Add files using upload-large-folder tool

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/__init__.py

@@ -0,0 +1,11 @@
+"""Connectivity and cut algorithms"""
+
+from .connectivity import *
+from .cuts import *
+from .edge_augmentation import *
+from .edge_kcomponents import *
+from .disjoint_paths import *
+from .kcomponents import *
+from .kcutsets import *
+from .stoerwagner import *
+from .utils import *

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/connectivity.py

@@ -0,0 +1,811 @@
+"""
+Flow based connectivity algorithms
+"""
+
+import itertools
+from operator import itemgetter
+
+import networkx as nx
+
+# Define the default maximum flow function to use in all flow based
+# connectivity algorithms.
+from networkx.algorithms.flow import (
+    boykov_kolmogorov,
+    build_residual_network,
+    dinitz,
+    edmonds_karp,
+    preflow_push,
+    shortest_augmenting_path,
+)
+
+default_flow_func = edmonds_karp
+
+from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity
+
+__all__ = [
+    "average_node_connectivity",
+    "local_node_connectivity",
+    "node_connectivity",
+    "local_edge_connectivity",
+    "edge_connectivity",
+    "all_pairs_node_connectivity",
+]
+
+
+@nx._dispatchable(graphs={"G": 0, "auxiliary?": 4}, preserve_graph_attrs={"auxiliary"})
+def local_node_connectivity(
+    G, s, t, flow_func=None, auxiliary=None, residual=None, cutoff=None
+):
+    r"""Computes local node connectivity for nodes s and t.
+
+    Local node connectivity for two non adjacent nodes s and t is the
+    minimum number of nodes that must be removed (along with their incident
+    edges) to disconnect them.
+
+    This is a flow based implementation of node connectivity. We compute the
+    maximum flow on an auxiliary digraph build from the original input
+    graph (see below for details).
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    s : node
+        Source node
+
+    t : node
+        Target node
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The choice
+        of the default function may change from version to version and
+        should not be relied on. Default value: None.
+
+    auxiliary : NetworkX DiGraph
+        Auxiliary digraph to compute flow based node connectivity. It has
+        to have a graph attribute called mapping with a dictionary mapping
+        node names in G and in the auxiliary digraph. If provided
+        it will be reused instead of recreated. Default value: None.
+
+    residual : NetworkX DiGraph
+        Residual network to compute maximum flow. If provided it will be
+        reused instead of recreated. Default value: None.
+
+    cutoff : integer, float, or None (default: None)
+        If specified, the maximum flow algorithm will terminate when the
+        flow value reaches or exceeds the cutoff. This only works for flows
+        that support the cutoff parameter (most do) and is ignored otherwise.
+
+    Returns
+    -------
+    K : integer
+        local node connectivity for nodes s and t
+
+    Examples
+    --------
+    This function is not imported in the base NetworkX namespace, so you
+    have to explicitly import it from the connectivity package:
+
+    >>> from networkx.algorithms.connectivity import local_node_connectivity
+
+    We use in this example the platonic icosahedral graph, which has node
+    connectivity 5.
+
+    >>> G = nx.icosahedral_graph()
+    >>> local_node_connectivity(G, 0, 6)
+    5
+
+    If you need to compute local connectivity on several pairs of
+    nodes in the same graph, it is recommended that you reuse the
+    data structures that NetworkX uses in the computation: the
+    auxiliary digraph for node connectivity, and the residual
+    network for the underlying maximum flow computation.
+
+    Example of how to compute local node connectivity among
+    all pairs of nodes of the platonic icosahedral graph reusing
+    the data structures.
+
+    >>> import itertools
+    >>> # You also have to explicitly import the function for
+    >>> # building the auxiliary digraph from the connectivity package
+    >>> from networkx.algorithms.connectivity import build_auxiliary_node_connectivity
+    >>> H = build_auxiliary_node_connectivity(G)
+    >>> # And the function for building the residual network from the
+    >>> # flow package
+    >>> from networkx.algorithms.flow import build_residual_network
+    >>> # Note that the auxiliary digraph has an edge attribute named capacity
+    >>> R = build_residual_network(H, "capacity")
+    >>> result = dict.fromkeys(G, dict())
+    >>> # Reuse the auxiliary digraph and the residual network by passing them
+    >>> # as parameters
+    >>> for u, v in itertools.combinations(G, 2):
+    ...     k = local_node_connectivity(G, u, v, auxiliary=H, residual=R)
+    ...     result[u][v] = k
+    >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
+    True
+
+    You can also use alternative flow algorithms for computing node
+    connectivity. For instance, in dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better than
+    the default :meth:`edmonds_karp` which is faster for sparse
+    networks with highly skewed degree distributions. Alternative flow
+    functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> local_node_connectivity(G, 0, 6, flow_func=shortest_augmenting_path)
+    5
+
+    Notes
+    -----
+    This is a flow based implementation of node connectivity. We compute the
+    maximum flow using, by default, the :meth:`edmonds_karp` algorithm (see:
+    :meth:`maximum_flow`) on an auxiliary digraph build from the original
+    input graph:
+
+    For an undirected graph G having `n` nodes and `m` edges we derive a
+    directed graph H with `2n` nodes and `2m+n` arcs by replacing each
+    original node `v` with two nodes `v_A`, `v_B` linked by an (internal)
+    arc in H. Then for each edge (`u`, `v`) in G we add two arcs
+    (`u_B`, `v_A`) and (`v_B`, `u_A`) in H. Finally we set the attribute
+    capacity = 1 for each arc in H [1]_ .
+
+    For a directed graph G having `n` nodes and `m` arcs we derive a
+    directed graph H with `2n` nodes and `m+n` arcs by replacing each
+    original node `v` with two nodes `v_A`, `v_B` linked by an (internal)
+    arc (`v_A`, `v_B`) in H. Then for each arc (`u`, `v`) in G we add one arc
+    (`u_B`, `v_A`) in H. Finally we set the attribute capacity = 1 for
+    each arc in H.
+
+    This is equal to the local node connectivity because the value of
+    a maximum s-t-flow is equal to the capacity of a minimum s-t-cut.
+
+    See also
+    --------
+    :meth:`local_edge_connectivity`
+    :meth:`node_connectivity`
+    :meth:`minimum_node_cut`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and
+        Erlebach, 'Network Analysis: Methodological Foundations', Lecture
+        Notes in Computer Science, Volume 3418, Springer-Verlag, 2005.
+        http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
+
+    """
+    if flow_func is None:
+        flow_func = default_flow_func
+
+    if auxiliary is None:
+        H = build_auxiliary_node_connectivity(G)
+    else:
+        H = auxiliary
+
+    mapping = H.graph.get("mapping", None)
+    if mapping is None:
+        raise nx.NetworkXError("Invalid auxiliary digraph.")
+
+    kwargs = {"flow_func": flow_func, "residual": residual}
+
+    if flow_func is not preflow_push:
+        kwargs["cutoff"] = cutoff
+
+    if flow_func is shortest_augmenting_path:
+        kwargs["two_phase"] = True
+
+    return nx.maximum_flow_value(H, f"{mapping[s]}B", f"{mapping[t]}A", **kwargs)
+
+
+@nx._dispatchable
+def node_connectivity(G, s=None, t=None, flow_func=None):
+    r"""Returns node connectivity for a graph or digraph G.
+
+    Node connectivity is equal to the minimum number of nodes that
+    must be removed to disconnect G or render it trivial. If source
+    and target nodes are provided, this function returns the local node
+    connectivity: the minimum number of nodes that must be removed to break
+    all paths from source to target in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    s : node
+        Source node. Optional. Default value: None.
+
+    t : node
+        Target node. Optional. Default value: None.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The
+        choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    Returns
+    -------
+    K : integer
+        Node connectivity of G, or local node connectivity if source
+        and target are provided.
+
+    Examples
+    --------
+    >>> # Platonic icosahedral graph is 5-node-connected
+    >>> G = nx.icosahedral_graph()
+    >>> nx.node_connectivity(G)
+    5
+
+    You can use alternative flow algorithms for the underlying maximum
+    flow computation. In dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better
+    than the default :meth:`edmonds_karp`, which is faster for
+    sparse networks with highly skewed degree distributions. Alternative
+    flow functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> nx.node_connectivity(G, flow_func=shortest_augmenting_path)
+    5
+
+    If you specify a pair of nodes (source and target) as parameters,
+    this function returns the value of local node connectivity.
+
+    >>> nx.node_connectivity(G, 3, 7)
+    5
+
+    If you need to perform several local computations among different
+    pairs of nodes on the same graph, it is recommended that you reuse
+    the data structures used in the maximum flow computations. See
+    :meth:`local_node_connectivity` for details.
+
+    Notes
+    -----
+    This is a flow based implementation of node connectivity. The
+    algorithm works by solving $O((n-\delta-1+\delta(\delta-1)/2))$
+    maximum flow problems on an auxiliary digraph. Where $\delta$
+    is the minimum degree of G. For details about the auxiliary
+    digraph and the computation of local node connectivity see
+    :meth:`local_node_connectivity`. This implementation is based
+    on algorithm 11 in [1]_.
+
+    See also
+    --------
+    :meth:`local_node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    if (s is not None and t is None) or (s is None and t is not None):
+        raise nx.NetworkXError("Both source and target must be specified.")
+
+    # Local node connectivity
+    if s is not None and t is not None:
+        if s not in G:
+            raise nx.NetworkXError(f"node {s} not in graph")
+        if t not in G:
+            raise nx.NetworkXError(f"node {t} not in graph")
+        return local_node_connectivity(G, s, t, flow_func=flow_func)
+
+    # Global node connectivity
+    if G.is_directed():
+        if not nx.is_weakly_connected(G):
+            return 0
+        iter_func = itertools.permutations
+        # It is necessary to consider both predecessors
+        # and successors for directed graphs
+
+        def neighbors(v):
+            return itertools.chain.from_iterable([G.predecessors(v), G.successors(v)])
+
+    else:
+        if not nx.is_connected(G):
+            return 0
+        iter_func = itertools.combinations
+        neighbors = G.neighbors
+
+    # Reuse the auxiliary digraph and the residual network
+    H = build_auxiliary_node_connectivity(G)
+    R = build_residual_network(H, "capacity")
+    kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
+
+    # Pick a node with minimum degree
+    # Node connectivity is bounded by degree.
+    v, K = min(G.degree(), key=itemgetter(1))
+    # compute local node connectivity with all its non-neighbors nodes
+    for w in set(G) - set(neighbors(v)) - {v}:
+        kwargs["cutoff"] = K
+        K = min(K, local_node_connectivity(G, v, w, **kwargs))
+    # Also for non adjacent pairs of neighbors of v
+    for x, y in iter_func(neighbors(v), 2):
+        if y in G[x]:
+            continue
+        kwargs["cutoff"] = K
+        K = min(K, local_node_connectivity(G, x, y, **kwargs))
+
+    return K
+
+
+@nx._dispatchable
+def average_node_connectivity(G, flow_func=None):
+    r"""Returns the average connectivity of a graph G.
+
+    The average connectivity `\bar{\kappa}` of a graph G is the average
+    of local node connectivity over all pairs of nodes of G [1]_ .
