros(num_nodes)
+
+    inv_sample_size = 1 / sample_size
+
+    source_paths = set(index_map[source])
+
+    # Calculate the path similarities
+    # between ``source`` (v) and ``node`` (v_j)
+    # using our inverted index mapping of
+    # vertices to paths
+    for node, paths in index_map.items():
+        # Only consider paths where both
+        # ``node`` and ``source`` are present
+        common_paths = source_paths.intersection(paths)
+        S[inv_node_map[node]] = len(common_paths) * inv_sample_size
+
+    # Retrieve top ``k`` similar
+    # Note: the below performed anywhere from 4-10x faster
+    # (depending on input sizes) vs the equivalent ``np.argsort(S)[::-1]``
+    top_k_unsorted = np.argpartition(S, -k)[-k:]
+    top_k_sorted = top_k_unsorted[np.argsort(S[top_k_unsorted])][::-1]
+
+    # Add back the similarity scores
+    top_k_sorted_names = (node_map[n] for n in top_k_sorted)
+    top_k_with_val = dict(zip(top_k_sorted_names, S[top_k_sorted]))
+
+    # Remove the self-similarity
+    top_k_with_val.pop(source, None)
+    return top_k_with_val
+
+
+@nx._dispatch(edge_attrs="weight")
+def generate_random_paths(
+    G, sample_size, path_length=5, index_map=None, weight="weight"
+):
+    """Randomly generate `sample_size` paths of length `path_length`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A NetworkX graph
+    sample_size : integer
+        The number of paths to generate. This is ``R`` in [1]_.
+    path_length : integer (default = 5)
+        The maximum size of the path to randomly generate.
+        This is ``T`` in [1]_. According to the paper, ``T >= 5`` is
+        recommended.
+    index_map : dictionary, optional
+        If provided, this will be populated with the inverted
+        index of nodes mapped to the set of generated random path
+        indices within ``paths``.
+    weight : string or None, optional (default="weight")
+        The name of an edge attribute that holds the numerical value
+        used as a weight. If None then each edge has weight 1.
+
+    Returns
+    -------
+    paths : generator of lists
+        Generator of `sample_size` paths each with length `path_length`.
+
+    Examples
+    --------
+    Note that the return value is the list of paths:
+
+    >>> G = nx.star_graph(3)
+    >>> random_path = nx.generate_random_paths(G, 2)
+
+    By passing a dictionary into `index_map`, it will build an
+    inverted index mapping of nodes to the paths in which that node is present:
+
+    >>> G = nx.star_graph(3)
+    >>> index_map = {}
+    >>> random_path = nx.generate_random_paths(G, 3, index_map=index_map)
+    >>> paths_containing_node_0 = [random_path[path_idx] for path_idx in index_map.get(0, [])]
+
+    References
+    ----------
+    .. [1] Zhang, J., Tang, J., Ma, C., Tong, H., Jing, Y., & Li, J.
+           Panther: Fast top-k similarity search on large networks.
+           In Proceedings of the ACM SIGKDD International Conference
+           on Knowledge Discovery and Data Mining (Vol. 2015-August, pp. 1445–1454).
+           Association for Computing Machinery. https://doi.org/10.1145/2783258.2783267.
+    """
+    import numpy as np
+
+    # Calculate transition probabilities between
+    # every pair of vertices according to Eq. (3)
+    adj_mat = nx.to_numpy_array(G, weight=weight)
+    inv_row_sums = np.reciprocal(adj_mat.sum(axis=1)).reshape(-1, 1)
+    transition_probabilities = adj_mat * inv_row_sums
+
+    node_map = np.array(G)
+    num_nodes = G.number_of_nodes()
+
+    for path_index in range(sample_size):
+        # Sample current vertex v = v_i uniformly at random
+        node_index = np.random.randint(0, high=num_nodes)
+        node = node_map[node_index]
+
+        # Add v into p_r and add p_r into the path set
+        # of v, i.e., P_v
+        path = [node]
+
+        # Build the inverted index (P_v) of vertices to paths
+        if index_map is not None:
+            if node in index_map:
+                index_map[node].add(path_index)
+            else:
+                index_map[node] = {path_index}
+
+        starting_index = node_index
+        for _ in range(path_length):
+            # Randomly sample a neighbor (v_j) according
+            # to transition probabilities from ``node`` (v) to its neighbors
+            neighbor_index = np.random.choice(
+                num_nodes, p=transition_probabilities[starting_index]
+            )
+
+            # Set current vertex (v = v_j)
+            starting_index = neighbor_index
+
+            # Add v into p_r
+            neighbor_node = node_map[neighbor_index]
+            path.append(neighbor_node)
+
+            # Add p_r into P_v
+            if index_map is not None:
+                if neighbor_node in index_map:
+                    index_map[neighbor_node].add(path_index)
+                else:
+                    index_map[neighbor_node] = {path_index}
+
+        yield path

tuning-competition-baseline/.venv/lib/python3.11/site-packages/networkx/algorithms/sparsifiers.py

@@ -0,0 +1,295 @@
+"""Functions for computing sparsifiers of graphs."""
