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

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+"""Distance measures approximated metrics."""
+
+import networkx as nx
+from networkx.utils.decorators import py_random_state
+
+__all__ = ["diameter"]
+
+
+@py_random_state(1)
+@nx._dispatch(name="approximate_diameter")
+def diameter(G, seed=None):
+    """Returns a lower bound on the diameter of the graph G.
+
+    The function computes a lower bound on the diameter (i.e., the maximum eccentricity)
+    of a directed or undirected graph G. The procedure used varies depending on the graph
+    being directed or not.
+
+    If G is an `undirected` graph, then the function uses the `2-sweep` algorithm [1]_.
+    The main idea is to pick the farthest node from a random node and return its eccentricity.
+
+    Otherwise, if G is a `directed` graph, the function uses the `2-dSweep` algorithm [2]_,
+    The procedure starts by selecting a random source node $s$ from which it performs a
+    forward and a backward BFS. Let $a_1$ and $a_2$ be the farthest nodes in the forward and
+    backward cases, respectively. Then, it computes the backward eccentricity of $a_1$ using
+    a backward BFS and the forward eccentricity of $a_2$ using a forward BFS.
+    Finally, it returns the best lower bound between the two.
+
+    In both cases, the time complexity is linear with respect to the size of G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    d : integer
+       Lower Bound on the Diameter of G
+
+    Raises
+    ------
+    NetworkXError
+        If the graph is empty or
+        If the graph is undirected and not connected or
+        If the graph is directed and not strongly connected.
+
+    See Also
+    --------
+    networkx.algorithms.distance_measures.diameter
+
+    References
+    ----------
+    .. [1] Magnien, Clémence, Matthieu Latapy, and Michel Habib.
+       *Fast computation of empirically tight bounds for the diameter of massive graphs.*
+       Journal of Experimental Algorithmics (JEA), 2009.
+       https://arxiv.org/pdf/0904.2728.pdf
+    .. [2] Crescenzi, Pierluigi, Roberto Grossi, Leonardo Lanzi, and Andrea Marino.
+       *On computing the diameter of real-world directed (weighted) graphs.*
+       International Symposium on Experimental Algorithms. Springer, Berlin, Heidelberg, 2012.
+       https://courses.cs.ut.ee/MTAT.03.238/2014_fall/uploads/Main/diameter.pdf
+    """
+    # if G is empty
+    if not G:
+        raise nx.NetworkXError("Expected non-empty NetworkX graph!")
+    # if there's only a node
+    if G.number_of_nodes() == 1:
+        return 0
+    # if G is directed
+    if G.is_directed():
+        return _two_sweep_directed(G, seed)
+    # else if G is undirected
+    return _two_sweep_undirected(G, seed)
+
+
+def _two_sweep_undirected(G, seed):
+    """Helper function for finding a lower bound on the diameter
+        for undirected Graphs.
+
+        The idea is to pick the farthest node from a random node
+        and return its eccentricity.
+
+        ``G`` is a NetworkX undirected graph.
+
+    .. note::
+
+        ``seed`` is a random.Random or numpy.random.RandomState instance
+    """
+    # select a random source node
+    source = seed.choice(list(G))
+    # get the distances to the other nodes
+    distances = nx.shortest_path_length(G, source)
+    # if some nodes have not been visited, then the graph is not connected
+    if len(distances) != len(G):
+        raise nx.NetworkXError("Graph not connected.")
+    # take a node that is (one of) the farthest nodes from the source
+    *_, node = distances
+    # return the eccentricity of the node
+    return nx.eccentricity(G, node)
+
+
+def _two_sweep_directed(G, seed):
+    """Helper function for finding a lower bound on the diameter
+        for directed Graphs.
+
+        It implements 2-dSweep, the directed version of the 2-sweep algorithm.
+        The algorithm follows the following steps.
+        1. Select a source node $s$ at random.
+        2. Perform a forward BFS from $s$ to select a node $a_1$ at the maximum
+        distance from the source, and compute $LB_1$, the backward eccentricity of $a_1$.
+        3. Perform a backward BFS from $s$ to select a node $a_2$ at the maximum
+        distance from the source, and compute $LB_2$, the forward eccentricity of $a_2$.
+        4. Return the maximum between $LB_1$ and $LB_2$.
+
+        ``G`` is a NetworkX directed graph.
+
+    .. note::
+
+        ``seed`` is a random.Random or numpy.random.RandomState instance
+    """
+    # get a new digraph G' with the edges reversed in the opposite direction
+    G_reversed = G.reverse()
+    # select a random source node
+    source = seed.choice(list(G))
+    # compute forward distances from source
+    forward_distances = nx.shortest_path_length(G, source)
+    # compute backward distances  from source
+    backward_distances = nx.shortest_path_length(G_reversed, source)
+    # if either the source can't reach every node or not every node
+    # can reach the source, then the graph is not strongly connected
+    n = len(G)
+    if len(forward_distances) != n or len(backward_distances) != n:
+        raise nx.NetworkXError("DiGraph not strongly connected.")
+    # take a node a_1 at the maximum distance from the source in G
+    *_, a_1 = forward_distances
+    # take a node a_2 at the maximum distance from the source in G_reversed
+    *_, a_2 = backward_distances
+    # return the max between the backward eccentricity of a_1 and the forward eccentricity of a_2
+    return max(nx.eccentricity(G_reversed, a_1), nx.eccentricity(G, a_2))

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

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+import networkx as nx
+from networkx.utils.decorators import not_implemented_for, py_random_state
+
+__all__ = ["randomized_partitioning", "one_exchange"]
+
+
+@not_implemented_for("directed", "multigraph")
+@py_random_state(1)
+@nx._dispatch(edge_attrs="weight")
+def randomized_partitioning(G, seed=None, p=0.5, weight=None):
+    """Compute a random partitioning of the graph nodes and its cut value.
+
+    A partitioning is calculated by observing each node
+    and deciding to add it to the partition with probability `p`,
+    returning a random cut and its corresponding value (the
+    sum of weights of edges connecting different partitions).
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    p : scalar
+        Probability for each node to be part of the first partition.
+        Should be in [0,1]
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    cut_size : scalar
+        Value of the minimum cut.
+
+    partition : pair of node sets
+        A partitioning of the nodes that defines a minimum cut.
+    """
+    cut = {node for node in G.nodes() if seed.random() < p}
+    cut_size = nx.algorithms.cut_size(G, cut, weight=weight)
+    partition = (cut, G.nodes - cut)
+    return cut_size, partition
+
+
+def _swap_node_partition(cut, node):
+    return cut - {node} if node in cut else cut.union({node})
+
+
+@not_implemented_for("directed", "multigraph")
+@py_random_state(2)
+@nx._dispatch(edge_attrs="weight")
+def one_exchange(G, initial_cut=None, seed=None, weight=None):
+    """Compute a partitioning of the graphs nodes and the corresponding cut value.
+
+    Use a greedy one exchange strategy to find a locally maximal cut
+    and its value, it works by finding the best node (one that gives
+    the highest gain to the cut value) to add to the current cut
+    and repeats this process until no improvement can be made.
+
+    Parameters
+    ----------
+    G : networkx Graph
+        Graph to find a maximum cut for.
+
+    initial_cut : set
+        Cut to use as a starting point. If not supplied the algorithm
+        starts with an empty cut.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    weight : object
+        Edge attribute key to use as weight. If not specified, edges
+        have weight one.
+
+    Returns
+    -------
+    cut_value : scalar
+        Value of the maximum cut.
+
+    partition : pair of node sets
+        A partitioning of the nodes that defines a maximum cut.
+    """
+    if initial_cut is None:
+        initial_cut = set()
+    cut = set(initial_cut)
+    current_cut_size = nx.algorithms.cut_size(G, cut, weight=weight)
+    while True:
+        nodes = list(G.nodes())
+        # Shuffling the nodes ensures random tie-breaks in the following call to max
+        seed.shuffle(nodes)
+        best_node_to_swap = max(
+            nodes,
+            key=lambda v: nx.algorithms.cut_size(
+                G, _swap_node_partition(cut, v), weight=weight
+            ),
+            default=None,
+        )
+        potential_cut = _swap_node_partition(cut, best_node_to_swap)
+        potential_cut_size = nx.algorithms.cut_size(G, potential_cut, weight=weight)
+
+        if potential_cut_size > current_cut_size:
+            cut = potential_cut
+            current_cut_size = potential_cut_size
+        else:
+            break
+
+    partition = (cut, G.nodes - cut)
+    return current_cut_size, partition