+
+    .. math::
+
+        \bar{\kappa}(G) = \frac{\sum_{u,v} \kappa_{G}(u,v)}{{n \choose 2}}
+
+    Parameters
+    ----------
+
+    G : NetworkX graph
+        Undirected graph
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See :meth:`local_node_connectivity`
+        for details. The choice of the default function may change from
+        version to version and should not be relied on. Default value: None.
+
+    Returns
+    -------
+    K : float
+        Average node connectivity
+
+    See also
+    --------
+    :meth:`local_node_connectivity`
+    :meth:`node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1]  Beineke, L., O. Oellermann, and R. Pippert (2002). The average
+            connectivity of a graph. Discrete mathematics 252(1-3), 31-45.
+            http://www.sciencedirect.com/science/article/pii/S0012365X01001807
+
+    """
+    if G.is_directed():
+        iter_func = itertools.permutations
+    else:
+        iter_func = itertools.combinations
+
+    # Reuse the auxiliary digraph and the residual network
+    H = build_auxiliary_node_connectivity(G)
+    R = build_residual_network(H, "capacity")
+    kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
+
+    num, den = 0, 0
+    for u, v in iter_func(G, 2):
+        num += local_node_connectivity(G, u, v, **kwargs)
+        den += 1
+
+    if den == 0:  # Null Graph
+        return 0
+    return num / den
+
+
+@nx._dispatchable
+def all_pairs_node_connectivity(G, nbunch=None, flow_func=None):
+    """Compute node connectivity between all pairs of nodes of G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    nbunch: container
+        Container of nodes. If provided node connectivity will be computed
+        only over pairs of nodes in nbunch.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The
+        choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    Returns
+    -------
+    all_pairs : dict
+        A dictionary with node connectivity between all pairs of nodes
+        in G, or in nbunch if provided.
+
+    See also
+    --------
+    :meth:`local_node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`local_edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    """
+    if nbunch is None:
+        nbunch = G
+    else:
+        nbunch = set(nbunch)
+
+    directed = G.is_directed()
+    if directed:
+        iter_func = itertools.permutations
+    else:
+        iter_func = itertools.combinations
+
+    all_pairs = {n: {} for n in nbunch}
+
+    # Reuse auxiliary digraph and residual network
+    H = build_auxiliary_node_connectivity(G)
+    mapping = H.graph["mapping"]
+    R = build_residual_network(H, "capacity")
+    kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
+
+    for u, v in iter_func(nbunch, 2):
+        K = local_node_connectivity(G, u, v, **kwargs)
+        all_pairs[u][v] = K
+        if not directed:
+            all_pairs[v][u] = K
+
+    return all_pairs
+
+
+@nx._dispatchable(graphs={"G": 0, "auxiliary?": 4})
+def local_edge_connectivity(
+    G, s, t, flow_func=None, auxiliary=None, residual=None, cutoff=None
+):
+    r"""Returns local edge connectivity for nodes s and t in G.
+
+    Local edge connectivity for two nodes s and t is the minimum number
+    of edges that must be removed to disconnect them.
+
+    This is a flow based implementation of edge connectivity. We compute the
+    maximum flow on an auxiliary digraph build from the original
+    network (see below for details). This is equal to the local edge
+    connectivity because the value of a maximum s-t-flow is equal to the
+    capacity of a minimum s-t-cut (Ford and Fulkerson theorem) [1]_ .
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected or directed graph
+
+    s : node
+        Source node
+
+    t : node
+        Target node
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The
+        choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    auxiliary : NetworkX DiGraph
+        Auxiliary digraph for computing flow based edge connectivity. If
+        provided it will be reused instead of recreated. Default value: None.
+
+    residual : NetworkX DiGraph
+        Residual network to compute maximum flow. If provided it will be
+        reused instead of recreated. Default value: None.
+
+    cutoff : integer, float, or None (default: None)
+        If specified, the maximum flow algorithm will terminate when the
+        flow value reaches or exceeds the cutoff. This only works for flows
+        that support the cutoff parameter (most do) and is ignored otherwise.
+
+    Returns
+    -------
+    K : integer
+        local edge connectivity for nodes s and t.
+
+    Examples
+    --------
+    This function is not imported in the base NetworkX namespace, so you
+    have to explicitly import it from the connectivity package:
+
+    >>> from networkx.algorithms.connectivity import local_edge_connectivity
+
+    We use in this example the platonic icosahedral graph, which has edge
+    connectivity 5.
+
+    >>> G = nx.icosahedral_graph()
+    >>> local_edge_connectivity(G, 0, 6)
+    5
+
+    If you need to compute local connectivity on several pairs of
+    nodes in the same graph, it is recommended that you reuse the
+    data structures that NetworkX uses in the computation: the
+    auxiliary digraph for edge connectivity, and the residual
+    network for the underlying maximum flow computation.
+
+    Example of how to compute local edge connectivity among
+    all pairs of nodes of the platonic icosahedral graph reusing
+    the data structures.
+
+    >>> import itertools
+    >>> # You also have to explicitly import the function for
+    >>> # building the auxiliary digraph from the connectivity package
+    >>> from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity
+    >>> H = build_auxiliary_edge_connectivity(G)
+    >>> # And the function for building the residual network from the
+    >>> # flow package
+    >>> from networkx.algorithms.flow import build_residual_network
+    >>> # Note that the auxiliary digraph has an edge attribute named capacity
+    >>> R = build_residual_network(H, "capacity")
+    >>> result = dict.fromkeys(G, dict())
+    >>> # Reuse the auxiliary digraph and the residual network by passing them
+    >>> # as parameters
+    >>> for u, v in itertools.combinations(G, 2):
+    ...     k = local_edge_connectivity(G, u, v, auxiliary=H, residual=R)
+    ...     result[u][v] = k
+    >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
+    True
+
+    You can also use alternative flow algorithms for computing edge
+    connectivity. For instance, in dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better than
+    the default :meth:`edmonds_karp` which is faster for sparse
+    networks with highly skewed degree distributions. Alternative flow
+    functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> local_edge_connectivity(G, 0, 6, flow_func=shortest_augmenting_path)
+    5
+
+    Notes
+    -----
+    This is a flow based implementation of edge connectivity. We compute the
+    maximum flow using, by default, the :meth:`edmonds_karp` algorithm on an
+    auxiliary digraph build from the original input graph:
+
+    If the input graph is undirected, we replace each edge (`u`,`v`) with
+    two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute
+    'capacity' for each arc to 1. If the input graph is directed we simply
+    add the 'capacity' attribute. This is an implementation of algorithm 1
+    in [1]_.
+
+    The maximum flow in the auxiliary network is equal to the local edge
+    connectivity because the value of a maximum s-t-flow is equal to the
+    capacity of a minimum s-t-cut (Ford and Fulkerson theorem).
+
+    See also
+    --------
+    :meth:`edge_connectivity`
+    :meth:`local_node_connectivity`
+    :meth:`node_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    if flow_func is None:
+        flow_func = default_flow_func
+
+    if auxiliary is None:
+        H = build_auxiliary_edge_connectivity(G)
+    else:
+        H = auxiliary
+
+    kwargs = {"flow_func": flow_func, "residual": residual}
+
+    if flow_func is not preflow_push:
+        kwargs["cutoff"] = cutoff
+
+    if flow_func is shortest_augmenting_path:
+        kwargs["two_phase"] = True
+
+    return nx.maximum_flow_value(H, s, t, **kwargs)
+
+
+@nx._dispatchable
+def edge_connectivity(G, s=None, t=None, flow_func=None, cutoff=None):
+    r"""Returns the edge connectivity of the graph or digraph G.
+
+    The edge connectivity is equal to the minimum number of edges that
+    must be removed to disconnect G or render it trivial. If source
+    and target nodes are provided, this function returns the local edge
+    connectivity: the minimum number of edges that must be removed to
+    break all paths from source to target in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected or directed graph
+
+    s : node
+        Source node. Optional. Default value: None.
+
+    t : node
+        Target node. Optional. Default value: None.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The
+        choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    cutoff : integer, float, or None (default: None)
+        If specified, the maximum flow algorithm will terminate when the
+        flow value reaches or exceeds the cutoff. This only works for flows
+        that support the cutoff parameter (most do) and is ignored otherwise.
+
+    Returns
+    -------
+    K : integer
+        Edge connectivity for G, or local edge connectivity if source
+        and target were provided
+
+    Examples
+    --------
+    >>> # Platonic icosahedral graph is 5-edge-connected
+    >>> G = nx.icosahedral_graph()
+    >>> nx.edge_connectivity(G)
+    5
+
+    You can use alternative flow algorithms for the underlying
+    maximum flow computation. In dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better
+    than the default :meth:`edmonds_karp`, which is faster for
+    sparse networks with highly skewed degree distributions.
+    Alternative flow functions have to be explicitly imported
+    from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> nx.edge_connectivity(G, flow_func=shortest_augmenting_path)
+    5
+
+    If you specify a pair of nodes (source and target) as parameters,
+    this function returns the value of local edge connectivity.
+
+    >>> nx.edge_connectivity(G, 3, 7)
+    5
+
+    If you need to perform several local computations among different
+    pairs of nodes on the same graph, it is recommended that you reuse
+    the data structures used in the maximum flow computations. See
+    :meth:`local_edge_connectivity` for details.
+
+    Notes
+    -----
+    This is a flow based implementation of global edge connectivity.
+    For undirected graphs the algorithm works by finding a 'small'
+    dominating set of nodes of G (see algorithm 7 in [1]_ ) and
+    computing local maximum flow (see :meth:`local_edge_connectivity`)
+    between an arbitrary node in the dominating set and the rest of
+    nodes in it. This is an implementation of algorithm 6 in [1]_ .
+    For directed graphs, the algorithm does n calls to the maximum
+    flow function. This is an implementation of algorithm 8 in [1]_ .
+
+    See also
+    --------
+    :meth:`local_edge_connectivity`
+    :meth:`local_node_connectivity`
+    :meth:`node_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+    :meth:`k_edge_components`
+    :meth:`k_edge_subgraphs`
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    if (s is not None and t is None) or (s is None and t is not None):
+        raise nx.NetworkXError("Both source and target must be specified.")
+
+    # Local edge connectivity
+    if s is not None and t is not None:
+        if s not in G:
+            raise nx.NetworkXError(f"node {s} not in graph")
+        if t not in G:
+            raise nx.NetworkXError(f"node {t} not in graph")
+        return local_edge_connectivity(G, s, t, flow_func=flow_func, cutoff=cutoff)
+
+    # Global edge connectivity
+    # reuse auxiliary digraph and residual network
+    H = build_auxiliary_edge_connectivity(G)
+    R = build_residual_network(H, "capacity")
+    kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
+
+    if G.is_directed():
+        # Algorithm 8 in [1]
+        if not nx.is_weakly_connected(G):
+            return 0
+
+        # initial value for \lambda is minimum degree
+        L = min(d for n, d in G.degree())
+        nodes = list(G)
+        n = len(nodes)
+
+        if cutoff is not None:
+            L = min(cutoff, L)
+
+        for i in range(n):
+            kwargs["cutoff"] = L
+            try:
+                L = min(L, local_edge_connectivity(G, nodes[i], nodes[i + 1], **kwargs))
+            except IndexError:  # last node!