+import math
+
+import networkx as nx
+from networkx.utils import not_implemented_for, py_random_state
+
+__all__ = ["spanner"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@py_random_state(3)
+@nx._dispatch(edge_attrs="weight")
+def spanner(G, stretch, weight=None, seed=None):
+    """Returns a spanner of the given graph with the given stretch.
+
+    A spanner of a graph G = (V, E) with stretch t is a subgraph
+    H = (V, E_S) such that E_S is a subset of E and the distance between
+    any pair of nodes in H is at most t times the distance between the
+    nodes in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected simple graph.
+
+    stretch : float
+        The stretch of the spanner.
+
+    weight : object
+        The edge attribute to use as distance.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    NetworkX graph
+        A spanner of the given graph with the given stretch.
+
+    Raises
+    ------
+    ValueError
+        If a stretch less than 1 is given.
+
+    Notes
+    -----
+    This function implements the spanner algorithm by Baswana and Sen,
+    see [1].
+
+    This algorithm is a randomized las vegas algorithm: The expected
+    running time is O(km) where k = (stretch + 1) // 2 and m is the
+    number of edges in G. The returned graph is always a spanner of the
+    given graph with the specified stretch. For weighted graphs the
+    number of edges in the spanner is O(k * n^(1 + 1 / k)) where k is
+    defined as above and n is the number of nodes in G. For unweighted
+    graphs the number of edges is O(n^(1 + 1 / k) + kn).
+
+    References
+    ----------
+    [1] S. Baswana, S. Sen. A Simple and Linear Time Randomized
+    Algorithm for Computing Sparse Spanners in Weighted Graphs.
+    Random Struct. Algorithms 30(4): 532-563 (2007).
+    """
+    if stretch < 1:
+        raise ValueError("stretch must be at least 1")
+
+    k = (stretch + 1) // 2
+
+    # initialize spanner H with empty edge set
+    H = nx.empty_graph()
+    H.add_nodes_from(G.nodes)
+
+    # phase 1: forming the clusters
+    # the residual graph has V' from the paper as its node set
+    # and E' from the paper as its edge set
+    residual_graph = _setup_residual_graph(G, weight)
+    # clustering is a dictionary that maps nodes in a cluster to the
+    # cluster center
+    clustering = {v: v for v in G.nodes}
+    sample_prob = math.pow(G.number_of_nodes(), -1 / k)
+    size_limit = 2 * math.pow(G.number_of_nodes(), 1 + 1 / k)
+
+    i = 0
+    while i < k - 1:
+        # step 1: sample centers
+        sampled_centers = set()
+        for center in set(clustering.values()):
+            if seed.random() < sample_prob:
+                sampled_centers.add(center)
+
+        # combined loop for steps 2 and 3
+        edges_to_add = set()
+        edges_to_remove = set()
+        new_clustering = {}
+        for v in residual_graph.nodes:
+            if clustering[v] in sampled_centers:
+                continue
+
+            # step 2: find neighboring (sampled) clusters and
+            # lightest edges to them
+            lightest_edge_neighbor, lightest_edge_weight = _lightest_edge_dicts(
+                residual_graph, clustering, v
+            )
+            neighboring_sampled_centers = (
+                set(lightest_edge_weight.keys()) & sampled_centers
+            )
+
+            # step 3: add edges to spanner
+            if not neighboring_sampled_centers:
+                # connect to each neighboring center via lightest edge
+                for neighbor in lightest_edge_neighbor.values():
+                    edges_to_add.add((v, neighbor))
+                # remove all incident edges
+                for neighbor in residual_graph.adj[v]:
+                    edges_to_remove.add((v, neighbor))
+
+            else:  # there is a neighboring sampled center
+                closest_center = min(
+                    neighboring_sampled_centers, key=lightest_edge_weight.get
+                )
+                closest_center_weight = lightest_edge_weight[closest_center]
+                closest_center_neighbor = lightest_edge_neighbor[closest_center]
+
+                edges_to_add.add((v, closest_center_neighbor))
+                new_clustering[v] = closest_center
+
+                # connect to centers with edge weight less than
+                # closest_center_weight
+                for center, edge_weight in lightest_edge_weight.items():
+                    if edge_weight < closest_center_weight:
+                        neighbor = lightest_edge_neighbor[center]
+                        edges_to_add.add((v, neighbor))
+
+                # remove edges to centers with edge weight less than
+                # closest_center_weight
+                for neighbor in residual_graph.adj[v]:
+                    neighbor_cluster = clustering[neighbor]
+                    neighbor_weight = lightest_edge_weight[neighbor_cluster]
+                    if (
+                        neighbor_cluster == closest_center