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

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+from itertools import chain
+
+import networkx as nx
+from networkx.utils import not_implemented_for, pairwise
+
+__all__ = ["metric_closure", "steiner_tree"]
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs="weight")
+def metric_closure(G, weight="weight"):
+    """Return the metric closure of a graph.
+
+    The metric closure of a graph *G* is the complete graph in which each edge
+    is weighted by the shortest path distance between the nodes in *G* .
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    NetworkX graph
+        Metric closure of the graph `G`.
+
+    """
+    M = nx.Graph()
+
+    Gnodes = set(G)
+
+    # check for connected graph while processing first node
+    all_paths_iter = nx.all_pairs_dijkstra(G, weight=weight)
+    u, (distance, path) = next(all_paths_iter)
+    if Gnodes - set(distance):
+        msg = "G is not a connected graph. metric_closure is not defined."
+        raise nx.NetworkXError(msg)
+    Gnodes.remove(u)
+    for v in Gnodes:
+        M.add_edge(u, v, distance=distance[v], path=path[v])
+
+    # first node done -- now process the rest
+    for u, (distance, path) in all_paths_iter:
+        Gnodes.remove(u)
+        for v in Gnodes:
+            M.add_edge(u, v, distance=distance[v], path=path[v])
+
+    return M
+
+
+def _mehlhorn_steiner_tree(G, terminal_nodes, weight):
+    paths = nx.multi_source_dijkstra_path(G, terminal_nodes)
+
+    d_1 = {}
+    s = {}
+    for v in G.nodes():
+        s[v] = paths[v][0]
+        d_1[(v, s[v])] = len(paths[v]) - 1
+
+    # G1-G4 names match those from the Mehlhorn 1988 paper.
+    G_1_prime = nx.Graph()
+    for u, v, data in G.edges(data=True):
+        su, sv = s[u], s[v]
+        weight_here = d_1[(u, su)] + data.get(weight, 1) + d_1[(v, sv)]
+        if not G_1_prime.has_edge(su, sv):
+            G_1_prime.add_edge(su, sv, weight=weight_here)
+        else:
+            new_weight = min(weight_here, G_1_prime[su][sv][weight])
+            G_1_prime.add_edge(su, sv, weight=new_weight)
+
+    G_2 = nx.minimum_spanning_edges(G_1_prime, data=True)
+
+    G_3 = nx.Graph()
+    for u, v, d in G_2:
+        path = nx.shortest_path(G, u, v, weight)
+        for n1, n2 in pairwise(path):
+            G_3.add_edge(n1, n2)
+
+    G_3_mst = list(nx.minimum_spanning_edges(G_3, data=False))
+    if G.is_multigraph():
+        G_3_mst = (
+            (u, v, min(G[u][v], key=lambda k: G[u][v][k][weight])) for u, v in G_3_mst
+        )
+    G_4 = G.edge_subgraph(G_3_mst).copy()
+    _remove_nonterminal_leaves(G_4, terminal_nodes)
+    return G_4.edges()
+
+
+def _kou_steiner_tree(G, terminal_nodes, weight):
+    # H is the subgraph induced by terminal_nodes in the metric closure M of G.
+    M = metric_closure(G, weight=weight)
+    H = M.subgraph(terminal_nodes)
+
+    # Use the 'distance' attribute of each edge provided by M.
+    mst_edges = nx.minimum_spanning_edges(H, weight="distance", data=True)
+
+    # Create an iterator over each edge in each shortest path; repeats are okay
+    mst_all_edges = chain.from_iterable(pairwise(d["path"]) for u, v, d in mst_edges)
+    if G.is_multigraph():
+        mst_all_edges = (
+            (u, v, min(G[u][v], key=lambda k: G[u][v][k][weight]))
+            for u, v in mst_all_edges
+        )
+
+    # Find the MST again, over this new set of edges
+    G_S = G.edge_subgraph(mst_all_edges)
+    T_S = nx.minimum_spanning_edges(G_S, weight="weight", data=False)
+
+    # Leaf nodes that are not terminal might still remain; remove them here
+    T_H = G.edge_subgraph(T_S).copy()
+    _remove_nonterminal_leaves(T_H, terminal_nodes)
+
+    return T_H.edges()
+
+
+def _remove_nonterminal_leaves(G, terminals):
+    terminals_set = set(terminals)
+    for n in list(G.nodes):
+        if n not in terminals_set and G.degree(n) == 1:
+            G.remove_node(n)
+
+
+ALGORITHMS = {
+    "kou": _kou_steiner_tree,
+    "mehlhorn": _mehlhorn_steiner_tree,
+}
+
+
+@not_implemented_for("directed")
+@nx._dispatch(edge_attrs="weight")
+def steiner_tree(G, terminal_nodes, weight="weight", method=None):
+    r"""Return an approximation to the minimum Steiner tree of a graph.
+
+    The minimum Steiner tree of `G` w.r.t a set of `terminal_nodes` (also *S*)
+    is a tree within `G` that spans those nodes and has minimum size (sum of
+    edge weights) among all such trees.
+
+    The approximation algorithm is specified with the `method` keyword
+    argument. All three available algorithms produce a tree whose weight is
+    within a ``(2 - (2 / l))`` factor of the weight of the optimal Steiner tree,
+    where ``l`` is the minimum number of leaf nodes across all possible Steiner
+    trees.
+
+    * ``"kou"`` [2]_ (runtime $O(|S| |V|^2)$) computes the minimum spanning tree of
+      the subgraph of the metric closure of *G* induced by the terminal nodes,
+      where the metric closure of *G* is the complete graph in which each edge is
+      weighted by the shortest path distance between the nodes in *G*.
+
+    * ``"mehlhorn"`` [3]_ (runtime $O(|E|+|V|\log|V|)$) modifies Kou et al.'s
+      algorithm, beginning by finding the closest terminal node for each
+      non-terminal. This data is used to create a complete graph containing only
+      the terminal nodes, in which edge is weighted with the shortest path
+      distance between them. The algorithm then proceeds in the same way as Kou
+      et al..
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    terminal_nodes : list
+         A list of terminal nodes for which minimum steiner tree is
+         to be found.
+
+    weight : string (default = 'weight')
+        Use the edge attribute specified by this string as the edge weight.
+        Any edge attribute not present defaults to 1.
+
+    method : string, optional (default = 'kou')
+        The algorithm to use to approximate the Steiner tree.
+        Supported options: 'kou', 'mehlhorn'.
+        Other inputs produce a ValueError.
+
+    Returns
+    -------
+    NetworkX graph
+        Approximation to the minimum steiner tree of `G` induced by
+        `terminal_nodes` .
+
+    Notes
+    -----
+    For multigraphs, the edge between two nodes with minimum weight is the
+    edge put into the Steiner tree.
+
+
+    References
+    ----------
+    .. [1] Steiner_tree_problem on Wikipedia.
+           https://en.wikipedia.org/wiki/Steiner_tree_problem
+    .. [2] Kou, L., G. Markowsky, and L. Berman. 1981.
+           ‘A Fast Algorithm for Steiner Trees’.
+           Acta Informatica 15 (2): 141–45.
+           https://doi.org/10.1007/BF00288961.
+    .. [3] Mehlhorn, Kurt. 1988.
+           ‘A Faster Approximation Algorithm for the Steiner Problem in Graphs’.
+           Information Processing Letters 27 (3): 125–28.
+           https://doi.org/10.1016/0020-0190(88)90066-X.
+    """
+    if method is None:
+        import warnings
+
+        msg = (
+            "steiner_tree will change default method from 'kou' to 'mehlhorn' "
+            "in version 3.2.\nSet the `method` kwarg to remove this warning."
+        )
+        warnings.warn(msg, FutureWarning, stacklevel=4)
+        method = "kou"
+
+    try:
+        algo = ALGORITHMS[method]
+    except KeyError as e:
+        msg = f"{method} is not a valid choice for an algorithm."
+        raise ValueError(msg) from e
+
+    edges = algo(G, terminal_nodes, weight)
+    # For multigraph we should add the minimal weight edge keys
+    if G.is_multigraph():
+        edges = (
+            (u, v, min(G[u][v], key=lambda k: G[u][v][k][weight])) for u, v in edges
+        )
+    T = G.edge_subgraph(edges)
+    return T

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

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+import pytest
+
+import networkx as nx
+from networkx.algorithms import approximation as approx
+
+
+def test_global_node_connectivity():
+    # Figure 1 chapter on Connectivity
+    G = nx.Graph()
+    G.add_edges_from(
+        [
+            (1, 2),
+            (1, 3),
+            (1, 4),
+            (1, 5),
+            (2, 3),
+            (2, 6),
+            (3, 4),
+            (3, 6),
+            (4, 6),
+            (4, 7),
+            (5, 7),
+            (6, 8),
+            (6, 9),
+            (7, 8),
+            (7, 10),
+            (8, 11),
+            (9, 10),
+            (9, 11),
+            (10, 11),
+        ]
+    )
+    assert 2 == approx.local_node_connectivity(G, 1, 11)
+    assert 2 == approx.node_connectivity(G)
+    assert 2 == approx.node_connectivity(G, 1, 11)
+
+
+def test_white_harary1():
+    # Figure 1b white and harary (2001)
+    # A graph with high adhesion (edge connectivity) and low cohesion
+    # (node connectivity)
+    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
+    G.remove_node(7)
+    for i in range(4, 7):
+        G.add_edge(0, i)
+    G = nx.disjoint_union(G, nx.complete_graph(4))
+    G.remove_node(G.order() - 1)
+    for i in range(7, 10):
+        G.add_edge(0, i)
+    assert 1 == approx.node_connectivity(G)
+
+
+def test_complete_graphs():
+    for n in range(5, 25, 5):
+        G = nx.complete_graph(n)
+        assert n - 1 == approx.node_connectivity(G)
+        assert n - 1 == approx.node_connectivity(G, 0, 3)
+
+
+def test_empty_graphs():
+    for k in range(5, 25, 5):
+        G = nx.empty_graph(k)
+        assert 0 == approx.node_connectivity(G)
+        assert 0 == approx.node_connectivity(G, 0, 3)
+
+
+def test_petersen():
+    G = nx.petersen_graph()
+    assert 3 == approx.node_connectivity(G)
+    assert 3 == approx.node_connectivity(G, 0, 5)
+
+
+# Approximation fails with tutte graph
+# def test_tutte():
+#    G = nx.tutte_graph()
+#    assert_equal(3, approx.node_connectivity(G))
+
+
+def test_dodecahedral():
+    G = nx.dodecahedral_graph()
+    assert 3 == approx.node_connectivity(G)
+    assert 3 == approx.node_connectivity(G, 0, 5)
+
+
+def test_octahedral():
+    G = nx.octahedral_graph()
+    assert 4 == approx.node_connectivity(G)
+    assert 4 == approx.node_connectivity(G, 0, 5)
+
+
+# Approximation can fail with icosahedral graph depending
+# on iteration order.
+# def test_icosahedral():
+#    G=nx.icosahedral_graph()
+#    assert_equal(5, approx.node_connectivity(G))
+#    assert_equal(5, approx.node_connectivity(G, 0, 5))
+
+
+def test_only_source():
+    G = nx.complete_graph(5)
+    pytest.raises(nx.NetworkXError, approx.node_connectivity, G, s=0)
+
+
+def test_only_target():
+    G = nx.complete_graph(5)
+    pytest.raises(nx.NetworkXError, approx.node_connectivity, G, t=0)
+
+
+def test_missing_source():
+    G = nx.path_graph(4)
+    pytest.raises(nx.NetworkXError, approx.node_connectivity, G, 10, 1)
+
+
+def test_missing_target():
+    G = nx.path_graph(4)
+    pytest.raises(nx.NetworkXError, approx.node_connectivity, G, 1, 10)
+
+
+def test_source_equals_target():
+    G = nx.complete_graph(5)
+    pytest.raises(nx.NetworkXError, approx.local_node_connectivity, G, 0, 0)
+
+
+def test_directed_node_connectivity():
+    G = nx.cycle_graph(10, create_using=nx.DiGraph())  # only one direction
+    D = nx.cycle_graph(10).to_directed()  # 2 reciprocal edges
+    assert 1 == approx.node_connectivity(G)
+    assert 1 == approx.node_connectivity(G, 1, 4)
+    assert 2 == approx.node_connectivity(D)
+    assert 2 == approx.node_connectivity(D, 1, 4)
+
+
+class TestAllPairsNodeConnectivityApprox:
+    @classmethod
+    def setup_class(cls):
+        cls.path = nx.path_graph(7)
+        cls.directed_path = nx.path_graph(7, create_using=nx.DiGraph())
+        cls.cycle = nx.cycle_graph(7)
+        cls.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
+        cls.gnp = nx.gnp_random_graph(30, 0.1)
+        cls.directed_gnp = nx.gnp_random_graph(30, 0.1, directed=True)
+        cls.K20 = nx.complete_graph(20)
+        cls.K10 = nx.complete_graph(10)
+        cls.K5 = nx.complete_graph(5)
+        cls.G_list = [
+            cls.path,
+            cls.directed_path,
+            cls.cycle,
+            cls.directed_cycle,
+            cls.gnp,
+            cls.directed_gnp,
+            cls.K10,
+            cls.K5,
+            cls.K20,
+        ]
+
+    def test_cycles(self):
+        K_undir = approx.all_pairs_node_connectivity(self.cycle)
+        for source in K_undir:
+            for target, k in K_undir[source].items():
+                assert k == 2
+        K_dir = approx.all_pairs_node_connectivity(self.directed_cycle)
+        for source in K_dir:
+            for target, k in K_dir[source].items():
+                assert k == 1
+
+    def test_complete(self):
+        for G in [self.K10, self.K5, self.K20]:
+            K = approx.all_pairs_node_connectivity(G)
+            for source in K:
+                for target, k in K[source].items():
+                    assert k == len(G) - 1
+
+    def test_paths(self):
+        K_undir = approx.all_pairs_node_connectivity(self.path)
+        for source in K_undir:
+            for target, k in K_undir[source].items():
+                assert k == 1
+        K_dir = approx.all_pairs_node_connectivity(self.directed_path)
+        for source in K_dir:
+            for target, k in K_dir[source].items():
+                if source < target:
+                    assert k == 1
+                else:
+                    assert k == 0
+
+    def test_cutoff(self):
+        for G in [self.K10, self.K5, self.K20]:
+            for mp in [2, 3, 4]:
+                paths = approx.all_pairs_node_connectivity(G, cutoff=mp)
+                for source in paths:
+                    for target, K in paths[source].items():
+                        assert K == mp
+
+    def test_all_pairs_connectivity_nbunch(self):
+        G = nx.complete_graph(5)
+        nbunch = [0, 2, 3]
+        C = approx.all_pairs_node_connectivity(G, nbunch=nbunch)
+        assert len(C) == len(nbunch)