+                L = min(L, local_edge_connectivity(G, nodes[i], nodes[0], **kwargs))
+        return L
+    else:  # undirected
+        # Algorithm 6 in [1]
+        if not nx.is_connected(G):
+            return 0
+
+        # initial value for \lambda is minimum degree
+        L = min(d for n, d in G.degree())
+
+        if cutoff is not None:
+            L = min(cutoff, L)
+
+        # A dominating set is \lambda-covering
+        # We need a dominating set with at least two nodes
+        for node in G:
+            D = nx.dominating_set(G, start_with=node)
+            v = D.pop()
+            if D:
+                break
+        else:
+            # in complete graphs the dominating sets will always be of one node
+            # thus we return min degree
+            return L
+
+        for w in D:
+            kwargs["cutoff"] = L
+            L = min(L, local_edge_connectivity(G, v, w, **kwargs))
+
+        return L

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/cuts.py

@@ -0,0 +1,612 @@
+"""
+Flow based cut algorithms
+"""
+
+import itertools
+
+import networkx as nx
+
+# Define the default maximum flow function to use in all flow based
+# cut algorithms.
+from networkx.algorithms.flow import build_residual_network, edmonds_karp
+
+default_flow_func = edmonds_karp
+
+from .utils import build_auxiliary_edge_connectivity, build_auxiliary_node_connectivity
+
+__all__ = [
+    "minimum_st_node_cut",
+    "minimum_node_cut",
+    "minimum_st_edge_cut",
+    "minimum_edge_cut",
+]
+
+
+@nx._dispatchable(
+    graphs={"G": 0, "auxiliary?": 4},
+    preserve_edge_attrs={"auxiliary": {"capacity": float("inf")}},
+    preserve_graph_attrs={"auxiliary"},
+)
+def minimum_st_edge_cut(G, s, t, flow_func=None, auxiliary=None, residual=None):
+    """Returns the edges of the cut-set of a minimum (s, t)-cut.
+
+    This function returns the set of edges of minimum cardinality that,
+    if removed, would destroy all paths among source and target in G.
+    Edge weights are not considered. See :meth:`minimum_cut` for
+    computing minimum cuts considering edge weights.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    s : node
+        Source node for the flow.
+
+    t : node
+        Sink node for the flow.
+
+    auxiliary : NetworkX DiGraph
+        Auxiliary digraph to compute flow based node connectivity. It has
+        to have a graph attribute called mapping with a dictionary mapping
+        node names in G and in the auxiliary digraph. If provided
+        it will be reused instead of recreated. Default value: None.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See :meth:`node_connectivity` for
+        details. The choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    residual : NetworkX DiGraph
+        Residual network to compute maximum flow. If provided it will be
+        reused instead of recreated. Default value: None.
+
+    Returns
+    -------
+    cutset : set
+        Set of edges that, if removed from the graph, will disconnect it.
+
+    See also
+    --------
+    :meth:`minimum_cut`
+    :meth:`minimum_node_cut`
+    :meth:`minimum_edge_cut`
+    :meth:`stoer_wagner`
+    :meth:`node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    Examples
+    --------
+    This function is not imported in the base NetworkX namespace, so you
+    have to explicitly import it from the connectivity package:
+
+    >>> from networkx.algorithms.connectivity import minimum_st_edge_cut
+
+    We use in this example the platonic icosahedral graph, which has edge
+    connectivity 5.
+
+    >>> G = nx.icosahedral_graph()
+    >>> len(minimum_st_edge_cut(G, 0, 6))
+    5
+
+    If you need to compute local edge cuts on several pairs of
+    nodes in the same graph, it is recommended that you reuse the
+    data structures that NetworkX uses in the computation: the
+    auxiliary digraph for edge connectivity, and the residual
+    network for the underlying maximum flow computation.
+
+    Example of how to compute local edge cuts among all pairs of
+    nodes of the platonic icosahedral graph reusing the data
+    structures.
+
+    >>> import itertools
+    >>> # You also have to explicitly import the function for
+    >>> # building the auxiliary digraph from the connectivity package
+    >>> from networkx.algorithms.connectivity import build_auxiliary_edge_connectivity
+    >>> H = build_auxiliary_edge_connectivity(G)
+    >>> # And the function for building the residual network from the
+    >>> # flow package
+    >>> from networkx.algorithms.flow import build_residual_network
+    >>> # Note that the auxiliary digraph has an edge attribute named capacity
+    >>> R = build_residual_network(H, "capacity")
+    >>> result = dict.fromkeys(G, dict())
+    >>> # Reuse the auxiliary digraph and the residual network by passing them
+    >>> # as parameters
+    >>> for u, v in itertools.combinations(G, 2):
+    ...     k = len(minimum_st_edge_cut(G, u, v, auxiliary=H, residual=R))
+    ...     result[u][v] = k
+    >>> all(result[u][v] == 5 for u, v in itertools.combinations(G, 2))
+    True
+
+    You can also use alternative flow algorithms for computing edge
+    cuts. For instance, in dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better than
+    the default :meth:`edmonds_karp` which is faster for sparse
+    networks with highly skewed degree distributions. Alternative flow
+    functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> len(minimum_st_edge_cut(G, 0, 6, flow_func=shortest_augmenting_path))
+    5
+
+    """
+    if flow_func is None:
+        flow_func = default_flow_func
+
+    if auxiliary is None:
+        H = build_auxiliary_edge_connectivity(G)
+    else:
+        H = auxiliary
+
+    kwargs = {"capacity": "capacity", "flow_func": flow_func, "residual": residual}
+
+    cut_value, partition = nx.minimum_cut(H, s, t, **kwargs)
+    reachable, non_reachable = partition
+    # Any edge in the original graph linking the two sets in the
+    # partition is part of the edge cutset
+    cutset = set()
+    for u, nbrs in ((n, G[n]) for n in reachable):
+        cutset.update((u, v) for v in nbrs if v in non_reachable)
+
+    return cutset
+
+
+@nx._dispatchable(
+    graphs={"G": 0, "auxiliary?": 4},
+    preserve_node_attrs={"auxiliary": {"id": None}},
+    preserve_graph_attrs={"auxiliary"},
+)
+def minimum_st_node_cut(G, s, t, flow_func=None, auxiliary=None, residual=None):
+    r"""Returns a set of nodes of minimum cardinality that disconnect source
+    from target in G.
+
+    This function returns the set of nodes of minimum cardinality that,
+    if removed, would destroy all paths among source and target in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    s : node
+        Source node.
+
+    t : node
+        Target node.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The choice
+        of the default function may change from version to version and
+        should not be relied on. Default value: None.
+
+    auxiliary : NetworkX DiGraph
+        Auxiliary digraph to compute flow based node connectivity. It has
+        to have a graph attribute called mapping with a dictionary mapping
+        node names in G and in the auxiliary digraph. If provided
+        it will be reused instead of recreated. Default value: None.
+
+    residual : NetworkX DiGraph
+        Residual network to compute maximum flow. If provided it will be
+        reused instead of recreated. Default value: None.
+
+    Returns
+    -------
+    cutset : set
+        Set of nodes that, if removed, would destroy all paths between
+        source and target in G.
+
+    Examples
+    --------
+    This function is not imported in the base NetworkX namespace, so you
+    have to explicitly import it from the connectivity package:
+
+    >>> from networkx.algorithms.connectivity import minimum_st_node_cut
+
+    We use in this example the platonic icosahedral graph, which has node
+    connectivity 5.
+
+    >>> G = nx.icosahedral_graph()
+    >>> len(minimum_st_node_cut(G, 0, 6))
+    5
+
+    If you need to compute local st cuts between several pairs of
+    nodes in the same graph, it is recommended that you reuse the
+    data structures that NetworkX uses in the computation: the
+    auxiliary digraph for node connectivity and node cuts, and the
+    residual network for the underlying maximum flow computation.
+
+    Example of how to compute local st node cuts reusing the data
+    structures:
+
+    >>> # You also have to explicitly import the function for
+    >>> # building the auxiliary digraph from the connectivity package
+    >>> from networkx.algorithms.connectivity import build_auxiliary_node_connectivity
+    >>> H = build_auxiliary_node_connectivity(G)
+    >>> # And the function for building the residual network from the
+    >>> # flow package
+    >>> from networkx.algorithms.flow import build_residual_network
+    >>> # Note that the auxiliary digraph has an edge attribute named capacity
+    >>> R = build_residual_network(H, "capacity")
+    >>> # Reuse the auxiliary digraph and the residual network by passing them
+    >>> # as parameters
+    >>> len(minimum_st_node_cut(G, 0, 6, auxiliary=H, residual=R))
+    5
+
+    You can also use alternative flow algorithms for computing minimum st
+    node cuts. For instance, in dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better than
+    the default :meth:`edmonds_karp` which is faster for sparse
+    networks with highly skewed degree distributions. Alternative flow
+    functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> len(minimum_st_node_cut(G, 0, 6, flow_func=shortest_augmenting_path))
+    5
+
+    Notes
+    -----
+    This is a flow based implementation of minimum node cut. The algorithm
+    is based in solving a number of maximum flow computations to determine
+    the capacity of the minimum cut on an auxiliary directed network that
+    corresponds to the minimum node cut of G. It handles both directed
+    and undirected graphs. This implementation is based on algorithm 11
+    in [1]_.
+
+    See also
+    --------
+    :meth:`minimum_node_cut`
+    :meth:`minimum_edge_cut`
+    :meth:`stoer_wagner`
+    :meth:`node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    if auxiliary is None:
+        H = build_auxiliary_node_connectivity(G)
+    else:
+        H = auxiliary
+
+    mapping = H.graph.get("mapping", None)
+    if mapping is None:
+        raise nx.NetworkXError("Invalid auxiliary digraph.")
+    if G.has_edge(s, t) or G.has_edge(t, s):
+        return {}
+    kwargs = {"flow_func": flow_func, "residual": residual, "auxiliary": H}
+
+    # The edge cut in the auxiliary digraph corresponds to the node cut in the
+    # original graph.
+    edge_cut = minimum_st_edge_cut(H, f"{mapping[s]}B", f"{mapping[t]}A", **kwargs)
+    # Each node in the original graph maps to two nodes of the auxiliary graph
+    node_cut = {H.nodes[node]["id"] for edge in edge_cut for node in edge}
+    return node_cut - {s, t}
+
+
+@nx._dispatchable
+def minimum_node_cut(G, s=None, t=None, flow_func=None):
+    r"""Returns a set of nodes of minimum cardinality that disconnects G.
+
+    If source and target nodes are provided, this function returns the
+    set of nodes of minimum cardinality that, if removed, would destroy
+    all paths among source and target in G. If not, it returns a set
+    of nodes of minimum cardinality that disconnects G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    s : node
+        Source node. Optional. Default value: None.