+                        or neighbor_weight < closest_center_weight
+                    ):
+                        edges_to_remove.add((v, neighbor))
+
+        # check whether iteration added too many edges to spanner,
+        # if so repeat
+        if len(edges_to_add) > size_limit:
+            # an iteration is repeated O(1) times on expectation
+            continue
+
+        # iteration succeeded
+        i = i + 1
+
+        # actually add edges to spanner
+        for u, v in edges_to_add:
+            _add_edge_to_spanner(H, residual_graph, u, v, weight)
+
+        # actually delete edges from residual graph
+        residual_graph.remove_edges_from(edges_to_remove)
+
+        # copy old clustering data to new_clustering
+        for node, center in clustering.items():
+            if center in sampled_centers:
+                new_clustering[node] = center
+        clustering = new_clustering
+
+        # step 4: remove intra-cluster edges
+        for u in residual_graph.nodes:
+            for v in list(residual_graph.adj[u]):
+                if clustering[u] == clustering[v]:
+                    residual_graph.remove_edge(u, v)
+
+        # update residual graph node set
+        for v in list(residual_graph.nodes):
+            if v not in clustering:
+                residual_graph.remove_node(v)
+
+    # phase 2: vertex-cluster joining
+    for v in residual_graph.nodes:
+        lightest_edge_neighbor, _ = _lightest_edge_dicts(residual_graph, clustering, v)
+        for neighbor in lightest_edge_neighbor.values():
+            _add_edge_to_spanner(H, residual_graph, v, neighbor, weight)
+
+    return H
+
+
+def _setup_residual_graph(G, weight):
+    """Setup residual graph as a copy of G with unique edges weights.
+
+    The node set of the residual graph corresponds to the set V' from
+    the Baswana-Sen paper and the edge set corresponds to the set E'
+    from the paper.
+
+    This function associates distinct weights to the edges of the
+    residual graph (even for unweighted input graphs), as required by
+    the algorithm.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        An undirected simple graph.
+
+    weight : object
+        The edge attribute to use as distance.
+
+    Returns
+    -------
+    NetworkX graph
+        The residual graph used for the Baswana-Sen algorithm.
+    """
+    residual_graph = G.copy()
+
+    # establish unique edge weights, even for unweighted graphs
+    for u, v in G.edges():
+        if not weight:
+            residual_graph[u][v]["weight"] = (id(u), id(v))
+        else:
+            residual_graph[u][v]["weight"] = (G[u][v][weight], id(u), id(v))
+
+    return residual_graph
+
+
+def _lightest_edge_dicts(residual_graph, clustering, node):
+    """Find the lightest edge to each cluster.
+
+    Searches for the minimum-weight edge to each cluster adjacent to
+    the given node.
+
+    Parameters
+    ----------
+    residual_graph : NetworkX graph
+        The residual graph used by the Baswana-Sen algorithm.
+
+    clustering : dictionary
+        The current clustering of the nodes.
+
+    node : node
+        The node from which the search originates.
+
+    Returns
+    -------
+    lightest_edge_neighbor, lightest_edge_weight : dictionary, dictionary
+        lightest_edge_neighbor is a dictionary that maps a center C to
+        a node v in the corresponding cluster such that the edge from
+        the given node to v is the lightest edge from the given node to
+        any node in cluster. lightest_edge_weight maps a center C to the
+        weight of the aforementioned edge.
+
+    Notes
+    -----
+    If a cluster has no node that is adjacent to the given node in the
+    residual graph then the center of the cluster is not a key in the
+    returned dictionaries.
+    """
+    lightest_edge_neighbor = {}
+    lightest_edge_weight = {}
+    for neighbor in residual_graph.adj[node]:
+        neighbor_center = clustering[neighbor]
+        weight = residual_graph[node][neighbor]["weight"]
+        if (
+            neighbor_center not in lightest_edge_weight
+            or weight < lightest_edge_weight[neighbor_center]
+        ):
+            lightest_edge_neighbor[neighbor_center] = neighbor
+            lightest_edge_weight[neighbor_center] = weight
+    return lightest_edge_neighbor, lightest_edge_weight
+
+
+def _add_edge_to_spanner(H, residual_graph, u, v, weight):
+    """Add the edge {u, v} to the spanner H and take weight from
+    the residual graph.
+
+    Parameters
+    ----------
+    H : NetworkX graph
+        The spanner under construction.
+
+    residual_graph : NetworkX graph
+        The residual graph used by the Baswana-Sen algorithm. The weight
+        for the edge is taken from this graph.
+
+    u : node
+        One endpoint of the edge.
+
+    v : node
+        The other endpoint of the edge.
+
+    weight : object
+        The edge attribute to use as distance.
+    """
+    H.add_edge(u, v)
+    if weight:
+        H[u][v][weight] = residual_graph[u][v]["weight"][0]