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

@@ -0,0 +1,78 @@
+import pytest
+
+import networkx as nx
+from networkx.algorithms.approximation import (
+    min_edge_dominating_set,
+    min_weighted_dominating_set,
+)
+
+
+class TestMinWeightDominatingSet:
+    def test_min_weighted_dominating_set(self):
+        graph = nx.Graph()
+        graph.add_edge(1, 2)
+        graph.add_edge(1, 5)
+        graph.add_edge(2, 3)
+        graph.add_edge(2, 5)
+        graph.add_edge(3, 4)
+        graph.add_edge(3, 6)
+        graph.add_edge(5, 6)
+
+        vertices = {1, 2, 3, 4, 5, 6}
+        # due to ties, this might be hard to test tight bounds
+        dom_set = min_weighted_dominating_set(graph)
+        for vertex in vertices - dom_set:
+            neighbors = set(graph.neighbors(vertex))
+            assert len(neighbors & dom_set) > 0, "Non dominating set found!"
+
+    def test_star_graph(self):
+        """Tests that an approximate dominating set for the star graph,
+        even when the center node does not have the smallest integer
+        label, gives just the center node.
+
+        For more information, see #1527.
+
+        """
+        # Create a star graph in which the center node has the highest
+        # label instead of the lowest.
+        G = nx.star_graph(10)
+        G = nx.relabel_nodes(G, {0: 9, 9: 0})
+        assert min_weighted_dominating_set(G) == {9}
+
+    def test_null_graph(self):
+        """Tests that the unique dominating set for the null graph is an empty set"""
+        G = nx.Graph()
+        assert min_weighted_dominating_set(G) == set()
+
+    def test_min_edge_dominating_set(self):
+        graph = nx.path_graph(5)
+        dom_set = min_edge_dominating_set(graph)
+
+        # this is a crappy way to test, but good enough for now.
+        for edge in graph.edges():
+            if edge in dom_set:
+                continue
+            else:
+                u, v = edge
+                found = False
+                for dom_edge in dom_set:
+                    found |= u == dom_edge[0] or u == dom_edge[1]
+                assert found, "Non adjacent edge found!"
+
+        graph = nx.complete_graph(10)
+        dom_set = min_edge_dominating_set(graph)
+
+        # this is a crappy way to test, but good enough for now.
+        for edge in graph.edges():
+            if edge in dom_set:
+                continue
+            else:
+                u, v = edge
+                found = False
+                for dom_edge in dom_set:
+                    found |= u == dom_edge[0] or u == dom_edge[1]
+                assert found, "Non adjacent edge found!"
+
+        graph = nx.Graph()  # empty Networkx graph
+        with pytest.raises(ValueError, match="Expected non-empty NetworkX graph!"):
+            min_edge_dominating_set(graph)

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

@@ -0,0 +1,252 @@
+"""Functions for computing treewidth decomposition.
+
+Treewidth of an undirected graph is a number associated with the graph.
+It can be defined as the size of the largest vertex set (bag) in a tree
+decomposition of the graph minus one.
+
+`Wikipedia: Treewidth <https://en.wikipedia.org/wiki/Treewidth>`_
+
+The notions of treewidth and tree decomposition have gained their
+attractiveness partly because many graph and network problems that are
+intractable (e.g., NP-hard) on arbitrary graphs become efficiently
+solvable (e.g., with a linear time algorithm) when the treewidth of the
+input graphs is bounded by a constant [1]_ [2]_.
+
+There are two different functions for computing a tree decomposition:
+:func:`treewidth_min_degree` and :func:`treewidth_min_fill_in`.
+
+.. [1] Hans L. Bodlaender and Arie M. C. A. Koster. 2010. "Treewidth
+      computations I.Upper bounds". Inf. Comput. 208, 3 (March 2010),259-275.
+      http://dx.doi.org/10.1016/j.ic.2009.03.008
+
+.. [2] Hans L. Bodlaender. "Discovering Treewidth". Institute of Information
+      and Computing Sciences, Utrecht University.
+      Technical Report UU-CS-2005-018.
+      http://www.cs.uu.nl
+
+.. [3] K. Wang, Z. Lu, and J. Hicks *Treewidth*.
+      https://web.archive.org/web/20210507025929/http://web.eecs.utk.edu/~cphill25/cs594_spring2015_projects/treewidth.pdf
+
+"""
+
+import itertools
+import sys
+from heapq import heapify, heappop, heappush
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["treewidth_min_degree", "treewidth_min_fill_in"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def treewidth_min_degree(G):
+    """Returns a treewidth decomposition using the Minimum Degree heuristic.
+
+    The heuristic chooses the nodes according to their degree, i.e., first
+    the node with the lowest degree is chosen, then the graph is updated
+    and the corresponding node is removed. Next, a new node with the lowest
+    degree is chosen, and so on.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    Treewidth decomposition : (int, Graph) tuple
+          2-tuple with treewidth and the corresponding decomposed tree.
+    """
+    deg_heuristic = MinDegreeHeuristic(G)
+    return treewidth_decomp(G, lambda graph: deg_heuristic.best_node(graph))
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatch
+def treewidth_min_fill_in(G):
+    """Returns a treewidth decomposition using the Minimum Fill-in heuristic.
+
+    The heuristic chooses a node from the graph, where the number of edges
+    added turning the neighbourhood of the chosen node into clique is as
+    small as possible.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    Treewidth decomposition : (int, Graph) tuple
+        2-tuple with treewidth and the corresponding decomposed tree.
+    """
+    return treewidth_decomp(G, min_fill_in_heuristic)
+
+
+class MinDegreeHeuristic:
+    """Implements the Minimum Degree heuristic.
+
+    The heuristic chooses the nodes according to their degree
+    (number of neighbours), i.e., first the node with the lowest degree is
+    chosen, then the graph is updated and the corresponding node is
+    removed. Next, a new node with the lowest degree is chosen, and so on.
+    """
+
+    def __init__(self, graph):
+        self._graph = graph
+
+        # nodes that have to be updated in the heap before each iteration
+        self._update_nodes = []
+
+        self._degreeq = []  # a heapq with 3-tuples (degree,unique_id,node)
+        self.count = itertools.count()
+
+        # build heap with initial degrees
+        for n in graph:
+            self._degreeq.append((len(graph[n]), next(self.count), n))
+        heapify(self._degreeq)
+
+    def best_node(self, graph):
+        # update nodes in self._update_nodes
+        for n in self._update_nodes:
+            # insert changed degrees into degreeq
+            heappush(self._degreeq, (len(graph[n]), next(self.count), n))
+
+        # get the next valid (minimum degree) node
+        while self._degreeq:
+            (min_degree, _, elim_node) = heappop(self._degreeq)
+            if elim_node not in graph or len(graph[elim_node]) != min_degree:
+                # outdated entry in degreeq
+                continue
+            elif min_degree == len(graph) - 1:
+                # fully connected: abort condition
+                return None
+
+            # remember to update nodes in the heap before getting the next node
+            self._update_nodes = graph[elim_node]
+            return elim_node
+
+        # the heap is empty: abort
+        return None
+
+
+def min_fill_in_heuristic(graph):
+    """Implements the Minimum Degree heuristic.
+
+    Returns the node from the graph, where the number of edges added when
+    turning the neighbourhood of the chosen node into clique is as small as
+    possible. This algorithm chooses the nodes using the Minimum Fill-In
+    heuristic. The running time of the algorithm is :math:`O(V^3)` and it uses
+    additional constant memory."""
+
+    if len(graph) == 0:
+        return None
+
+    min_fill_in_node = None
+
+    min_fill_in = sys.maxsize
+
+    # sort nodes by degree
+    nodes_by_degree = sorted(graph, key=lambda x: len(graph[x]))
+    min_degree = len(graph[nodes_by_degree[0]])
+
+    # abort condition (handle complete graph)
+    if min_degree == len(graph) - 1:
+        return None
+
+    for node in nodes_by_degree:
+        num_fill_in = 0
+        nbrs = graph[node]
+        for nbr in nbrs:
+            # count how many nodes in nbrs current nbr is not connected to
+            # subtract 1 for the node itself
+            num_fill_in += len(nbrs - graph[nbr]) - 1
+            if num_fill_in >= 2 * min_fill_in:
+                break
+
+        num_fill_in /= 2  # divide by 2 because of double counting
+
+        if num_fill_in < min_fill_in:  # update min-fill-in node
+            if num_fill_in == 0:
+                return node
+            min_fill_in = num_fill_in
+            min_fill_in_node = node
+
+    return min_fill_in_node
+
+
+@nx._dispatch
+def treewidth_decomp(G, heuristic=min_fill_in_heuristic):
+    """Returns a treewidth decomposition using the passed heuristic.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+    heuristic : heuristic function
+
+    Returns
+    -------
+    Treewidth decomposition : (int, Graph) tuple
+        2-tuple with treewidth and the corresponding decomposed tree.
+    """
+
+    # make dict-of-sets structure
+    graph = {n: set(G[n]) - {n} for n in G}
+
+    # stack containing nodes and neighbors in the order from the heuristic
+    node_stack = []
+
+    # get first node from heuristic
+    elim_node = heuristic(graph)
+    while elim_node is not None:
+        # connect all neighbours with each other
+        nbrs = graph[elim_node]
+        for u, v in itertools.permutations(nbrs, 2):
+            if v not in graph[u]:
+                graph[u].add(v)
+
+        # push node and its current neighbors on stack
+        node_stack.append((elim_node, nbrs))
+
+        # remove node from graph
+        for u in graph[elim_node]:
+            graph[u].remove(elim_node)
+
+        del graph[elim_node]
+        elim_node = heuristic(graph)
+
+    # the abort condition is met; put all remaining nodes into one bag
+    decomp = nx.Graph()
+    first_bag = frozenset(graph.keys())
+    decomp.add_node(first_bag)
+
+    treewidth = len(first_bag) - 1
+
+    while node_stack:
+        # get node and its neighbors from the stack
+        (curr_node, nbrs) = node_stack.pop()
+
+        # find a bag all neighbors are in
+        old_bag = None
+        for bag in decomp.nodes:
+            if nbrs <= bag:
+                old_bag = bag
+                break
+
+        if old_bag is None:
+            # no old_bag was found: just connect to the first_bag
+            old_bag = first_bag
+
+        # create new node for decomposition
+        nbrs.add(curr_node)
+        new_bag = frozenset(nbrs)
+
+        # update treewidth
+        treewidth = max(treewidth, len(new_bag) - 1)
+
+        # add edge to decomposition (implicitly also adds the new node)
+        decomp.add_edge(old_bag, new_bag)
+
+    return treewidth, decomp