+
+    t : node
+        Target node. Optional. Default value: None.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The
+        choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    Returns
+    -------
+    cutset : set
+        Set of nodes that, if removed, would disconnect G. If source
+        and target nodes are provided, the set contains the nodes that
+        if removed, would destroy all paths between source and target.
+
+    Examples
+    --------
+    >>> # Platonic icosahedral graph has node connectivity 5
+    >>> G = nx.icosahedral_graph()
+    >>> node_cut = nx.minimum_node_cut(G)
+    >>> len(node_cut)
+    5
+
+    You can use alternative flow algorithms for the underlying maximum
+    flow computation. In dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better
+    than the default :meth:`edmonds_karp`, which is faster for
+    sparse networks with highly skewed degree distributions. Alternative
+    flow functions have to be explicitly imported from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> node_cut == nx.minimum_node_cut(G, flow_func=shortest_augmenting_path)
+    True
+
+    If you specify a pair of nodes (source and target) as parameters,
+    this function returns a local st node cut.
+
+    >>> len(nx.minimum_node_cut(G, 3, 7))
+    5
+
+    If you need to perform several local st cuts among different
+    pairs of nodes on the same graph, it is recommended that you reuse
+    the data structures used in the maximum flow computations. See
+    :meth:`minimum_st_node_cut` for details.
+
+    Notes
+    -----
+    This is a flow based implementation of minimum node cut. The algorithm
+    is based in solving a number of maximum flow computations to determine
+    the capacity of the minimum cut on an auxiliary directed network that
+    corresponds to the minimum node cut of G. It handles both directed
+    and undirected graphs. This implementation is based on algorithm 11
+    in [1]_.
+
+    See also
+    --------
+    :meth:`minimum_st_node_cut`
+    :meth:`minimum_cut`
+    :meth:`minimum_edge_cut`
+    :meth:`stoer_wagner`
+    :meth:`node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    if (s is not None and t is None) or (s is None and t is not None):
+        raise nx.NetworkXError("Both source and target must be specified.")
+
+    # Local minimum node cut.
+    if s is not None and t is not None:
+        if s not in G:
+            raise nx.NetworkXError(f"node {s} not in graph")
+        if t not in G:
+            raise nx.NetworkXError(f"node {t} not in graph")
+        return minimum_st_node_cut(G, s, t, flow_func=flow_func)
+
+    # Global minimum node cut.
+    # Analog to the algorithm 11 for global node connectivity in [1].
+    if G.is_directed():
+        if not nx.is_weakly_connected(G):
+            raise nx.NetworkXError("Input graph is not connected")
+        iter_func = itertools.permutations
+
+        def neighbors(v):
+            return itertools.chain.from_iterable([G.predecessors(v), G.successors(v)])
+
+    else:
+        if not nx.is_connected(G):
+            raise nx.NetworkXError("Input graph is not connected")
+        iter_func = itertools.combinations
+        neighbors = G.neighbors
+
+    # Reuse the auxiliary digraph and the residual network.
+    H = build_auxiliary_node_connectivity(G)
+    R = build_residual_network(H, "capacity")
+    kwargs = {"flow_func": flow_func, "auxiliary": H, "residual": R}
+
+    # Choose a node with minimum degree.
+    v = min(G, key=G.degree)
+    # Initial node cutset is all neighbors of the node with minimum degree.
+    min_cut = set(G[v])
+    # Compute st node cuts between v and all its non-neighbors nodes in G.
+    for w in set(G) - set(neighbors(v)) - {v}:
+        this_cut = minimum_st_node_cut(G, v, w, **kwargs)
+        if len(min_cut) >= len(this_cut):
+            min_cut = this_cut
+    # Also for non adjacent pairs of neighbors of v.
+    for x, y in iter_func(neighbors(v), 2):
+        if y in G[x]:
+            continue
+        this_cut = minimum_st_node_cut(G, x, y, **kwargs)
+        if len(min_cut) >= len(this_cut):
+            min_cut = this_cut
+
+    return min_cut
+
+
+@nx._dispatchable
+def minimum_edge_cut(G, s=None, t=None, flow_func=None):
+    r"""Returns a set of edges of minimum cardinality that disconnects G.
+
+    If source and target nodes are provided, this function returns the
+    set of edges of minimum cardinality that, if removed, would break
+    all paths among source and target in G. If not, it returns a set of
+    edges of minimum cardinality that disconnects G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    s : node
+        Source node. Optional. Default value: None.
+
+    t : node
+        Target node. Optional. Default value: None.
+
+    flow_func : function
+        A function for computing the maximum flow among a pair of nodes.
+        The function has to accept at least three parameters: a Digraph,
+        a source node, and a target node. And return a residual network
+        that follows NetworkX conventions (see :meth:`maximum_flow` for
+        details). If flow_func is None, the default maximum flow function
+        (:meth:`edmonds_karp`) is used. See below for details. The
+        choice of the default function may change from version
+        to version and should not be relied on. Default value: None.
+
+    Returns
+    -------
+    cutset : set
+        Set of edges that, if removed, would disconnect G. If source
+        and target nodes are provided, the set contains the edges that
+        if removed, would destroy all paths between source and target.
+
+    Examples
+    --------
+    >>> # Platonic icosahedral graph has edge connectivity 5
+    >>> G = nx.icosahedral_graph()
+    >>> len(nx.minimum_edge_cut(G))
+    5
+
+    You can use alternative flow algorithms for the underlying
+    maximum flow computation. In dense networks the algorithm
+    :meth:`shortest_augmenting_path` will usually perform better
+    than the default :meth:`edmonds_karp`, which is faster for
+    sparse networks with highly skewed degree distributions.
+    Alternative flow functions have to be explicitly imported
+    from the flow package.
+
+    >>> from networkx.algorithms.flow import shortest_augmenting_path
+    >>> len(nx.minimum_edge_cut(G, flow_func=shortest_augmenting_path))
+    5
+
+    If you specify a pair of nodes (source and target) as parameters,
+    this function returns the value of local edge connectivity.
+
+    >>> nx.edge_connectivity(G, 3, 7)
+    5
+
+    If you need to perform several local computations among different
+    pairs of nodes on the same graph, it is recommended that you reuse
+    the data structures used in the maximum flow computations. See
+    :meth:`local_edge_connectivity` for details.
+
+    Notes
+    -----
+    This is a flow based implementation of minimum edge cut. For
+    undirected graphs the algorithm works by finding a 'small' dominating
+    set of nodes of G (see algorithm 7 in [1]_) and computing the maximum
+    flow between an arbitrary node in the dominating set and the rest of
+    nodes in it. This is an implementation of algorithm 6 in [1]_. For
+    directed graphs, the algorithm does n calls to the max flow function.
+    The function raises an error if the directed graph is not weakly
+    connected and returns an empty set if it is weakly connected.
+    It is an implementation of algorithm 8 in [1]_.
+
+    See also
+    --------
+    :meth:`minimum_st_edge_cut`
+    :meth:`minimum_node_cut`
+    :meth:`stoer_wagner`
+    :meth:`node_connectivity`
+    :meth:`edge_connectivity`
+    :meth:`maximum_flow`
+    :meth:`edmonds_karp`
+    :meth:`preflow_push`
+    :meth:`shortest_augmenting_path`
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms.
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+
+    """
+    if (s is not None and t is None) or (s is None and t is not None):
+        raise nx.NetworkXError("Both source and target must be specified.")
+
+    # reuse auxiliary digraph and residual network
+    H = build_auxiliary_edge_connectivity(G)
+    R = build_residual_network(H, "capacity")
+    kwargs = {"flow_func": flow_func, "residual": R, "auxiliary": H}
+
+    # Local minimum edge cut if s and t are not None
+    if s is not None and t is not None:
+        if s not in G:
+            raise nx.NetworkXError(f"node {s} not in graph")
+        if t not in G:
+            raise nx.NetworkXError(f"node {t} not in graph")
+        return minimum_st_edge_cut(H, s, t, **kwargs)
+
+    # Global minimum edge cut
+    # Analog to the algorithm for global edge connectivity
+    if G.is_directed():
+        # Based on algorithm 8 in [1]
+        if not nx.is_weakly_connected(G):
+            raise nx.NetworkXError("Input graph is not connected")
+
+        # Initial cutset is all edges of a node with minimum degree
+        node = min(G, key=G.degree)
+        min_cut = set(G.edges(node))
+        nodes = list(G)
+        n = len(nodes)
+        for i in range(n):
+            try:
+                this_cut = minimum_st_edge_cut(H, nodes[i], nodes[i + 1], **kwargs)
+                if len(this_cut) <= len(min_cut):
+                    min_cut = this_cut
+            except IndexError:  # Last node!
+                this_cut = minimum_st_edge_cut(H, nodes[i], nodes[0], **kwargs)
+                if len(this_cut) <= len(min_cut):
+                    min_cut = this_cut
+
+        return min_cut
+
+    else:  # undirected
+        # Based on algorithm 6 in [1]
+        if not nx.is_connected(G):
+            raise nx.NetworkXError("Input graph is not connected")
+
+        # Initial cutset is all edges of a node with minimum degree
+        node = min(G, key=G.degree)
+        min_cut = set(G.edges(node))
+        # A dominating set is \lambda-covering
+        # We need a dominating set with at least two nodes
+        for node in G:
+            D = nx.dominating_set(G, start_with=node)
+            v = D.pop()
+            if D:
+                break
+        else:
+            # in complete graphs the dominating set will always be of one node
+            # thus we return min_cut, which now contains the edges of a node
+            # with minimum degree
+            return min_cut
+        for w in D:
+            this_cut = minimum_st_edge_cut(H, v, w, **kwargs)
+            if len(this_cut) <= len(min_cut):
+                min_cut = this_cut
+
+        return min_cut

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/edge_augmentation.py

@@ -0,0 +1,1270 @@
+"""
+Algorithms for finding k-edge-augmentations
+
+A k-edge-augmentation is a set of edges, that once added to a graph, ensures
+that the graph is k-edge-connected; i.e. the graph cannot be disconnected
+unless k or more edges are removed.  Typically, the goal is to find the
+augmentation with minimum weight.  In general, it is not guaranteed that a
+k-edge-augmentation exists.
+
+See Also
+--------
+:mod:`edge_kcomponents` : algorithms for finding k-edge-connected components
+:mod:`connectivity` : algorithms for determining edge connectivity.
+"""
+
+import itertools as it
+import math
+from collections import defaultdict, namedtuple
+
+import networkx as nx
+from networkx.utils import not_implemented_for, py_random_state
+
+__all__ = ["k_edge_augmentation", "is_k_edge_connected", "is_locally_k_edge_connected"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def is_k_edge_connected(G, k):
+    """Tests to see if a graph is k-edge-connected.
+
+    Is it impossible to disconnect the graph by removing fewer than k edges?
+    If so, then G is k-edge-connected.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    k : integer
+        edge connectivity to test for
+
+    Returns
+    -------
+    boolean
+        True if G is k-edge-connected.