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

@@ -0,0 +1,321 @@
+"""
+==========================
+Bipartite Graph Algorithms
+==========================
+"""
+import networkx as nx
+from networkx.algorithms.components import connected_components
+from networkx.exception import AmbiguousSolution
+
+__all__ = [
+    "is_bipartite",
+    "is_bipartite_node_set",
+    "color",
+    "sets",
+    "density",
+    "degrees",
+]
+
+
+@nx._dispatch
+def color(G):
+    """Returns a two-coloring of the graph.
+
+    Raises an exception if the graph is not bipartite.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Returns
+    -------
+    color : dictionary
+        A dictionary keyed by node with a 1 or 0 as data for each node color.
+
+    Raises
+    ------
+    NetworkXError
+        If the graph is not two-colorable.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> c = bipartite.color(G)
+    >>> print(c)
+    {0: 1, 1: 0, 2: 1, 3: 0}
+
+    You can use this to set a node attribute indicating the bipartite set:
+
+    >>> nx.set_node_attributes(G, c, "bipartite")
+    >>> print(G.nodes[0]["bipartite"])
+    1
+    >>> print(G.nodes[1]["bipartite"])
+    0
+    """
+    if G.is_directed():
+        import itertools
+
+        def neighbors(v):
+            return itertools.chain.from_iterable([G.predecessors(v), G.successors(v)])
+
+    else:
+        neighbors = G.neighbors
+
+    color = {}
+    for n in G:  # handle disconnected graphs
+        if n in color or len(G[n]) == 0:  # skip isolates
+            continue
+        queue = [n]
+        color[n] = 1  # nodes seen with color (1 or 0)
+        while queue:
+            v = queue.pop()
+            c = 1 - color[v]  # opposite color of node v
+            for w in neighbors(v):
+                if w in color:
+                    if color[w] == color[v]:
+                        raise nx.NetworkXError("Graph is not bipartite.")
+                else:
+                    color[w] = c
+                    queue.append(w)
+    # color isolates with 0
+    color.update(dict.fromkeys(nx.isolates(G), 0))
+    return color
+
+
+@nx._dispatch
+def is_bipartite(G):
+    """Returns True if graph G is bipartite, False if not.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> print(bipartite.is_bipartite(G))
+    True
+
+    See Also
+    --------
+    color, is_bipartite_node_set
+    """
+    try:
+        color(G)
+        return True
+    except nx.NetworkXError:
+        return False
+
+
+@nx._dispatch
+def is_bipartite_node_set(G, nodes):
+    """Returns True if nodes and G/nodes are a bipartition of G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nodes: list or container
+      Check if nodes are a one of a bipartite set.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> X = set([1, 3])
+    >>> bipartite.is_bipartite_node_set(G, X)
+    True
+
+    Notes
+    -----
+    An exception is raised if the input nodes are not distinct, because in this
+    case some bipartite algorithms will yield incorrect results.
+    For connected graphs the bipartite sets are unique.  This function handles
+    disconnected graphs.
+    """
+    S = set(nodes)
+
+    if len(S) < len(nodes):
+        # this should maybe just return False?
+        raise AmbiguousSolution(
+            "The input node set contains duplicates.\n"
+            "This may lead to incorrect results when using it in bipartite algorithms.\n"
+            "Consider using set(nodes) as the input"
+        )
+
+    for CC in (G.subgraph(c).copy() for c in connected_components(G)):
+        X, Y = sets(CC)
+        if not (
+            (X.issubset(S) and Y.isdisjoint(S)) or (Y.issubset(S) and X.isdisjoint(S))
+        ):
+            return False
+    return True
+
+
+@nx._dispatch
+def sets(G, top_nodes=None):
+    """Returns bipartite node sets of graph G.
+
+    Raises an exception if the graph is not bipartite or if the input
+    graph is disconnected and thus more than one valid solution exists.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    top_nodes : container, optional
+      Container with all nodes in one bipartite node set. If not supplied
+      it will be computed. But if more than one solution exists an exception
+      will be raised.
+
+    Returns
+    -------
+    X : set
+      Nodes from one side of the bipartite graph.
+    Y : set
+      Nodes from the other side.
+
+    Raises
+    ------
+    AmbiguousSolution
+      Raised if the input bipartite graph is disconnected and no container
+      with all nodes in one bipartite set is provided. When determining
+      the nodes in each bipartite set more than one valid solution is
+      possible if the input graph is disconnected.
+    NetworkXError
+      Raised if the input graph is not bipartite.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> X, Y = bipartite.sets(G)
+    >>> list(X)
+    [0, 2]
+    >>> list(Y)
+    [1, 3]
+
+    See Also
+    --------
+    color
+
+    """
+    if G.is_directed():
+        is_connected = nx.is_weakly_connected
+    else:
+        is_connected = nx.is_connected
+    if top_nodes is not None:
+        X = set(top_nodes)
+        Y = set(G) - X
+    else:
+        if not is_connected(G):
+            msg = "Disconnected graph: Ambiguous solution for bipartite sets."
+            raise nx.AmbiguousSolution(msg)
+        c = color(G)
+        X = {n for n, is_top in c.items() if is_top}
+        Y = {n for n, is_top in c.items() if not is_top}
+    return (X, Y)
+
+
+@nx._dispatch(graphs="B")
+def density(B, nodes):
+    """Returns density of bipartite graph B.
+
+    Parameters
+    ----------
+    B : NetworkX graph
+
+    nodes: list or container
+      Nodes in one node set of the bipartite graph.
+
+    Returns
+    -------
+    d : float
+       The bipartite density
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.complete_bipartite_graph(3, 2)
+    >>> X = set([0, 1, 2])
+    >>> bipartite.density(G, X)
+    1.0
+    >>> Y = set([3, 4])
+    >>> bipartite.density(G, Y)
+    1.0
+
+    Notes
+    -----
+    The container of nodes passed as argument must contain all nodes
+    in one of the two bipartite node sets to avoid ambiguity in the
+    case of disconnected graphs.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    See Also
+    --------
+    color
+    """
+    n = len(B)
+    m = nx.number_of_edges(B)
+    nb = len(nodes)
+    nt = n - nb
+    if m == 0:  # includes cases n==0 and n==1
+        d = 0.0
+    else:
+        if B.is_directed():
+            d = m / (2 * nb * nt)
+        else:
+            d = m / (nb * nt)
+    return d
+
+
+@nx._dispatch(graphs="B", edge_attrs="weight")
+def degrees(B, nodes, weight=None):
+    """Returns the degrees of the two node sets in the bipartite graph B.
+
+    Parameters
+    ----------
+    B : NetworkX graph
+
+    nodes: list or container
+      Nodes in one node set of the bipartite graph.
+
+    weight : string or None, optional (default=None)
+       The edge attribute that holds the numerical value used as a weight.
+       If None, then each edge has weight 1.
+       The degree is the sum of the edge weights adjacent to the node.
+
+    Returns
+    -------
+    (degX,degY) : tuple of dictionaries
+       The degrees of the two bipartite sets as dictionaries keyed by node.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.complete_bipartite_graph(3, 2)
+    >>> Y = set([3, 4])
+    >>> degX, degY = bipartite.degrees(G, Y)
+    >>> dict(degX)
+    {0: 2, 1: 2, 2: 2}
+
+    Notes
+    -----
+    The container of nodes passed as argument must contain all nodes
+    in one of the two bipartite node sets to avoid ambiguity in the
+    case of disconnected graphs.
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    See Also
+    --------
+    color, density
+    """
+    bottom = set(nodes)
+    top = set(B) - bottom
+    return (B.degree(top, weight), B.degree(bottom, weight))

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

@@ -0,0 +1,105 @@
+""" Provides a function for computing the extendability of a graph which is
+undirected, simple, connected and bipartite and contains at least one perfect matching."""
+
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = ["maximal_extendability"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+def maximal_extendability(G):
+    """Computes the extendability of a graph.
+
+    The extendability of a graph is defined as the maximum $k$ for which `G`
+    is $k$-extendable. Graph `G` is $k$-extendable if and only if `G` has a
+    perfect matching and every set of $k$ independent edges can be extended
+    to a perfect matching in `G`.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A fully-connected bipartite graph without self-loops
+
+    Returns
+    -------
+    extendability : int
+
+    Raises
+    ------
+    NetworkXError
+       If the graph `G` is disconnected.
+       If the graph `G` is not bipartite.
+       If the graph `G` does not contain a perfect matching.
+       If the residual graph of `G` is not strongly connected.
+
+    Notes
+    -----
+    Definition:
+    Let `G` be a simple, connected, undirected and bipartite graph with a perfect
+    matching M and bipartition (U,V). The residual graph of `G`, denoted by $G_M$,
+    is the graph obtained from G by directing the edges of M from V to U and the
+    edges that do not belong to M from U to V.
+
+    Lemma [1]_ :
+    Let M be a perfect matching of `G`. `G` is $k$-extendable if and only if its residual
+    graph $G_M$ is strongly connected and there are $k$ vertex-disjoint directed
+    paths between every vertex of U and every vertex of V.
+
+    Assuming that input graph `G` is undirected, simple, connected, bipartite and contains
+    a perfect matching M, this function constructs the residual graph $G_M$ of G and
+    returns the minimum value among the maximum vertex-disjoint directed paths between
+    every vertex of U and every vertex of V in $G_M$. By combining the definitions
+    and the lemma, this value represents the extendability of the graph `G`.
+
+    Time complexity O($n^3$ $m^2$)) where $n$ is the number of vertices
+    and $m$ is the number of edges.
+
+    References
+    ----------
+    .. [1] "A polynomial algorithm for the extendability problem in bipartite graphs",
+          J. Lakhal, L. Litzler, Information Processing Letters, 1998.
+    .. [2] "On n-extendible graphs", M. D. Plummer, Discrete Mathematics, 31:201–210, 1980
+          https://doi.org/10.1016/0012-365X(80)90037-0
+
+    """
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Graph G is not connected")
+
+    if not nx.bipartite.is_bipartite(G):
+        raise nx.NetworkXError("Graph G is not bipartite")
+
+    U, V = nx.bipartite.sets(G)
+
+    maximum_matching = nx.bipartite.hopcroft_karp_matching(G)
+
+    if not nx.is_perfect_matching(G, maximum_matching):
+        raise nx.NetworkXError("Graph G does not contain a perfect matching")
+
+    # list of edges in perfect matching, directed from V to U
+    pm = [(node, maximum_matching[node]) for node in V & maximum_matching.keys()]
+
+    # Direct all the edges of G, from V to U if in matching, else from U to V
+    directed_edges = [
+        (x, y) if (x in V and (x, y) in pm) or (x in U and (y, x) not in pm) else (y, x)
+        for x, y in G.edges
+    ]
+
+    # Construct the residual graph of G
+    residual_G = nx.DiGraph()
+    residual_G.add_nodes_from(G)
+    residual_G.add_edges_from(directed_edges)
+
+    if not nx.is_strongly_connected(residual_G):
+        raise nx.NetworkXError("The residual graph of G is not strongly connected")
+
+    # For node-pairs between V & U, keep min of max number of node-disjoint paths
+    # Variable $k$ stands for the extendability of graph G
+    k = float("Inf")
+    for u in U:
+        for v in V:
+            num_paths = sum(1 for _ in nx.node_disjoint_paths(residual_G, u, v))
+            k = k if k < num_paths else num_paths
+    return k

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

@@ -0,0 +1,589 @@
+# This module uses material from the Wikipedia article Hopcroft--Karp algorithm
+# <https://en.wikipedia.org/wiki/Hopcroft%E2%80%93Karp_algorithm>, accessed on
+# January 3, 2015, which is released under the Creative Commons
+# Attribution-Share-Alike License 3.0
+# <http://creativecommons.org/licenses/by-sa/3.0/>. That article includes
+# pseudocode, which has been translated into the corresponding Python code.
+#
+# Portions of this module use code from David Eppstein's Python Algorithms and
+# Data Structures (PADS) library, which is dedicated to the public domain (for
+# proof, see <http://www.ics.uci.edu/~eppstein/PADS/ABOUT-PADS.txt>).
+"""Provides functions for computing maximum cardinality matchings and minimum
+weight full matchings in a bipartite graph.
+
+If you don't care about the particular implementation of the maximum matching
+algorithm, simply use the :func:`maximum_matching`. If you do care, you can
+import one of the named maximum matching algorithms directly.
+
+For example, to find a maximum matching in the complete bipartite graph with
+two vertices on the left and three vertices on the right:
+
+>>> G = nx.complete_bipartite_graph(2, 3)
+>>> left, right = nx.bipartite.sets(G)
+>>> list(left)
+[0, 1]
+>>> list(right)
+[2, 3, 4]
+>>> nx.bipartite.maximum_matching(G)
+{0: 2, 1: 3, 2: 0, 3: 1}
+
+The dictionary returned by :func:`maximum_matching` includes a mapping for
+vertices in both the left and right vertex sets.
+
+Similarly, :func:`minimum_weight_full_matching` produces, for a complete
+weighted bipartite graph, a matching whose cardinality is the cardinality of
+the smaller of the two partitions, and for which the sum of the weights of the
+edges included in the matching is minimal.
+
+"""
+import collections
+import itertools
+
+import networkx as nx
+from networkx.algorithms.bipartite import sets as bipartite_sets
+from networkx.algorithms.bipartite.matrix import biadjacency_matrix
+
+__all__ = [
+    "maximum_matching",
+    "hopcroft_karp_matching",
+    "eppstein_matching",
+    "to_vertex_cover",
+    "minimum_weight_full_matching",
+]
+
+INFINITY = float("inf")
+
+
+@nx._dispatch
+def hopcroft_karp_matching(G, top_nodes=None):
+    """Returns the maximum cardinality matching of the bipartite graph `G`.
+
+    A matching is a set of edges that do not share any nodes. A maximum
+    cardinality matching is a matching with the most edges possible. It
+    is not always unique. Finding a matching in a bipartite graph can be
+    treated as a networkx flow problem.
+
+    The functions ``hopcroft_karp_matching`` and ``maximum_matching``
+    are aliases of the same function.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+      Undirected bipartite graph
+
+    top_nodes : container of nodes
+
+      Container with all nodes in one bipartite node set. If not supplied
+      it will be computed. But if more than one solution exists an exception
+      will be raised.
+
+    Returns
+    -------
+    matches : dictionary
+
+      The matching is returned as a dictionary, `matches`, such that
+      ``matches[v] == w`` if node `v` is matched to node `w`. Unmatched
+      nodes do not occur as a key in `matches`.
+
+    Raises
+    ------
+    AmbiguousSolution
+      Raised if the input bipartite graph is disconnected and no container
+      with all nodes in one bipartite set is provided. When determining
+      the nodes in each bipartite set more than one valid solution is
+      possible if the input graph is disconnected.
+
+    Notes
+    -----
+    This function is implemented with the `Hopcroft--Karp matching algorithm
+    <https://en.wikipedia.org/wiki/Hopcroft%E2%80%93Karp_algorithm>`_ for
+    bipartite graphs.
+
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    See Also
+    --------
+    maximum_matching
+    hopcroft_karp_matching
+    eppstein_matching
+
+    References
+    ----------
+    .. [1] John E. Hopcroft and Richard M. Karp. "An n^{5 / 2} Algorithm for
+       Maximum Matchings in Bipartite Graphs" In: **SIAM Journal of Computing**
+       2.4 (1973), pp. 225--231. <https://doi.org/10.1137/0202019>.
+
+    """
+
+    # First we define some auxiliary search functions.
+    #
+    # If you are a human reading these auxiliary search functions, the "global"
+    # variables `leftmatches`, `rightmatches`, `distances`, etc. are defined
+    # below the functions, so that they are initialized close to the initial
+    # invocation of the search functions.
+    def breadth_first_search():
+        for v in left:
+            if leftmatches[v] is None:
+                distances[v] = 0
+                queue.append(v)
+            else:
+                distances[v] = INFINITY
+        distances[None] = INFINITY
+        while queue:
+            v = queue.popleft()
+            if distances[v] < distances[None]:
+                for u in G[v]:
+                    if distances[rightmatches[u]] is INFINITY:
+                        distances[rightmatches[u]] = distances[v] + 1
+                        queue.append(rightmatches[u])
+        return distances[None] is not INFINITY
+
+    def depth_first_search(v):
+        if v is not None:
+            for u in G[v]:
+                if distances[rightmatches[u]] == distances[v] + 1:
+                    if depth_first_search(rightmatches[u]):
+                        rightmatches[u] = v
+                        leftmatches[v] = u
+                        return True
+            distances[v] = INFINITY
+            return False
+        return True
+
+    # Initialize the "global" variables that maintain state during the search.
+    left, right = bipartite_sets(G, top_nodes)
+    leftmatches = {v: None for v in left}
+    rightmatches = {v: None for v in right}
+    distances = {}
+    queue = collections.deque()
+
+    # Implementation note: this counter is incremented as pairs are matched but
+    # it is currently not used elsewhere in the computation.
+    num_matched_pairs = 0
+    while breadth_first_search():
+        for v in left:
+            if leftmatches[v] is None:
+                if depth_first_search(v):
+                    num_matched_pairs += 1
+
+    # Strip the entries matched to `None`.
+    leftmatches = {k: v for k, v in leftmatches.items() if v is not None}
+    rightmatches = {k: v for k, v in rightmatches.items() if v is not None}
+
+    # At this point, the left matches and the right matches are inverses of one
+    # another. In other words,
+    #
+    #     leftmatches == {v, k for k, v in rightmatches.items()}
+    #
+    # Finally, we combine both the left matches and right matches.
+    return dict(itertools.chain(leftmatches.items(), rightmatches.items()))
+
+
+@nx._dispatch
+def eppstein_matching(G, top_nodes=None):
+    """Returns the maximum cardinality matching of the bipartite graph `G`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+      Undirected bipartite graph
+
+    top_nodes : container
+
+      Container with all nodes in one bipartite node set. If not supplied
+      it will be computed. But if more than one solution exists an exception
+      will be raised.
+
+    Returns
+    -------
+    matches : dictionary
+
+      The matching is returned as a dictionary, `matching`, such that
+      ``matching[v] == w`` if node `v` is matched to node `w`. Unmatched
+      nodes do not occur as a key in `matching`.
+
+    Raises
+    ------
+    AmbiguousSolution
+      Raised if the input bipartite graph is disconnected and no container
+      with all nodes in one bipartite set is provided. When determining
+      the nodes in each bipartite set more than one valid solution is
+      possible if the input graph is disconnected.
+
+    Notes
+    -----
+    This function is implemented with David Eppstein's version of the algorithm
+    Hopcroft--Karp algorithm (see :func:`hopcroft_karp_matching`), which
+    originally appeared in the `Python Algorithms and Data Structures library
+    (PADS) <http://www.ics.uci.edu/~eppstein/PADS/ABOUT-PADS.txt>`_.
+
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    See Also
+    --------
+
+    hopcroft_karp_matching
+
+    """
+    # Due to its original implementation, a directed graph is needed
+    # so that the two sets of bipartite nodes can be distinguished
+    left, right = bipartite_sets(G, top_nodes)
+    G = nx.DiGraph(G.edges(left))
+    # initialize greedy matching (redundant, but faster than full search)
+    matching = {}
+    for u in G:
+        for v in G[u]:
+            if v not in matching:
+                matching[v] = u
+                break
+    while True:
+        # structure residual graph into layers
+        # pred[u] gives the neighbor in the previous layer for u in U
+        # preds[v] gives a list of neighbors in the previous layer for v in V
+        # unmatched gives a list of unmatched vertices in final layer of V,
+        # and is also used as a flag value for pred[u] when u is in the first
+        # layer
+        preds = {}
+        unmatched = []
+        pred = {u: unmatched for u in G}
+        for v in matching:
+            del pred[matching[v]]
+        layer = list(pred)
+
+        # repeatedly extend layering structure by another pair of layers
+        while layer and not unmatched:
+            newLayer = {}
+            for u in layer:
+                for v in G[u]:
+                    if v not in preds:
+                        newLayer.setdefault(v, []).append(u)
+            layer = []
+            for v in newLayer:
+                preds[v] = newLayer[v]
+                if v in matching:
+                    layer.append(matching[v])
+                    pred[matching[v]] = v
+                else:
+                    unmatched.append(v)
+
+        # did we finish layering without finding any alternating paths?
+        if not unmatched:
+            # TODO - The lines between --- were unused and were thus commented
+            # out. This whole commented chunk should be reviewed to determine
+            # whether it should be built upon or completely removed.
+            # ---
+            # unlayered = {}
+            # for u in G:
+            #     # TODO Why is extra inner loop necessary?
+            #     for v in G[u]:
+            #         if v not in preds:
+            #             unlayered[v] = None
+            # ---
+            # TODO Originally, this function returned a three-tuple:
+            #
+            #     return (matching, list(pred), list(unlayered))
+            #
+            # For some reason, the documentation for this function
+            # indicated that the second and third elements of the returned
+            # three-tuple would be the vertices in the left and right vertex
+            # sets, respectively, that are also in the maximum independent set.
+            # However, what I think the author meant was that the second
+            # element is the list of vertices that were unmatched and the third
+            # element was the list of vertices that were matched. Since that
+            # seems to be the case, they don't really need to be returned,
+            # since that information can be inferred from the matching
+            # dictionary.
+
+            # All the matched nodes must be a key in the dictionary
+            for key in matching.copy():
+                matching[matching[key]] = key
+            return matching
+
+        # recursively search backward through layers to find alternating paths
+        # recursion returns true if found path, false otherwise
+        def recurse(v):
+            if v in preds:
+                L = preds.pop(v)
+                for u in L:
+                    if u in pred:
+                        pu = pred.pop(u)
+                        if pu is unmatched or recurse(pu):
+                            matching[v] = u
+                            return True
+            return False
+
+        for v in unmatched:
+            recurse(v)
+
+
+def _is_connected_by_alternating_path(G, v, matched_edges, unmatched_edges, targets):
+    """Returns True if and only if the vertex `v` is connected to one of
+    the target vertices by an alternating path in `G`.
+
+    An *alternating path* is a path in which every other edge is in the
+    specified maximum matching (and the remaining edges in the path are not in
+    the matching). An alternating path may have matched edges in the even
+    positions or in the odd positions, as long as the edges alternate between
+    'matched' and 'unmatched'.
+
+    `G` is an undirected bipartite NetworkX graph.
+
+    `v` is a vertex in `G`.
+
+    `matched_edges` is a set of edges present in a maximum matching in `G`.
+
+    `unmatched_edges` is a set of edges not present in a maximum
+    matching in `G`.
+
+    `targets` is a set of vertices.
+
+    """
+
+    def _alternating_dfs(u, along_matched=True):
+        """Returns True if and only if `u` is connected to one of the
+        targets by an alternating path.
+
+        `u` is a vertex in the graph `G`.
+
+        If `along_matched` is True, this step of the depth-first search
+        will continue only through edges in the given matching. Otherwise, it
+        will continue only through edges *not* in the given matching.
+
+        """
+        visited = set()
+        # Follow matched edges when depth is even,
+        # and follow unmatched edges when depth is odd.
+        initial_depth = 0 if along_matched else 1
+        stack = [(u, iter(G[u]), initial_depth)]
+        while stack:
+            parent, children, depth = stack[-1]
+            valid_edges = matched_edges if depth % 2 else unmatched_edges
+            try:
+                child = next(children)
+                if child not in visited:
+                    if (parent, child) in valid_edges or (child, parent) in valid_edges:
+                        if child in targets:
+                            return True
+                        visited.add(child)
+                        stack.append((child, iter(G[child]), depth + 1))
+            except StopIteration:
+                stack.pop()
+        return False
+
+    # Check for alternating paths starting with edges in the matching, then
+    # check for alternating paths starting with edges not in the
+    # matching.
+    return _alternating_dfs(v, along_matched=True) or _alternating_dfs(
+        v, along_matched=False
+    )
+
+
+def _connected_by_alternating_paths(G, matching, targets):
+    """Returns the set of vertices that are connected to one of the target
+    vertices by an alternating path in `G` or are themselves a target.
+
+    An *alternating path* is a path in which every other edge is in the
+    specified maximum matching (and the remaining edges in the path are not in
+    the matching). An alternating path may have matched edges in the even
+    positions or in the odd positions, as long as the edges alternate between
+    'matched' and 'unmatched'.
+
+    `G` is an undirected bipartite NetworkX graph.
+
+    `matching` is a dictionary representing a maximum matching in `G`, as
+    returned by, for example, :func:`maximum_matching`.
+
+    `targets` is a set of vertices.
+
+    """
+    # Get the set of matched edges and the set of unmatched edges. Only include
+    # one version of each undirected edge (for example, include edge (1, 2) but
+    # not edge (2, 1)). Using frozensets as an intermediary step we do not
+    # require nodes to be orderable.
+    edge_sets = {frozenset((u, v)) for u, v in matching.items()}
+    matched_edges = {tuple(edge) for edge in edge_sets}
+    unmatched_edges = {
+        (u, v) for (u, v) in G.edges() if frozenset((u, v)) not in edge_sets
+    }
+
+    return {
+        v
+        for v in G
+        if v in targets
+        or _is_connected_by_alternating_path(
+            G, v, matched_edges, unmatched_edges, targets
+        )
+    }
+
+
+@nx._dispatch
+def to_vertex_cover(G, matching, top_nodes=None):
+    """Returns the minimum vertex cover corresponding to the given maximum
+    matching of the bipartite graph `G`.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+      Undirected bipartite graph
+
+    matching : dictionary
+
+      A dictionary whose keys are vertices in `G` and whose values are the
+      distinct neighbors comprising the maximum matching for `G`, as returned
+      by, for example, :func:`maximum_matching`. The dictionary *must*
+      represent the maximum matching.
+
+    top_nodes : container
+
+      Container with all nodes in one bipartite node set. If not supplied
+      it will be computed. But if more than one solution exists an exception
+      will be raised.
+
+    Returns
+    -------
+    vertex_cover : :class:`set`
+
+      The minimum vertex cover in `G`.
+
+    Raises
+    ------
+    AmbiguousSolution
+      Raised if the input bipartite graph is disconnected and no container
+      with all nodes in one bipartite set is provided. When determining
+      the nodes in each bipartite set more than one valid solution is
+      possible if the input graph is disconnected.
+
+    Notes
+    -----
+    This function is implemented using the procedure guaranteed by `Konig's
+    theorem
+    <https://en.wikipedia.org/wiki/K%C3%B6nig%27s_theorem_%28graph_theory%29>`_,
+    which proves an equivalence between a maximum matching and a minimum vertex
+    cover in bipartite graphs.
+
+    Since a minimum vertex cover is the complement of a maximum independent set
+    for any graph, one can compute the maximum independent set of a bipartite
+    graph this way:
+
+    >>> G = nx.complete_bipartite_graph(2, 3)
+    >>> matching = nx.bipartite.maximum_matching(G)
+    >>> vertex_cover = nx.bipartite.to_vertex_cover(G, matching)
+    >>> independent_set = set(G) - vertex_cover
+    >>> print(list(independent_set))
+    [2, 3, 4]
+
+    See :mod:`bipartite documentation <networkx.algorithms.bipartite>`
+    for further details on how bipartite graphs are handled in NetworkX.
+
+    """
+    # This is a Python implementation of the algorithm described at
+    # <https://en.wikipedia.org/wiki/K%C3%B6nig%27s_theorem_%28graph_theory%29#Proof>.
+    L, R = bipartite_sets(G, top_nodes)
+    # Let U be the set of unmatched vertices in the left vertex set.
+    unmatched_vertices = set(G) - set(matching)
+    U = unmatched_vertices & L
+    # Let Z be the set of vertices that are either in U or are connected to U
+    # by alternating paths.
+    Z = _connected_by_alternating_paths(G, matching, U)
+    # At this point, every edge either has a right endpoint in Z or a left
+    # endpoint not in Z. This gives us the vertex cover.
+    return (L - Z) | (R & Z)
+
+
+#: Returns the maximum cardinality matching in the given bipartite graph.
+#:
+#: This function is simply an alias for :func:`hopcroft_karp_matching`.
+maximum_matching = hopcroft_karp_matching
+
+
+@nx._dispatch(edge_attrs="weight")
+def minimum_weight_full_matching(G, top_nodes=None, weight="weight"):
+    r"""Returns a minimum weight full matching of the bipartite graph `G`.
+
+    Let :math:`G = ((U, V), E)` be a weighted bipartite graph with real weights
+    :math:`w : E \to \mathbb{R}`. This function then produces a matching
+    :math:`M \subseteq E` with cardinality
+
+    .. math::
+       \lvert M \rvert = \min(\lvert U \rvert, \lvert V \rvert),
+
+    which minimizes the sum of the weights of the edges included in the
+    matching, :math:`\sum_{e \in M} w(e)`, or raises an error if no such
+    matching exists.
+
+    When :math:`\lvert U \rvert = \lvert V \rvert`, this is commonly
+    referred to as a perfect matching; here, since we allow
+    :math:`\lvert U \rvert` and :math:`\lvert V \rvert` to differ, we
+    follow Karp [1]_ and refer to the matching as *full*.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+      Undirected bipartite graph
+
+    top_nodes : container
+
+      Container with all nodes in one bipartite node set. If not supplied
+      it will be computed.
+
+    weight : string, optional (default='weight')
+
+       The edge data key used to provide each value in the matrix.
+       If None, then each edge has weight 1.
+
+    Returns
+    -------
+    matches : dictionary
+
+      The matching is returned as a dictionary, `matches`, such that
+      ``matches[v] == w`` if node `v` is matched to node `w`. Unmatched
+      nodes do not occur as a key in `matches`.
+
+    Raises
+    ------
+    ValueError
+      Raised if no full matching exists.
+
+    ImportError
+      Raised if SciPy is not available.
+
+    Notes
+    -----
+    The problem of determining a minimum weight full matching is also known as
+    the rectangular linear assignment problem. This implementation defers the
+    calculation of the assignment to SciPy.
+
+    References
+    ----------
+    .. [1] Richard Manning Karp:
+       An algorithm to Solve the m x n Assignment Problem in Expected Time
+       O(mn log n).
+       Networks, 10(2):143–152, 1980.
+
+    """
+    import numpy as np
+    import scipy as sp
+
+    left, right = nx.bipartite.sets(G, top_nodes)
+    U = list(left)
+    V = list(right)
+    # We explicitly create the biadjacency matrix having infinities
+    # where edges are missing (as opposed to zeros, which is what one would
+    # get by using toarray on the sparse matrix).
+    weights_sparse = biadjacency_matrix(
+        G, row_order=U, column_order=V, weight=weight, format="coo"
+    )
+    weights = np.full(weights_sparse.shape, np.inf)
+    weights[weights_sparse.row, weights_sparse.col] = weights_sparse.data
+    left_matches = sp.optimize.linear_sum_assignment(weights)
+    d = {U[u]: V[v] for u, v in zip(*left_matches)}
+    # d will contain the matching from edges in left to right; we need to
+    # add the ones from right to left as well.
+    d.update({v: u for u, v in d.items()})
+    return d