+
+    See Also
+    --------
+    :func:`is_locally_k_edge_connected`
+
+    Examples
+    --------
+    >>> G = nx.barbell_graph(10, 0)
+    >>> nx.is_k_edge_connected(G, k=1)
+    True
+    >>> nx.is_k_edge_connected(G, k=2)
+    False
+    """
+    if k < 1:
+        raise ValueError(f"k must be positive, not {k}")
+    # First try to quickly determine if G is not k-edge-connected
+    if G.number_of_nodes() < k + 1:
+        return False
+    elif any(d < k for n, d in G.degree()):
+        return False
+    else:
+        # Otherwise perform the full check
+        if k == 1:
+            return nx.is_connected(G)
+        elif k == 2:
+            return nx.is_connected(G) and not nx.has_bridges(G)
+        else:
+            return nx.edge_connectivity(G, cutoff=k) >= k
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def is_locally_k_edge_connected(G, s, t, k):
+    """Tests to see if an edge in a graph is locally k-edge-connected.
+
+    Is it impossible to disconnect s and t by removing fewer than k edges?
+    If so, then s and t are locally k-edge-connected in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    s : node
+        Source node
+
+    t : node
+        Target node
+
+    k : integer
+        local edge connectivity for nodes s and t
+
+    Returns
+    -------
+    boolean
+        True if s and t are locally k-edge-connected in G.
+
+    See Also
+    --------
+    :func:`is_k_edge_connected`
+
+    Examples
+    --------
+    >>> from networkx.algorithms.connectivity import is_locally_k_edge_connected
+    >>> G = nx.barbell_graph(10, 0)
+    >>> is_locally_k_edge_connected(G, 5, 15, k=1)
+    True
+    >>> is_locally_k_edge_connected(G, 5, 15, k=2)
+    False
+    >>> is_locally_k_edge_connected(G, 1, 5, k=2)
+    True
+    """
+    if k < 1:
+        raise ValueError(f"k must be positive, not {k}")
+
+    # First try to quickly determine s, t is not k-locally-edge-connected in G
+    if G.degree(s) < k or G.degree(t) < k:
+        return False
+    else:
+        # Otherwise perform the full check
+        if k == 1:
+            return nx.has_path(G, s, t)
+        else:
+            localk = nx.connectivity.local_edge_connectivity(G, s, t, cutoff=k)
+            return localk >= k
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def k_edge_augmentation(G, k, avail=None, weight=None, partial=False):
+    """Finds set of edges to k-edge-connect G.
+
+    Adding edges from the augmentation to G make it impossible to disconnect G
+    unless k or more edges are removed. This function uses the most efficient
+    function available (depending on the value of k and if the problem is
+    weighted or unweighted) to search for a minimum weight subset of available
+    edges that k-edge-connects G. In general, finding a k-edge-augmentation is
+    NP-hard, so solutions are not guaranteed to be minimal. Furthermore, a
+    k-edge-augmentation may not exist.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    k : integer
+        Desired edge connectivity
+
+    avail : dict or a set of 2 or 3 tuples
+        The available edges that can be used in the augmentation.
+
+        If unspecified, then all edges in the complement of G are available.
+        Otherwise, each item is an available edge (with an optional weight).
+
+        In the unweighted case, each item is an edge ``(u, v)``.
+
+        In the weighted case, each item is a 3-tuple ``(u, v, d)`` or a dict
+        with items ``(u, v): d``.  The third item, ``d``, can be a dictionary
+        or a real number.  If ``d`` is a dictionary ``d[weight]``
+        correspondings to the weight.
+
+    weight : string
+        key to use to find weights if ``avail`` is a set of 3-tuples where the
+        third item in each tuple is a dictionary.
+
+    partial : boolean
+        If partial is True and no feasible k-edge-augmentation exists, then all
+        a partial k-edge-augmentation is generated. Adding the edges in a
+        partial augmentation to G, minimizes the number of k-edge-connected
+        components and maximizes the edge connectivity between those
+        components. For details, see :func:`partial_k_edge_augmentation`.
+
+    Yields
+    ------
+    edge : tuple
+        Edges that, once added to G, would cause G to become k-edge-connected.
+        If partial is False, an error is raised if this is not possible.
+        Otherwise, generated edges form a partial augmentation, which
+        k-edge-connects any part of G where it is possible, and maximally
+        connects the remaining parts.
+
+    Raises
+    ------
+    NetworkXUnfeasible
+        If partial is False and no k-edge-augmentation exists.
+
+    NetworkXNotImplemented
+        If the input graph is directed or a multigraph.
+
+    ValueError:
+        If k is less than 1
+
+    Notes
+    -----
+    When k=1 this returns an optimal solution.
+
+    When k=2 and ``avail`` is None, this returns an optimal solution.
+    Otherwise when k=2, this returns a 2-approximation of the optimal solution.
+
+    For k>3, this problem is NP-hard and this uses a randomized algorithm that
+        produces a feasible solution, but provides no guarantees on the
+        solution weight.
+
+    Examples
+    --------
+    >>> # Unweighted cases
+    >>> G = nx.path_graph((1, 2, 3, 4))
+    >>> G.add_node(5)
+    >>> sorted(nx.k_edge_augmentation(G, k=1))
+    [(1, 5)]
+    >>> sorted(nx.k_edge_augmentation(G, k=2))
+    [(1, 5), (5, 4)]
+    >>> sorted(nx.k_edge_augmentation(G, k=3))
+    [(1, 4), (1, 5), (2, 5), (3, 5), (4, 5)]
+    >>> complement = list(nx.k_edge_augmentation(G, k=5, partial=True))
+    >>> G.add_edges_from(complement)
+    >>> nx.edge_connectivity(G)
+    4
+
+    >>> # Weighted cases
+    >>> G = nx.path_graph((1, 2, 3, 4))
+    >>> G.add_node(5)
+    >>> # avail can be a tuple with a dict
+    >>> avail = [(1, 5, {"weight": 11}), (2, 5, {"weight": 10})]
+    >>> sorted(nx.k_edge_augmentation(G, k=1, avail=avail, weight="weight"))
+    [(2, 5)]
+    >>> # or avail can be a 3-tuple with a real number
+    >>> avail = [(1, 5, 11), (2, 5, 10), (4, 3, 1), (4, 5, 51)]
+    >>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail))
+    [(1, 5), (2, 5), (4, 5)]
+    >>> # or avail can be a dict
+    >>> avail = {(1, 5): 11, (2, 5): 10, (4, 3): 1, (4, 5): 51}
+    >>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail))
+    [(1, 5), (2, 5), (4, 5)]
+    >>> # If augmentation is infeasible, then a partial solution can be found
+    >>> avail = {(1, 5): 11}
+    >>> sorted(nx.k_edge_augmentation(G, k=2, avail=avail, partial=True))
+    [(1, 5)]
+    """
+    try:
+        if k <= 0:
+            raise ValueError(f"k must be a positive integer, not {k}")
+        elif G.number_of_nodes() < k + 1:
+            msg = f"impossible to {k} connect in graph with less than {k + 1} nodes"
+            raise nx.NetworkXUnfeasible(msg)
+        elif avail is not None and len(avail) == 0:
+            if not nx.is_k_edge_connected(G, k):
+                raise nx.NetworkXUnfeasible("no available edges")
+            aug_edges = []
+        elif k == 1:
+            aug_edges = one_edge_augmentation(
+                G, avail=avail, weight=weight, partial=partial
+            )
+        elif k == 2:
+            aug_edges = bridge_augmentation(G, avail=avail, weight=weight)
+        else:
+            # raise NotImplementedError(f'not implemented for k>2. k={k}')
+            aug_edges = greedy_k_edge_augmentation(
+                G, k=k, avail=avail, weight=weight, seed=0
+            )
+        # Do eager evaluation so we can catch any exceptions
+        # Before executing partial code.
+        yield from list(aug_edges)
+    except nx.NetworkXUnfeasible:
+        if partial:
+            # Return all available edges
+            if avail is None:
+                aug_edges = complement_edges(G)
+            else:
+                # If we can't k-edge-connect the entire graph, try to
+                # k-edge-connect as much as possible
+                aug_edges = partial_k_edge_augmentation(
+                    G, k=k, avail=avail, weight=weight
+                )
+            yield from aug_edges
+        else:
+            raise
+
+
+@nx._dispatchable
+def partial_k_edge_augmentation(G, k, avail, weight=None):
+    """Finds augmentation that k-edge-connects as much of the graph as possible.
+
+    When a k-edge-augmentation is not possible, we can still try to find a
+    small set of edges that partially k-edge-connects as much of the graph as
+    possible. All possible edges are generated between remaining parts.
+    This minimizes the number of k-edge-connected subgraphs in the resulting
+    graph and maximizes the edge connectivity between those subgraphs.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    k : integer
+        Desired edge connectivity
+
+    avail : dict or a set of 2 or 3 tuples
+        For more details, see :func:`k_edge_augmentation`.
+
+    weight : string
+        key to use to find weights if ``avail`` is a set of 3-tuples.
+        For more details, see :func:`k_edge_augmentation`.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the partial augmentation of G. These edges k-edge-connect any
+        part of G where it is possible, and maximally connects the remaining
+        parts. In other words, all edges from avail are generated except for
+        those within subgraphs that have already become k-edge-connected.
+
+    Notes
+    -----
+    Construct H that augments G with all edges in avail.
+    Find the k-edge-subgraphs of H.
+    For each k-edge-subgraph, if the number of nodes is more than k, then find
+    the k-edge-augmentation of that graph and add it to the solution. Then add
+    all edges in avail between k-edge subgraphs to the solution.
+
+    See Also
+    --------
+    :func:`k_edge_augmentation`
+
+    Examples
+    --------
+    >>> G = nx.path_graph((1, 2, 3, 4, 5, 6, 7))
+    >>> G.add_node(8)
+    >>> avail = [(1, 3), (1, 4), (1, 5), (2, 4), (2, 5), (3, 5), (1, 8)]
+    >>> sorted(partial_k_edge_augmentation(G, k=2, avail=avail))
+    [(1, 5), (1, 8)]
+    """
+
+    def _edges_between_disjoint(H, only1, only2):
+        """finds edges between disjoint nodes"""
+        only1_adj = {u: set(H.adj[u]) for u in only1}
+        for u, neighbs in only1_adj.items():
+            # Find the neighbors of u in only1 that are also in only2
+            neighbs12 = neighbs.intersection(only2)
+            for v in neighbs12:
+                yield (u, v)
+
+    avail_uv, avail_w = _unpack_available_edges(avail, weight=weight, G=G)
+
+    # Find which parts of the graph can be k-edge-connected
+    H = G.copy()
+    H.add_edges_from(
+        (
+            (u, v, {"weight": w, "generator": (u, v)})
+            for (u, v), w in zip(avail, avail_w)
+        )
+    )
+    k_edge_subgraphs = list(nx.k_edge_subgraphs(H, k=k))
+
+    # Generate edges to k-edge-connect internal subgraphs
+    for nodes in k_edge_subgraphs:
+        if len(nodes) > 1:
+            # Get the k-edge-connected subgraph
+            C = H.subgraph(nodes).copy()
+            # Find the internal edges that were available
+            sub_avail = {
+                d["generator"]: d["weight"]
+                for (u, v, d) in C.edges(data=True)
+                if "generator" in d
+            }
+            # Remove potential augmenting edges
+            C.remove_edges_from(sub_avail.keys())
+            # Find a subset of these edges that makes the component
+            # k-edge-connected and ignore the rest
+            yield from nx.k_edge_augmentation(C, k=k, avail=sub_avail)
+
+    # Generate all edges between CCs that could not be k-edge-connected
+    for cc1, cc2 in it.combinations(k_edge_subgraphs, 2):
+        for u, v in _edges_between_disjoint(H, cc1, cc2):
+            d = H.get_edge_data(u, v)
+            edge = d.get("generator", None)
+            if edge is not None:
+                yield edge
+
+
+@not_implemented_for("multigraph")
+@not_implemented_for("directed")
+@nx._dispatchable
+def one_edge_augmentation(G, avail=None, weight=None, partial=False):
+    """Finds minimum weight set of edges to connect G.