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

@@ -0,0 +1,111 @@
+"""Node redundancy for bipartite graphs."""
+from itertools import combinations
+
+import networkx as nx
+from networkx import NetworkXError
+
+__all__ = ["node_redundancy"]
+
+
+@nx._dispatch
+def node_redundancy(G, nodes=None):
+    r"""Computes the node redundancy coefficients for the nodes in the bipartite
+    graph `G`.
+
+    The redundancy coefficient of a node `v` is the fraction of pairs of
+    neighbors of `v` that are both linked to other nodes. In a one-mode
+    projection these nodes would be linked together even if `v` were
+    not there.
+
+    More formally, for any vertex `v`, the *redundancy coefficient of `v`* is
+    defined by
+
+    .. math::
+
+        rc(v) = \frac{|\{\{u, w\} \subseteq N(v),
+        \: \exists v' \neq  v,\: (v',u) \in E\:
+        \mathrm{and}\: (v',w) \in E\}|}{ \frac{|N(v)|(|N(v)|-1)}{2}},
+
+    where `N(v)` is the set of neighbors of `v` in `G`.
+
+    Parameters
+    ----------
+    G : graph
+        A bipartite graph
+
+    nodes : list or iterable (optional)
+        Compute redundancy for these nodes. The default is all nodes in G.
+
+    Returns
+    -------
+    redundancy : dictionary
+        A dictionary keyed by node with the node redundancy value.
+
+    Examples
+    --------
+    Compute the redundancy coefficient of each node in a graph::
+
+        >>> from networkx.algorithms import bipartite
+        >>> G = nx.cycle_graph(4)
+        >>> rc = bipartite.node_redundancy(G)
+        >>> rc[0]
+        1.0
+
+    Compute the average redundancy for the graph::
+
+        >>> from networkx.algorithms import bipartite
+        >>> G = nx.cycle_graph(4)
+        >>> rc = bipartite.node_redundancy(G)
+        >>> sum(rc.values()) / len(G)
+        1.0
+
+    Compute the average redundancy for a set of nodes::
+
+        >>> from networkx.algorithms import bipartite
+        >>> G = nx.cycle_graph(4)
+        >>> rc = bipartite.node_redundancy(G)
+        >>> nodes = [0, 2]
+        >>> sum(rc[n] for n in nodes) / len(nodes)
+        1.0
+
+    Raises
+    ------
+    NetworkXError
+        If any of the nodes in the graph (or in `nodes`, if specified) has
+        (out-)degree less than two (which would result in division by zero,
+        according to the definition of the redundancy coefficient).
+
+    References
+    ----------
+    .. [1] Latapy, Matthieu, Clémence Magnien, and Nathalie Del Vecchio (2008).
+       Basic notions for the analysis of large two-mode networks.
+       Social Networks 30(1), 31--48.
+
+    """
+    if nodes is None:
+        nodes = G
+    if any(len(G[v]) < 2 for v in nodes):
+        raise NetworkXError(
+            "Cannot compute redundancy coefficient for a node"
+            " that has fewer than two neighbors."
+        )
+    # TODO This can be trivially parallelized.
+    return {v: _node_redundancy(G, v) for v in nodes}
+
+
+def _node_redundancy(G, v):
+    """Returns the redundancy of the node `v` in the bipartite graph `G`.
+
+    If `G` is a graph with `n` nodes, the redundancy of a node is the ratio
+    of the "overlap" of `v` to the maximum possible overlap of `v`
+    according to its degree. The overlap of `v` is the number of pairs of
+    neighbors that have mutual neighbors themselves, other than `v`.
+
+    `v` must have at least two neighbors in `G`.
+
+    """
+    n = len(G[v])
+    overlap = sum(
+        1 for (u, w) in combinations(G[v], 2) if (set(G[u]) & set(G[w])) - {v}
+    )
+    return (2 * overlap) / (n * (n - 1))

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

@@ -0,0 +1,68 @@
+"""
+Spectral bipartivity measure.
+"""
+import networkx as nx
+
+__all__ = ["spectral_bipartivity"]
+
+
+@nx._dispatch(edge_attrs="weight")
+def spectral_bipartivity(G, nodes=None, weight="weight"):
+    """Returns the spectral bipartivity.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    nodes : list or container  optional(default is all nodes)
+      Nodes to return value of spectral bipartivity contribution.
+
+    weight : string or None  optional (default = 'weight')
+      Edge data key to use for edge weights. If None, weights set to 1.
+
+    Returns
+    -------
+    sb : float or dict
+       A single number if the keyword nodes is not specified, or
+       a dictionary keyed by node with the spectral bipartivity contribution
+       of that node as the value.
+
+    Examples
+    --------
+    >>> from networkx.algorithms import bipartite
+    >>> G = nx.path_graph(4)
+    >>> bipartite.spectral_bipartivity(G)
+    1.0
+
+    Notes
+    -----
+    This implementation uses Numpy (dense) matrices which are not efficient
+    for storing large sparse graphs.
+
+    See Also
+    --------
+    color
+
+    References
+    ----------
+    .. [1] E. Estrada and J. A. Rodríguez-Velázquez, "Spectral measures of
+       bipartivity in complex networks", PhysRev E 72, 046105 (2005)
+    """
+    import scipy as sp
+
+    nodelist = list(G)  # ordering of nodes in matrix
+    A = nx.to_numpy_array(G, nodelist, weight=weight)
+    expA = sp.linalg.expm(A)
+    expmA = sp.linalg.expm(-A)
+    coshA = 0.5 * (expA + expmA)
+    if nodes is None:
+        # return single number for entire graph
+        return coshA.diagonal().sum() / expA.diagonal().sum()
+    else:
+        # contribution for individual nodes
+        index = dict(zip(nodelist, range(len(nodelist))))
+        sb = {}
+        for n in nodes:
+            i = index[n]
+            sb[n] = coshA[i, i] / expA[i, i]
+        return sb

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

@@ -0,0 +1,29 @@
+"""Helper functions for community-finding algorithms."""
+import networkx as nx
+
+__all__ = ["is_partition"]
+
+
+@nx._dispatch
+def is_partition(G, communities):
+    """Returns *True* if `communities` is a partition of the nodes of `G`.
+
+    A partition of a universe set is a family of pairwise disjoint sets
+    whose union is the entire universe set.
+
+    Parameters
+    ----------
+    G : NetworkX graph.
+
+    communities : list or iterable of sets of nodes
+        If not a list, the iterable is converted internally to a list.
+        If it is an iterator it is exhausted.
+
+    """
+    # Alternate implementation:
+    # return all(sum(1 if v in c else 0 for c in communities) == 1 for v in G)
+    if not isinstance(communities, list):
+        communities = list(communities)
+    nodes = {n for c in communities for n in c if n in G}
+
+    return len(G) == len(nodes) == sum(len(c) for c in communities)