+
+    Equivalent to :func:`k_edge_augmentation` when k=1. Adding the resulting
+    edges to G will make it 1-edge-connected. The solution is optimal for both
+    weighted and non-weighted variants.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    avail : dict or a set of 2 or 3 tuples
+        For more details, see :func:`k_edge_augmentation`.
+
+    weight : string
+        key to use to find weights if ``avail`` is a set of 3-tuples.
+        For more details, see :func:`k_edge_augmentation`.
+
+    partial : boolean
+        If partial is True and no feasible k-edge-augmentation exists, then the
+        augmenting edges minimize the number of connected components.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the one-augmentation of G
+
+    Raises
+    ------
+    NetworkXUnfeasible
+        If partial is False and no one-edge-augmentation exists.
+
+    Notes
+    -----
+    Uses either :func:`unconstrained_one_edge_augmentation` or
+    :func:`weighted_one_edge_augmentation` depending on whether ``avail`` is
+    specified. Both algorithms are based on finding a minimum spanning tree.
+    As such both algorithms find optimal solutions and run in linear time.
+
+    See Also
+    --------
+    :func:`k_edge_augmentation`
+    """
+    if avail is None:
+        return unconstrained_one_edge_augmentation(G)
+    else:
+        return weighted_one_edge_augmentation(
+            G, avail=avail, weight=weight, partial=partial
+        )
+
+
+@not_implemented_for("multigraph")
+@not_implemented_for("directed")
+@nx._dispatchable
+def bridge_augmentation(G, avail=None, weight=None):
+    """Finds the a set of edges that bridge connects G.
+
+    Equivalent to :func:`k_edge_augmentation` when k=2, and partial=False.
+    Adding the resulting edges to G will make it 2-edge-connected.  If no
+    constraints are specified the returned set of edges is minimum an optimal,
+    otherwise the solution is approximated.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    avail : dict or a set of 2 or 3 tuples
+        For more details, see :func:`k_edge_augmentation`.
+
+    weight : string
+        key to use to find weights if ``avail`` is a set of 3-tuples.
+        For more details, see :func:`k_edge_augmentation`.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the bridge-augmentation of G
+
+    Raises
+    ------
+    NetworkXUnfeasible
+        If no bridge-augmentation exists.
+
+    Notes
+    -----
+    If there are no constraints the solution can be computed in linear time
+    using :func:`unconstrained_bridge_augmentation`. Otherwise, the problem
+    becomes NP-hard and is the solution is approximated by
+    :func:`weighted_bridge_augmentation`.
+
+    See Also
+    --------
+    :func:`k_edge_augmentation`
+    """
+    if G.number_of_nodes() < 3:
+        raise nx.NetworkXUnfeasible("impossible to bridge connect less than 3 nodes")
+    if avail is None:
+        return unconstrained_bridge_augmentation(G)
+    else:
+        return weighted_bridge_augmentation(G, avail, weight=weight)
+
+
+# --- Algorithms and Helpers ---
+
+
+def _ordered(u, v):
+    """Returns the nodes in an undirected edge in lower-triangular order"""
+    return (u, v) if u < v else (v, u)
+
+
+def _unpack_available_edges(avail, weight=None, G=None):
+    """Helper to separate avail into edges and corresponding weights"""
+    if weight is None:
+        weight = "weight"
+    if isinstance(avail, dict):
+        avail_uv = list(avail.keys())
+        avail_w = list(avail.values())
+    else:
+
+        def _try_getitem(d):
+            try:
+                return d[weight]
+            except TypeError:
+                return d
+
+        avail_uv = [tup[0:2] for tup in avail]
+        avail_w = [1 if len(tup) == 2 else _try_getitem(tup[-1]) for tup in avail]
+
+    if G is not None:
+        # Edges already in the graph are filtered
+        flags = [not G.has_edge(u, v) for u, v in avail_uv]
+        avail_uv = list(it.compress(avail_uv, flags))
+        avail_w = list(it.compress(avail_w, flags))
+    return avail_uv, avail_w
+
+
+MetaEdge = namedtuple("MetaEdge", ("meta_uv", "uv", "w"))
+
+
+def _lightest_meta_edges(mapping, avail_uv, avail_w):
+    """Maps available edges in the original graph to edges in the metagraph.
+
+    Parameters
+    ----------
+    mapping : dict
+        mapping produced by :func:`collapse`, that maps each node in the
+        original graph to a node in the meta graph
+
+    avail_uv : list
+        list of edges
+
+    avail_w : list
+        list of edge weights
+
+    Notes
+    -----
+    Each node in the metagraph is a k-edge-connected component in the original
+    graph.  We don't care about any edge within the same k-edge-connected
+    component, so we ignore self edges.  We also are only interested in the
+    minimum weight edge bridging each k-edge-connected component so, we group
+    the edges by meta-edge and take the lightest in each group.
+
+    Examples
+    --------
+    >>> # Each group represents a meta-node
+    >>> groups = ([1, 2, 3], [4, 5], [6])
+    >>> mapping = {n: meta_n for meta_n, ns in enumerate(groups) for n in ns}
+    >>> avail_uv = [(1, 2), (3, 6), (1, 4), (5, 2), (6, 1), (2, 6), (3, 1)]
+    >>> avail_w = [20, 99, 20, 15, 50, 99, 20]
+    >>> sorted(_lightest_meta_edges(mapping, avail_uv, avail_w))
+    [MetaEdge(meta_uv=(0, 1), uv=(5, 2), w=15), MetaEdge(meta_uv=(0, 2), uv=(6, 1), w=50)]
+    """
+    grouped_wuv = defaultdict(list)
+    for w, (u, v) in zip(avail_w, avail_uv):
+        # Order the meta-edge so it can be used as a dict key
+        meta_uv = _ordered(mapping[u], mapping[v])
+        # Group each available edge using the meta-edge as a key
+        grouped_wuv[meta_uv].append((w, u, v))
+
+    # Now that all available edges are grouped, choose one per group
+    for (mu, mv), choices_wuv in grouped_wuv.items():
+        # Ignore available edges within the same meta-node
+        if mu != mv:
+            # Choose the lightest available edge belonging to each meta-edge
+            w, u, v = min(choices_wuv)
+            yield MetaEdge((mu, mv), (u, v), w)
+
+
+@nx._dispatchable
+def unconstrained_one_edge_augmentation(G):
+    """Finds the smallest set of edges to connect G.
+
+    This is a variant of the unweighted MST problem.
+    If G is not empty, a feasible solution always exists.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the one-edge-augmentation of G
+
+    See Also
+    --------
+    :func:`one_edge_augmentation`
+    :func:`k_edge_augmentation`
+
+    Examples
+    --------
+    >>> G = nx.Graph([(1, 2), (2, 3), (4, 5)])
+    >>> G.add_nodes_from([6, 7, 8])
+    >>> sorted(unconstrained_one_edge_augmentation(G))
+    [(1, 4), (4, 6), (6, 7), (7, 8)]
+    """
+    ccs1 = list(nx.connected_components(G))
+    C = collapse(G, ccs1)
+    # When we are not constrained, we can just make a meta graph tree.
+    meta_nodes = list(C.nodes())
+    # build a path in the metagraph
+    meta_aug = list(zip(meta_nodes, meta_nodes[1:]))
+    # map that path to the original graph
+    inverse = defaultdict(list)
+    for k, v in C.graph["mapping"].items():
+        inverse[v].append(k)
+    for mu, mv in meta_aug:
+        yield (inverse[mu][0], inverse[mv][0])
+
+
+@nx._dispatchable
+def weighted_one_edge_augmentation(G, avail, weight=None, partial=False):
+    """Finds the minimum weight set of edges to connect G if one exists.
+
+    This is a variant of the weighted MST problem.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    avail : dict or a set of 2 or 3 tuples
+        For more details, see :func:`k_edge_augmentation`.
+
+    weight : string
+        key to use to find weights if ``avail`` is a set of 3-tuples.
+        For more details, see :func:`k_edge_augmentation`.
+
+    partial : boolean
+        If partial is True and no feasible k-edge-augmentation exists, then the
+        augmenting edges minimize the number of connected components.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the subset of avail chosen to connect G.
+
+    See Also
+    --------
+    :func:`one_edge_augmentation`
+    :func:`k_edge_augmentation`
+
+    Examples
+    --------
+    >>> G = nx.Graph([(1, 2), (2, 3), (4, 5)])
+    >>> G.add_nodes_from([6, 7, 8])
+    >>> # any edge not in avail has an implicit weight of infinity
+    >>> avail = [(1, 3), (1, 5), (4, 7), (4, 8), (6, 1), (8, 1), (8, 2)]
+    >>> sorted(weighted_one_edge_augmentation(G, avail))
+    [(1, 5), (4, 7), (6, 1), (8, 1)]
+    >>> # find another solution by giving large weights to edges in the
+    >>> # previous solution (note some of the old edges must be used)
+    >>> avail = [(1, 3), (1, 5, 99), (4, 7, 9), (6, 1, 99), (8, 1, 99), (8, 2)]
+    >>> sorted(weighted_one_edge_augmentation(G, avail))
+    [(1, 5), (4, 7), (6, 1), (8, 2)]
+    """
+    avail_uv, avail_w = _unpack_available_edges(avail, weight=weight, G=G)
+    # Collapse CCs in the original graph into nodes in a metagraph
+    # Then find an MST of the metagraph instead of the original graph
+    C = collapse(G, nx.connected_components(G))
+    mapping = C.graph["mapping"]
+    # Assign each available edge to an edge in the metagraph
+    candidate_mapping = _lightest_meta_edges(mapping, avail_uv, avail_w)
+    # nx.set_edge_attributes(C, name='weight', values=0)
+    C.add_edges_from(
+        (mu, mv, {"weight": w, "generator": uv})
+        for (mu, mv), uv, w in candidate_mapping
+    )
+    # Find MST of the meta graph
+    meta_mst = nx.minimum_spanning_tree(C)
+    if not partial and not nx.is_connected(meta_mst):
+        raise nx.NetworkXUnfeasible("Not possible to connect G with available edges")
+    # Yield the edge that generated the meta-edge
+    for mu, mv, d in meta_mst.edges(data=True):
+        if "generator" in d:
+            edge = d["generator"]
+            yield edge
+
+
+@nx._dispatchable
+def unconstrained_bridge_augmentation(G):
+    """Finds an optimal 2-edge-augmentation of G using the fewest edges.
+
+    This is an implementation of the algorithm detailed in [1]_.
+    The basic idea is to construct a meta-graph of bridge-ccs, connect leaf
+    nodes of the trees to connect the entire graph, and finally connect the
+    leafs of the tree in dfs-preorder to bridge connect the entire graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the bridge augmentation of G
+
+    Notes
+    -----
+    Input: a graph G.
+    First find the bridge components of G and collapse each bridge-cc into a
+    node of a metagraph graph C, which is guaranteed to be a forest of trees.
+
+    C contains p "leafs" --- nodes with exactly one incident edge.
+    C contains q "isolated nodes" --- nodes with no incident edges.
+
+    Theorem: If p + q > 1, then at least :math:`ceil(p / 2) + q` edges are
+        needed to bridge connect C. This algorithm achieves this min number.
+
+    The method first adds enough edges to make G into a tree and then pairs
+    leafs in a simple fashion.
+
+    Let n be the number of trees in C. Let v(i) be an isolated vertex in the
+    i-th tree if one exists, otherwise it is a pair of distinct leafs nodes
+    in the i-th tree. Alternating edges from these sets (i.e.  adding edges
+    A1 = [(v(i)[0], v(i + 1)[1]), v(i + 1)[0], v(i + 2)[1])...]) connects C
+    into a tree T. This tree has p' = p + 2q - 2(n -1) leafs and no isolated
+    vertices. A1 has n - 1 edges. The next step finds ceil(p' / 2) edges to
+    biconnect any tree with p' leafs.
+
+    Convert T into an arborescence T' by picking an arbitrary root node with
+    degree >= 2 and directing all edges away from the root. Note the
+    implementation implicitly constructs T'.
+
+    The leafs of T are the nodes with no existing edges in T'.
+    Order the leafs of T' by DFS preorder. Then break this list in half
+    and add the zipped pairs to A2.
+
+    The set A = A1 + A2 is the minimum augmentation in the metagraph.
+
+    To convert this to edges in the original graph
+
+    References
+    ----------
+    .. [1] Eswaran, Kapali P., and R. Endre Tarjan. (1975) Augmentation problems.
+        http://epubs.siam.org/doi/abs/10.1137/0205044
+
+    See Also
+    --------
+    :func:`bridge_augmentation`
+    :func:`k_edge_augmentation`
+
+    Examples
+    --------
+    >>> G = nx.path_graph((1, 2, 3, 4, 5, 6, 7))
+    >>> sorted(unconstrained_bridge_augmentation(G))
+    [(1, 7)]
+    >>> G = nx.path_graph((1, 2, 3, 2, 4, 5, 6, 7))
+    >>> sorted(unconstrained_bridge_augmentation(G))
+    [(1, 3), (3, 7)]
+    >>> G = nx.Graph([(0, 1), (0, 2), (1, 2)])
+    >>> G.add_node(4)
+    >>> sorted(unconstrained_bridge_augmentation(G))
+    [(1, 4), (4, 0)]
+    """
+    # -----
+    # Mapping of terms from (Eswaran and Tarjan):
+    #     G = G_0 - the input graph
+    #     C = G_0' - the bridge condensation of G. (This is a forest of trees)
+    #     A1 = A_1 - the edges to connect the forest into a tree
+    #         leaf = pendant - a node with degree of 1
+
+    #     alpha(v) = maps the node v in G to its meta-node in C
+    #     beta(x) = maps the meta-node x in C to any node in the bridge
+    #         component of G corresponding to x.
+
+    # find the 2-edge-connected components of G
+    bridge_ccs = list(nx.connectivity.bridge_components(G))
+    # condense G into an forest C
+    C = collapse(G, bridge_ccs)
+
+    # Choose pairs of distinct leaf nodes in each tree. If this is not
+    # possible then make a pair using the single isolated node in the tree.
+    vset1 = [
+        tuple(cc) * 2  # case1: an isolated node
+        if len(cc) == 1
+        else sorted(cc, key=C.degree)[0:2]  # case2: pair of leaf nodes
+        for cc in nx.connected_components(C)
+    ]
+    if len(vset1) > 1:
+        # Use this set to construct edges that connect C into a tree.
+        nodes1 = [vs[0] for vs in vset1]
+        nodes2 = [vs[1] for vs in vset1]
+        A1 = list(zip(nodes1[1:], nodes2))
+    else:
+        A1 = []
+    # Connect each tree in the forest to construct an arborescence
+    T = C.copy()
+    T.add_edges_from(A1)
+
+    # If there are only two leaf nodes, we simply connect them.
+    leafs = [n for n, d in T.degree() if d == 1]
+    if len(leafs) == 1:
+        A2 = []
+    if len(leafs) == 2:
+        A2 = [tuple(leafs)]
+    else:
+        # Choose an arbitrary non-leaf root
+        try:
+            root = next(n for n, d in T.degree() if d > 1)
+        except StopIteration:  # no nodes found with degree > 1
+            return
+        # order the leaves of C by (induced directed) preorder
+        v2 = [n for n in nx.dfs_preorder_nodes(T, root) if T.degree(n) == 1]
+        # connecting first half of the leafs in pre-order to the second
+        # half will bridge connect the tree with the fewest edges.
+        half = math.ceil(len(v2) / 2)
+        A2 = list(zip(v2[:half], v2[-half:]))
+
+    # collect the edges used to augment the original forest
+    aug_tree_edges = A1 + A2
+
+    # Construct the mapping (beta) from meta-nodes to regular nodes
+    inverse = defaultdict(list)
+    for k, v in C.graph["mapping"].items():
+        inverse[v].append(k)
+    # sort so we choose minimum degree nodes first
+    inverse = {
+        mu: sorted(mapped, key=lambda u: (G.degree(u), u))
+        for mu, mapped in inverse.items()
+    }
+
+    # For each meta-edge, map back to an arbitrary pair in the original graph
+    G2 = G.copy()
+    for mu, mv in aug_tree_edges:
+        # Find the first available edge that doesn't exist and return it
+        for u, v in it.product(inverse[mu], inverse[mv]):
+            if not G2.has_edge(u, v):
+                G2.add_edge(u, v)
+                yield u, v
+                break
+
+
+@nx._dispatchable
+def weighted_bridge_augmentation(G, avail, weight=None):
+    """Finds an approximate min-weight 2-edge-augmentation of G.
+
+    This is an implementation of the approximation algorithm detailed in [1]_.
+    It chooses a set of edges from avail to add to G that renders it
+    2-edge-connected if such a subset exists.  This is done by finding a
+    minimum spanning arborescence of a specially constructed metagraph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    avail : set of 2 or 3 tuples.
+        candidate edges (with optional weights) to choose from
+
+    weight : string
+        key to use to find weights if avail is a set of 3-tuples where the
+        third item in each tuple is a dictionary.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the subset of avail chosen to bridge augment G.
+
+    Notes
+    -----
+    Finding a weighted 2-edge-augmentation is NP-hard.
+    Any edge not in ``avail`` is considered to have a weight of infinity.
+    The approximation factor is 2 if ``G`` is connected and 3 if it is not.
+    Runs in :math:`O(m + n log(n))` time
+
+    References
+    ----------
+    .. [1] Khuller, Samir, and Ramakrishna Thurimella. (1993) Approximation
+        algorithms for graph augmentation.
+        http://www.sciencedirect.com/science/article/pii/S0196677483710102
+
+    See Also
+    --------
+    :func:`bridge_augmentation`
+    :func:`k_edge_augmentation`
+
+    Examples
+    --------
+    >>> G = nx.path_graph((1, 2, 3, 4))
+    >>> # When the weights are equal, (1, 4) is the best
+    >>> avail = [(1, 4, 1), (1, 3, 1), (2, 4, 1)]
+    >>> sorted(weighted_bridge_augmentation(G, avail))
+    [(1, 4)]
+    >>> # Giving (1, 4) a high weight makes the two edge solution the best.
+    >>> avail = [(1, 4, 1000), (1, 3, 1), (2, 4, 1)]
+    >>> sorted(weighted_bridge_augmentation(G, avail))
+    [(1, 3), (2, 4)]
+    >>> # ------
+    >>> G = nx.path_graph((1, 2, 3, 4))
+    >>> G.add_node(5)
+    >>> avail = [(1, 5, 11), (2, 5, 10), (4, 3, 1), (4, 5, 1)]
+    >>> sorted(weighted_bridge_augmentation(G, avail=avail))
+    [(1, 5), (4, 5)]
+    >>> avail = [(1, 5, 11), (2, 5, 10), (4, 3, 1), (4, 5, 51)]
+    >>> sorted(weighted_bridge_augmentation(G, avail=avail))
+    [(1, 5), (2, 5), (4, 5)]
+    """
+
+    if weight is None:
+        weight = "weight"
+
+    # If input G is not connected the approximation factor increases to 3
+    if not nx.is_connected(G):
+        H = G.copy()
+        connectors = list(one_edge_augmentation(H, avail=avail, weight=weight))
+        H.add_edges_from(connectors)
+
+        yield from connectors
+    else:
+        connectors = []
+        H = G
+
+    if len(avail) == 0:
+        if nx.has_bridges(H):
+            raise nx.NetworkXUnfeasible("no augmentation possible")
+
+    avail_uv, avail_w = _unpack_available_edges(avail, weight=weight, G=H)
+
+    # Collapse input into a metagraph. Meta nodes are bridge-ccs
+    bridge_ccs = nx.connectivity.bridge_components(H)
+    C = collapse(H, bridge_ccs)
+
+    # Use the meta graph to shrink avail to a small feasible subset
+    mapping = C.graph["mapping"]
+    # Choose the minimum weight feasible edge in each group
+    meta_to_wuv = {
+        (mu, mv): (w, uv)
+        for (mu, mv), uv, w in _lightest_meta_edges(mapping, avail_uv, avail_w)
+    }
+
+    # Mapping of terms from (Khuller and Thurimella):
+    #     C         : G_0 = (V, E^0)
+    #        This is the metagraph where each node is a 2-edge-cc in G.
+    #        The edges in C represent bridges in the original graph.
+    #     (mu, mv)  : E - E^0  # they group both avail and given edges in E
+    #     T         : \Gamma
+    #     D         : G^D = (V, E_D)
+
+    #     The paper uses ancestor because children point to parents, which is
+    #     contrary to networkx standards.  So, we actually need to run
+    #     nx.least_common_ancestor on the reversed Tree.
+
+    # Pick an arbitrary leaf from C as the root
+    try:
+        root = next(n for n, d in C.degree() if d == 1)
+    except StopIteration:  # no nodes found with degree == 1
+        return
+    # Root C into a tree TR by directing all edges away from the root
+    # Note in their paper T directs edges towards the root
+    TR = nx.dfs_tree(C, root)
+
+    # Add to D the directed edges of T and set their weight to zero
+    # This indicates that it costs nothing to use edges that were given.
+    D = nx.reverse(TR).copy()
+
+    nx.set_edge_attributes(D, name="weight", values=0)
+
+    # The LCA of mu and mv in T is the shared ancestor of mu and mv that is
+    # located farthest from the root.