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

@@ -0,0 +1,79 @@
+from collections import defaultdict
+
+import networkx as nx
+
+__all__ = ["k_clique_communities"]
+
+
+@nx._dispatch
+def k_clique_communities(G, k, cliques=None):
+    """Find k-clique communities in graph using the percolation method.
+
+    A k-clique community is the union of all cliques of size k that
+    can be reached through adjacent (sharing k-1 nodes) k-cliques.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    k : int
+       Size of smallest clique
+
+    cliques: list or generator
+       Precomputed cliques (use networkx.find_cliques(G))
+
+    Returns
+    -------
+    Yields sets of nodes, one for each k-clique community.
+
+    Examples
+    --------
+    >>> G = nx.complete_graph(5)
+    >>> K5 = nx.convert_node_labels_to_integers(G, first_label=2)
+    >>> G.add_edges_from(K5.edges())
+    >>> c = list(nx.community.k_clique_communities(G, 4))
+    >>> sorted(list(c[0]))
+    [0, 1, 2, 3, 4, 5, 6]
+    >>> list(nx.community.k_clique_communities(G, 6))
+    []
+
+    References
+    ----------
+    .. [1] Gergely Palla, Imre Derényi, Illés Farkas1, and Tamás Vicsek,
+       Uncovering the overlapping community structure of complex networks
+       in nature and society Nature 435, 814-818, 2005,
+       doi:10.1038/nature03607
+    """
+    if k < 2:
+        raise nx.NetworkXError(f"k={k}, k must be greater than 1.")
+    if cliques is None:
+        cliques = nx.find_cliques(G)
+    cliques = [frozenset(c) for c in cliques if len(c) >= k]
+
+    # First index which nodes are in which cliques
+    membership_dict = defaultdict(list)
+    for clique in cliques:
+        for node in clique:
+            membership_dict[node].append(clique)
+
+    # For each clique, see which adjacent cliques percolate
+    perc_graph = nx.Graph()
+    perc_graph.add_nodes_from(cliques)
+    for clique in cliques:
+        for adj_clique in _get_adjacent_cliques(clique, membership_dict):
+            if len(clique.intersection(adj_clique)) >= (k - 1):
+                perc_graph.add_edge(clique, adj_clique)
+
+    # Connected components of clique graph with perc edges
+    # are the percolated cliques
+    for component in nx.connected_components(perc_graph):
+        yield (frozenset.union(*component))
+
+
+def _get_adjacent_cliques(clique, membership_dict):
+    adjacent_cliques = set()
+    for n in clique:
+        for adj_clique in membership_dict[n]:
+            if clique != adj_clique:
+                adjacent_cliques.add(adj_clique)
+    return adjacent_cliques

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

@@ -0,0 +1,139 @@
+"""Functions for computing the Kernighan–Lin bipartition algorithm."""
+
+from itertools import count
+
+import networkx as nx
+from networkx.algorithms.community.community_utils import is_partition
+from networkx.utils import BinaryHeap, not_implemented_for, py_random_state
+
+__all__ = ["kernighan_lin_bisection"]
+
+
+def _kernighan_lin_sweep(edges, side):
+    """
+    This is a modified form of Kernighan-Lin, which moves single nodes at a
+    time, alternating between sides to keep the bisection balanced.  We keep
+    two min-heaps of swap costs to make optimal-next-move selection fast.
+    """
+    costs0, costs1 = costs = BinaryHeap(), BinaryHeap()
+    for u, side_u, edges_u in zip(count(), side, edges):
+        cost_u = sum(w if side[v] else -w for v, w in edges_u)
+        costs[side_u].insert(u, cost_u if side_u else -cost_u)
+
+    def _update_costs(costs_x, x):
+        for y, w in edges[x]:
+            costs_y = costs[side[y]]
+            cost_y = costs_y.get(y)
+            if cost_y is not None:
+                cost_y += 2 * (-w if costs_x is costs_y else w)
+                costs_y.insert(y, cost_y, True)
+
+    i = 0
+    totcost = 0
+    while costs0 and costs1:
+        u, cost_u = costs0.pop()
+        _update_costs(costs0, u)
+        v, cost_v = costs1.pop()
+        _update_costs(costs1, v)
+        totcost += cost_u + cost_v
+        i += 1
+        yield totcost, i, (u, v)
+
+
+@not_implemented_for("directed")
+@py_random_state(4)
+@nx._dispatch(edge_attrs="weight")
+def kernighan_lin_bisection(G, partition=None, max_iter=10, weight="weight", seed=None):
+    """Partition a graph into two blocks using the Kernighan–Lin
+    algorithm.
+
+    This algorithm partitions a network into two sets by iteratively
+    swapping pairs of nodes to reduce the edge cut between the two sets.  The
+    pairs are chosen according to a modified form of Kernighan-Lin [1]_, which
+    moves node individually, alternating between sides to keep the bisection
+    balanced.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Graph must be undirected.
+
+    partition : tuple
+        Pair of iterables containing an initial partition. If not
+        specified, a random balanced partition is used.
+
+    max_iter : int
+        Maximum number of times to attempt swaps to find an
+        improvement before giving up.
+
+    weight : key
+        Edge data key to use as weight. If None, the weights are all
+        set to one.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+        Only used if partition is None
+
+    Returns
+    -------
+    partition : tuple
+        A pair of sets of nodes representing the bipartition.
+
+    Raises
+    ------
+    NetworkXError
+        If partition is not a valid partition of the nodes of the graph.
+
+    References
+    ----------
+    .. [1] Kernighan, B. W.; Lin, Shen (1970).
+       "An efficient heuristic procedure for partitioning graphs."
+       *Bell Systems Technical Journal* 49: 291--307.
+       Oxford University Press 2011.
+
+    """
+    n = len(G)
+    labels = list(G)
+    seed.shuffle(labels)
+    index = {v: i for i, v in enumerate(labels)}
+
+    if partition is None:
+        side = [0] * (n // 2) + [1] * ((n + 1) // 2)
+    else:
+        try:
+            A, B = partition
+        except (TypeError, ValueError) as err:
+            raise nx.NetworkXError("partition must be two sets") from err
+        if not is_partition(G, (A, B)):
+            raise nx.NetworkXError("partition invalid")
+        side = [0] * n
+        for a in A:
+            side[index[a]] = 1
+
+    if G.is_multigraph():
+        edges = [
+            [
+                (index[u], sum(e.get(weight, 1) for e in d.values()))
+                for u, d in G[v].items()
+            ]
+            for v in labels
+        ]
+    else:
+        edges = [
+            [(index[u], e.get(weight, 1)) for u, e in G[v].items()] for v in labels
+        ]
+
+    for i in range(max_iter):
+        costs = list(_kernighan_lin_sweep(edges, side))
+        min_cost, min_i, _ = min(costs)
+        if min_cost >= 0:
+            break
+
+        for _, _, (u, v) in costs[:min_i]:
+            side[u] = 1
+            side[v] = 0
+
+    A = {u for u, s in zip(labels, side) if s == 0}
+    B = {u for u, s in zip(labels, side) if s == 1}
+    return A, B

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

@@ -0,0 +1,337 @@
+"""
+Label propagation community detection algorithms.
+"""
+from collections import Counter, defaultdict, deque
+
+import networkx as nx
+from networkx.utils import groups, not_implemented_for, py_random_state
+
+__all__ = [
+    "label_propagation_communities",
+    "asyn_lpa_communities",
+    "fast_label_propagation_communities",
+]
+
+
+@py_random_state("seed")
+@nx._dispatch(edge_attrs="weight")
+def fast_label_propagation_communities(G, *, weight=None, seed=None):
+    """Returns communities in `G` as detected by fast label propagation.
+
+    The fast label propagation algorithm is described in [1]_. The algorithm is
+    probabilistic and the found communities may vary in different executions.
+
+    The algorithm operates as follows. First, the community label of each node is
+    set to a unique label. The algorithm then repeatedly updates the labels of
+    the nodes to the most frequent label in their neighborhood. In case of ties,
+    a random label is chosen from the most frequent labels.
+
+    The algorithm maintains a queue of nodes that still need to be processed.
+    Initially, all nodes are added to the queue in a random order. Then the nodes
+    are removed from the queue one by one and processed. If a node updates its label,
+    all its neighbors that have a different label are added to the queue (if not
+    already in the queue). The algorithm stops when the queue is empty.
+
+    Parameters
+    ----------
+    G : Graph, DiGraph, MultiGraph, or MultiDiGraph
+      Any NetworkX graph.
+
+    weight : string, or None (default)
+      The edge attribute representing a non-negative weight of an edge. If None,
+      each edge is assumed to have weight one. The weight of an edge is used in
+      determining the frequency with which a label appears among the neighbors of
+      a node (edge with weight `w` is equivalent to `w` unweighted edges).
+
+    seed : integer, random_state, or None (default)
+      Indicator of random number generation state. See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    communities : iterable
+      Iterable of communities given as sets of nodes.
+
+    Notes
+    -----
+    Edge directions are ignored for directed graphs.
+    Edge weights must be non-negative numbers.
+
+    References
+    ----------
+    .. [1] Vincent A. Traag & Lovro Šubelj. "Large network community detection by
+    fast label propagation." Scientific Reports 13 (2023): 2701.
+    https://doi.org/10.1038/s41598-023-29610-z
+    """
+
+    # Queue of nodes to be processed.
+    nodes_queue = deque(G)
+    seed.shuffle(nodes_queue)
+
+    # Set of nodes in the queue.
+    nodes_set = set(G)
+
+    # Assign unique label to each node.
+    comms = {node: i for i, node in enumerate(G)}
+
+    while nodes_queue:
+        # Remove next node from the queue to process.
+        node = nodes_queue.popleft()
+        nodes_set.remove(node)
+
+        # Isolated nodes retain their initial label.
+        if G.degree(node) > 0:
+            # Compute frequency of labels in node's neighborhood.
+            label_freqs = _fast_label_count(G, comms, node, weight)
+            max_freq = max(label_freqs.values())
+
+            # Always sample new label from most frequent labels.
+            comm = seed.choice(
+                [comm for comm in label_freqs if label_freqs[comm] == max_freq]
+            )
+
+            if comms[node] != comm:
+                comms[node] = comm
+
+                # Add neighbors that have different label to the queue.
+                for nbr in nx.all_neighbors(G, node):
+                    if comms[nbr] != comm and nbr not in nodes_set:
+                        nodes_queue.append(nbr)
+                        nodes_set.add(nbr)
+
+    yield from groups(comms).values()
+
+
+def _fast_label_count(G, comms, node, weight=None):
+    """Computes the frequency of labels in the neighborhood of a node.
+
+    Returns a dictionary keyed by label to the frequency of that label.
+    """
+
+    if weight is None:
+        # Unweighted (un)directed simple graph.
+        if not G.is_multigraph():
+            label_freqs = Counter(map(comms.get, nx.all_neighbors(G, node)))
+
+        # Unweighted (un)directed multigraph.
+        else:
+            label_freqs = defaultdict(int)
+            for nbr in G[node]:
+                label_freqs[comms[nbr]] += len(G[node][nbr])
+
+            if G.is_directed():
+                for nbr in G.pred[node]:
+                    label_freqs[comms[nbr]] += len(G.pred[node][nbr])
+
+    else:
+        # Weighted undirected simple/multigraph.
+        label_freqs = defaultdict(float)
+        for _, nbr, w in G.edges(node, data=weight, default=1):
+            label_freqs[comms[nbr]] += w
+
+        # Weighted directed simple/multigraph.
+        if G.is_directed():
+            for nbr, _, w in G.in_edges(node, data=weight, default=1):
+                label_freqs[comms[nbr]] += w
+
+    return label_freqs
+
+
+@py_random_state(2)
+@nx._dispatch(edge_attrs="weight")
+def asyn_lpa_communities(G, weight=None, seed=None):
+    """Returns communities in `G` as detected by asynchronous label
+    propagation.
+
+    The asynchronous label propagation algorithm is described in
+    [1]_. The algorithm is probabilistic and the found communities may
+    vary on different executions.
+
+    The algorithm proceeds as follows. After initializing each node with
+    a unique label, the algorithm repeatedly sets the label of a node to
+    be the label that appears most frequently among that nodes
+    neighbors. The algorithm halts when each node has the label that
+    appears most frequently among its neighbors. The algorithm is
+    asynchronous because each node is updated without waiting for
+    updates on the remaining nodes.
+
+    This generalized version of the algorithm in [1]_ accepts edge
+    weights.
+
+    Parameters
+    ----------
+    G : Graph
+
+    weight : string
+        The edge attribute representing the weight of an edge.
+        If None, each edge is assumed to have weight one. In this
+        algorithm, the weight of an edge is used in determining the
+        frequency with which a label appears among the neighbors of a
+        node: a higher weight means the label appears more often.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    communities : iterable
+        Iterable of communities given as sets of nodes.
+
+    Notes
+    -----
+    Edge weight attributes must be numerical.
+
+    References
+    ----------
+    .. [1] Raghavan, Usha Nandini, Réka Albert, and Soundar Kumara. "Near
+           linear time algorithm to detect community structures in large-scale
+           networks." Physical Review E 76.3 (2007): 036106.
+    """
+
+    labels = {n: i for i, n in enumerate(G)}
+    cont = True
+
+    while cont:
+        cont = False
+        nodes = list(G)
+        seed.shuffle(nodes)
+
+        for node in nodes:
+            if not G[node]:
+                continue
+
+            # Get label frequencies among adjacent nodes.
+            # Depending on the order they are processed in,
+            # some nodes will be in iteration t and others in t-1,
+            # making the algorithm asynchronous.
+            if weight is None:
+                # initialising a Counter from an iterator of labels is
+                # faster for getting unweighted label frequencies
+                label_freq = Counter(map(labels.get, G[node]))
+            else:
+                # updating a defaultdict is substantially faster
+                # for getting weighted label frequencies
+                label_freq = defaultdict(float)
+                for _, v, wt in G.edges(node, data=weight, default=1):
+                    label_freq[labels[v]] += wt
+
+            # Get the labels that appear with maximum frequency.
+            max_freq = max(label_freq.values())
+            best_labels = [
+                label for label, freq in label_freq.items() if freq == max_freq
+            ]
+
+            # If the node does not have one of the maximum frequency labels,
+            # randomly choose one of them and update the node's label.
+            # Continue the iteration as long as at least one node
+            # doesn't have a maximum frequency label.
+            if labels[node] not in best_labels:
+                labels[node] = seed.choice(best_labels)
+                cont = True
+
+    yield from groups(labels).values()
+
+
+@not_implemented_for("directed")
+@nx._dispatch
+def label_propagation_communities(G):
+    """Generates community sets determined by label propagation
+
+    Finds communities in `G` using a semi-synchronous label propagation
+    method [1]_. This method combines the advantages of both the synchronous
+    and asynchronous models. Not implemented for directed graphs.
+
+    Parameters
+    ----------
+    G : graph
+        An undirected NetworkX graph.
+
+    Returns
+    -------
+    communities : iterable
+        A dict_values object that contains a set of nodes for each community.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+       If the graph is directed
+
+    References
+    ----------
+    .. [1] Cordasco, G., & Gargano, L. (2010, December). Community detection
+       via semi-synchronous label propagation algorithms. In Business
+       Applications of Social Network Analysis (BASNA), 2010 IEEE International
+       Workshop on (pp. 1-8). IEEE.
+    """
+    coloring = _color_network(G)
+    # Create a unique label for each node in the graph
+    labeling = {v: k for k, v in enumerate(G)}
+    while not _labeling_complete(labeling, G):
+        # Update the labels of every node with the same color.
+        for color, nodes in coloring.items():
+            for n in nodes:
+                _update_label(n, labeling, G)
+
+    clusters = defaultdict(set)
+    for node, label in labeling.items():
+        clusters[label].add(node)
+    return clusters.values()
+
+
+def _color_network(G):
+    """Colors the network so that neighboring nodes all have distinct colors.
+
+    Returns a dict keyed by color to a set of nodes with that color.
+    """
+    coloring = {}  # color => set(node)
+    colors = nx.coloring.greedy_color(G)
+    for node, color in colors.items():
+        if color in coloring:
+            coloring[color].add(node)
+        else:
+            coloring[color] = {node}
+    return coloring
+
+
+def _labeling_complete(labeling, G):
+    """Determines whether or not LPA is done.
+
+    Label propagation is complete when all nodes have a label that is
+    in the set of highest frequency labels amongst its neighbors.
+
+    Nodes with no neighbors are considered complete.
+    """
+    return all(
+        labeling[v] in _most_frequent_labels(v, labeling, G) for v in G if len(G[v]) > 0
+    )
+
+
+def _most_frequent_labels(node, labeling, G):
+    """Returns a set of all labels with maximum frequency in `labeling`.
+
+    Input `labeling` should be a dict keyed by node to labels.
+    """
+    if not G[node]:
+        # Nodes with no neighbors are themselves a community and are labeled
+        # accordingly, hence the immediate if statement.
+        return {labeling[node]}
+
+    # Compute the frequencies of all neighbours of node
+    freqs = Counter(labeling[q] for q in G[node])
+    max_freq = max(freqs.values())
+    return {label for label, freq in freqs.items() if freq == max_freq}
+
+
+def _update_label(node, labeling, G):
+    """Updates the label of a node using the Prec-Max tie breaking algorithm
+
+    The algorithm is explained in: 'Community Detection via Semi-Synchronous
+    Label Propagation Algorithms' Cordasco and Gargano, 2011
+    """
+    high_labels = _most_frequent_labels(node, labeling, G)
+    if len(high_labels) == 1:
+        labeling[node] = high_labels.pop()
+    elif len(high_labels) > 1:
+        # Prec-Max
+        if labeling[node] not in high_labels:
+            labeling[node] = max(high_labels)

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

@@ -0,0 +1,129 @@
+import pytest
+
+import networkx as nx
+from networkx import Graph, NetworkXError
+from networkx.algorithms.community import asyn_fluidc
+
+
+def test_exceptions():
+    test = Graph()
+    test.add_node("a")
+    pytest.raises(NetworkXError, asyn_fluidc, test, "hi")
+    pytest.raises(NetworkXError, asyn_fluidc, test, -1)
+    pytest.raises(NetworkXError, asyn_fluidc, test, 3)
+    test.add_node("b")
+    pytest.raises(NetworkXError, asyn_fluidc, test, 1)
+
+
+def test_single_node():
+    test = Graph()
+
+    test.add_node("a")
+
+    # ground truth
+    ground_truth = {frozenset(["a"])}
+
+    communities = asyn_fluidc(test, 1)
+    result = {frozenset(c) for c in communities}
+    assert result == ground_truth
+
+
+def test_two_nodes():
+    test = Graph()
+
+    test.add_edge("a", "b")
+
+    # ground truth
+    ground_truth = {frozenset(["a"]), frozenset(["b"])}
+
+    communities = asyn_fluidc(test, 2)
+    result = {frozenset(c) for c in communities}
+    assert result == ground_truth
+
+
+def test_two_clique_communities():
+    test = Graph()
+
+    # c1
+    test.add_edge("a", "b")
+    test.add_edge("a", "c")
+    test.add_edge("b", "c")
+
+    # connection
+    test.add_edge("c", "d")
+
+    # c2
+    test.add_edge("d", "e")
+    test.add_edge("d", "f")
+    test.add_edge("f", "e")
+
+    # ground truth
+    ground_truth = {frozenset(["a", "c", "b"]), frozenset(["e", "d", "f"])}
+
+    communities = asyn_fluidc(test, 2, seed=7)
+    result = {frozenset(c) for c in communities}
+    assert result == ground_truth
+
+
+def test_five_clique_ring():
+    test = Graph()
+
+    # c1
+    test.add_edge("1a", "1b")
+    test.add_edge("1a", "1c")
+    test.add_edge("1a", "1d")
+    test.add_edge("1b", "1c")
+    test.add_edge("1b", "1d")
+    test.add_edge("1c", "1d")
+
+    # c2
+    test.add_edge("2a", "2b")
+    test.add_edge("2a", "2c")
+    test.add_edge("2a", "2d")
+    test.add_edge("2b", "2c")
+    test.add_edge("2b", "2d")
+    test.add_edge("2c", "2d")
+
+    # c3
+    test.add_edge("3a", "3b")
+    test.add_edge("3a", "3c")
+    test.add_edge("3a", "3d")
+    test.add_edge("3b", "3c")
+    test.add_edge("3b", "3d")
+    test.add_edge("3c", "3d")
+
+    # c4
+    test.add_edge("4a", "4b")
+    test.add_edge("4a", "4c")
+    test.add_edge("4a", "4d")
+    test.add_edge("4b", "4c")
+    test.add_edge("4b", "4d")
+    test.add_edge("4c", "4d")
+
+    # c5
+    test.add_edge("5a", "5b")
+    test.add_edge("5a", "5c")
+    test.add_edge("5a", "5d")
+    test.add_edge("5b", "5c")
+    test.add_edge("5b", "5d")
+    test.add_edge("5c", "5d")
+
+    # connections
+    test.add_edge("1a", "2c")
+    test.add_edge("2a", "3c")
+    test.add_edge("3a", "4c")
+    test.add_edge("4a", "5c")
+    test.add_edge("5a", "1c")
+
+    # ground truth
+    ground_truth = {
+        frozenset(["1a", "1b", "1c", "1d"]),
+        frozenset(["2a", "2b", "2c", "2d"]),
+        frozenset(["3a", "3b", "3c", "3d"]),
+        frozenset(["4a", "4b", "4c", "4d"]),
+        frozenset(["5a", "5b", "5c", "5d"]),
+    }
+
+    communities = asyn_fluidc(test, 5, seed=9)
+    result = {frozenset(c) for c in communities}
+    assert result == ground_truth

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

@@ -0,0 +1,84 @@
+"""Unit tests for the :mod:`networkx.algorithms.community.centrality`
+module.
+
+"""
+from operator import itemgetter
+
+import networkx as nx
+
+
+def set_of_sets(iterable):
+    return set(map(frozenset, iterable))
+
+
+def validate_communities(result, expected):
+    assert set_of_sets(result) == set_of_sets(expected)
+
+
+def validate_possible_communities(result, *expected):
+    assert any(set_of_sets(result) == set_of_sets(p) for p in expected)
+
+
+class TestGirvanNewman:
+    """Unit tests for the
+    :func:`networkx.algorithms.community.centrality.girvan_newman`
+    function.
+
+    """
+
+    def test_no_edges(self):
+        G = nx.empty_graph(3)
+        communities = list(nx.community.girvan_newman(G))
+        assert len(communities) == 1
+        validate_communities(communities[0], [{0}, {1}, {2}])
+
+    def test_undirected(self):
+        # Start with the graph .-.-.-.
+        G = nx.path_graph(4)
+        communities = list(nx.community.girvan_newman(G))
+        assert len(communities) == 3
+        # After one removal, we get the graph .-. .-.
+        validate_communities(communities[0], [{0, 1}, {2, 3}])
+        # After the next, we get the graph .-. . ., but there are two
+        # symmetric possible versions.
+        validate_possible_communities(
+            communities[1], [{0}, {1}, {2, 3}], [{0, 1}, {2}, {3}]
+        )
+        # After the last removal, we always get the empty graph.
+        validate_communities(communities[2], [{0}, {1}, {2}, {3}])
+
+    def test_directed(self):
+        G = nx.DiGraph(nx.path_graph(4))
+        communities = list(nx.community.girvan_newman(G))
+        assert len(communities) == 3
+        validate_communities(communities[0], [{0, 1}, {2, 3}])
+        validate_possible_communities(
+            communities[1], [{0}, {1}, {2, 3}], [{0, 1}, {2}, {3}]
+        )
+        validate_communities(communities[2], [{0}, {1}, {2}, {3}])
+
+    def test_selfloops(self):
+        G = nx.path_graph(4)
+        G.add_edge(0, 0)
+        G.add_edge(2, 2)
+        communities = list(nx.community.girvan_newman(G))
+        assert len(communities) == 3
+        validate_communities(communities[0], [{0, 1}, {2, 3}])
+        validate_possible_communities(
+            communities[1], [{0}, {1}, {2, 3}], [{0, 1}, {2}, {3}]
+        )
+        validate_communities(communities[2], [{0}, {1}, {2}, {3}])
+
+    def test_most_valuable_edge(self):
+        G = nx.Graph()
+        G.add_weighted_edges_from([(0, 1, 3), (1, 2, 2), (2, 3, 1)])
+        # Let the most valuable edge be the one with the highest weight.
+
+        def heaviest(G):
+            return max(G.edges(data="weight"), key=itemgetter(2))[:2]
+
+        communities = list(nx.community.girvan_newman(G, heaviest))
+        assert len(communities) == 3
+        validate_communities(communities[0], [{0}, {1, 2, 3}])
+        validate_communities(communities[1], [{0}, {1}, {2, 3}])
+        validate_communities(communities[2], [{0}, {1}, {2}, {3}])