+    lca_gen = nx.tree_all_pairs_lowest_common_ancestor(
+        TR, root=root, pairs=meta_to_wuv.keys()
+    )
+
+    for (mu, mv), lca in lca_gen:
+        w, uv = meta_to_wuv[(mu, mv)]
+        if lca == mu:
+            # If u is an ancestor of v in TR, then add edge u->v to D
+            D.add_edge(lca, mv, weight=w, generator=uv)
+        elif lca == mv:
+            # If v is an ancestor of u in TR, then add edge v->u to D
+            D.add_edge(lca, mu, weight=w, generator=uv)
+        else:
+            # If neither u nor v is a ancestor of the other in TR
+            # let t = lca(TR, u, v) and add edges t->u and t->v
+            # Track the original edge that GENERATED these edges.
+            D.add_edge(lca, mu, weight=w, generator=uv)
+            D.add_edge(lca, mv, weight=w, generator=uv)
+
+    # Then compute a minimum rooted branching
+    try:
+        # Note the original edges must be directed towards to root for the
+        # branching to give us a bridge-augmentation.
+        A = _minimum_rooted_branching(D, root)
+    except nx.NetworkXException as err:
+        # If there is no branching then augmentation is not possible
+        raise nx.NetworkXUnfeasible("no 2-edge-augmentation possible") from err
+
+    # For each edge e, in the branching that did not belong to the directed
+    # tree T, add the corresponding edge that **GENERATED** it (this is not
+    # necessarily e itself!)
+
+    # ensure the third case does not generate edges twice
+    bridge_connectors = set()
+    for mu, mv in A.edges():
+        data = D.get_edge_data(mu, mv)
+        if "generator" in data:
+            # Add the avail edge that generated the branching edge.
+            edge = data["generator"]
+            bridge_connectors.add(edge)
+
+    yield from bridge_connectors
+
+
+def _minimum_rooted_branching(D, root):
+    """Helper function to compute a minimum rooted branching (aka rooted
+    arborescence)
+
+    Before the branching can be computed, the directed graph must be rooted by
+    removing the predecessors of root.
+
+    A branching / arborescence of rooted graph G is a subgraph that contains a
+    directed path from the root to every other vertex. It is the directed
+    analog of the minimum spanning tree problem.
+
+    References
+    ----------
+    [1] Khuller, Samir (2002) Advanced Algorithms Lecture 24 Notes.
+    https://web.archive.org/web/20121030033722/https://www.cs.umd.edu/class/spring2011/cmsc651/lec07.pdf
+    """
+    rooted = D.copy()
+    # root the graph by removing all predecessors to `root`.
+    rooted.remove_edges_from([(u, root) for u in D.predecessors(root)])
+    # Then compute the branching / arborescence.
+    A = nx.minimum_spanning_arborescence(rooted)
+    return A
+
+
+@nx._dispatchable(returns_graph=True)
+def collapse(G, grouped_nodes):
+    """Collapses each group of nodes into a single node.
+
+    This is similar to condensation, but works on undirected graphs.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    grouped_nodes:  list or generator
+       Grouping of nodes to collapse. The grouping must be disjoint.
+       If grouped_nodes are strongly_connected_components then this is
+       equivalent to :func:`condensation`.
+
+    Returns
+    -------
+    C : NetworkX Graph
+       The collapsed graph C of G with respect to the node grouping.  The node
+       labels are integers corresponding to the index of the component in the
+       list of grouped_nodes.  C has a graph attribute named 'mapping' with a
+       dictionary mapping the original nodes to the nodes in C to which they
+       belong.  Each node in C also has a node attribute 'members' with the set
+       of original nodes in G that form the group that the node in C
+       represents.
+
+    Examples
+    --------
+    >>> # Collapses a graph using disjoint groups, but not necessarily connected
+    >>> G = nx.Graph([(1, 0), (2, 3), (3, 1), (3, 4), (4, 5), (5, 6), (5, 7)])
+    >>> G.add_node("A")
+    >>> grouped_nodes = [{0, 1, 2, 3}, {5, 6, 7}]
+    >>> C = collapse(G, grouped_nodes)
+    >>> members = nx.get_node_attributes(C, "members")
+    >>> sorted(members.keys())
+    [0, 1, 2, 3]
+    >>> member_values = set(map(frozenset, members.values()))
+    >>> assert {0, 1, 2, 3} in member_values
+    >>> assert {4} in member_values
+    >>> assert {5, 6, 7} in member_values
+    >>> assert {"A"} in member_values
+    """
+    mapping = {}
+    members = {}
+    C = G.__class__()
+    i = 0  # required if G is empty
+    remaining = set(G.nodes())
+    for i, group in enumerate(grouped_nodes):
+        group = set(group)
+        assert remaining.issuperset(
+            group
+        ), "grouped nodes must exist in G and be disjoint"
+        remaining.difference_update(group)
+        members[i] = group
+        mapping.update((n, i) for n in group)
+    # remaining nodes are in their own group
+    for i, node in enumerate(remaining, start=i + 1):
+        group = {node}
+        members[i] = group
+        mapping.update((n, i) for n in group)
+    number_of_groups = i + 1
+    C.add_nodes_from(range(number_of_groups))
+    C.add_edges_from(
+        (mapping[u], mapping[v]) for u, v in G.edges() if mapping[u] != mapping[v]
+    )
+    # Add a list of members (ie original nodes) to each node (ie scc) in C.
+    nx.set_node_attributes(C, name="members", values=members)
+    # Add mapping dict as graph attribute
+    C.graph["mapping"] = mapping
+    return C
+
+
+@nx._dispatchable
+def complement_edges(G):
+    """Returns only the edges in the complement of G
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the complement of G
+
+    Examples
+    --------
+    >>> G = nx.path_graph((1, 2, 3, 4))
+    >>> sorted(complement_edges(G))
+    [(1, 3), (1, 4), (2, 4)]
+    >>> G = nx.path_graph((1, 2, 3, 4), nx.DiGraph())
+    >>> sorted(complement_edges(G))
+    [(1, 3), (1, 4), (2, 1), (2, 4), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)]
+    >>> G = nx.complete_graph(1000)
+    >>> sorted(complement_edges(G))
+    []
+    """
+    G_adj = G._adj  # Store as a variable to eliminate attribute lookup
+    if G.is_directed():
+        for u, v in it.combinations(G.nodes(), 2):
+            if v not in G_adj[u]:
+                yield (u, v)
+            if u not in G_adj[v]:
+                yield (v, u)
+    else:
+        for u, v in it.combinations(G.nodes(), 2):
+            if v not in G_adj[u]:
+                yield (u, v)
+
+
+def _compat_shuffle(rng, input):
+    """wrapper around rng.shuffle for python 2 compatibility reasons"""
+    rng.shuffle(input)
+
+
+@not_implemented_for("multigraph")
+@not_implemented_for("directed")
+@py_random_state(4)
+@nx._dispatchable
+def greedy_k_edge_augmentation(G, k, avail=None, weight=None, seed=None):
+    """Greedy algorithm for finding a k-edge-augmentation
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    k : integer
+        Desired edge connectivity
+
+    avail : dict or a set of 2 or 3 tuples
+        For more details, see :func:`k_edge_augmentation`.
+
+    weight : string
+        key to use to find weights if ``avail`` is a set of 3-tuples.
+        For more details, see :func:`k_edge_augmentation`.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Yields
+    ------
+    edge : tuple
+        Edges in the greedy augmentation of G
+
+    Notes
+    -----
+    The algorithm is simple. Edges are incrementally added between parts of the
+    graph that are not yet locally k-edge-connected. Then edges are from the
+    augmenting set are pruned as long as local-edge-connectivity is not broken.
+
+    This algorithm is greedy and does not provide optimality guarantees. It
+    exists only to provide :func:`k_edge_augmentation` with the ability to
+    generate a feasible solution for arbitrary k.
+
+    See Also
+    --------
+    :func:`k_edge_augmentation`
+
+    Examples
+    --------
+    >>> G = nx.path_graph((1, 2, 3, 4, 5, 6, 7))
+    >>> sorted(greedy_k_edge_augmentation(G, k=2))
+    [(1, 7)]
+    >>> sorted(greedy_k_edge_augmentation(G, k=1, avail=[]))
+    []
+    >>> G = nx.path_graph((1, 2, 3, 4, 5, 6, 7))
+    >>> avail = {(u, v): 1 for (u, v) in complement_edges(G)}
+    >>> # randomized pruning process can produce different solutions
+    >>> sorted(greedy_k_edge_augmentation(G, k=4, avail=avail, seed=2))
+    [(1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 4), (2, 6), (3, 7), (5, 7)]
+    >>> sorted(greedy_k_edge_augmentation(G, k=4, avail=avail, seed=3))
+    [(1, 3), (1, 5), (1, 6), (2, 4), (2, 6), (3, 7), (4, 7), (5, 7)]
+    """
+    # Result set
+    aug_edges = []
+
+    done = is_k_edge_connected(G, k)
+    if done:
+        return
+    if avail is None:
+        # all edges are available
+        avail_uv = list(complement_edges(G))
+        avail_w = [1] * len(avail_uv)
+    else:
+        # Get the unique set of unweighted edges
+        avail_uv, avail_w = _unpack_available_edges(avail, weight=weight, G=G)
+
+    # Greedy: order lightest edges. Use degree sum to tie-break
+    tiebreaker = [sum(map(G.degree, uv)) for uv in avail_uv]
+    avail_wduv = sorted(zip(avail_w, tiebreaker, avail_uv))
+    avail_uv = [uv for w, d, uv in avail_wduv]
+
+    # Incrementally add edges in until we are k-connected
+    H = G.copy()
+    for u, v in avail_uv:
+        done = False
+        if not is_locally_k_edge_connected(H, u, v, k=k):
+            # Only add edges in parts that are not yet locally k-edge-connected
+            aug_edges.append((u, v))
+            H.add_edge(u, v)
+            # Did adding this edge help?
+            if H.degree(u) >= k and H.degree(v) >= k:
+                done = is_k_edge_connected(H, k)
+        if done:
+            break
+
+    # Check for feasibility
+    if not done:
+        raise nx.NetworkXUnfeasible("not able to k-edge-connect with available edges")
+
+    # Randomized attempt to reduce the size of the solution
+    _compat_shuffle(seed, aug_edges)
+    for u, v in list(aug_edges):
+        # Don't remove if we know it would break connectivity
+        if H.degree(u) <= k or H.degree(v) <= k:
+            continue
+        H.remove_edge(u, v)
+        aug_edges.remove((u, v))
+        if not is_k_edge_connected(H, k=k):
+            # If removing this edge breaks feasibility, undo
+            H.add_edge(u, v)
+            aug_edges.append((u, v))
+
+    # Generate results
+    yield from aug_edges

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/edge_kcomponents.py

@@ -0,0 +1,592 @@
+"""
+Algorithms for finding k-edge-connected components and subgraphs.
+
+A k-edge-connected component (k-edge-cc) is a maximal set of nodes in G, such
+that all pairs of node have an edge-connectivity of at least k.
+
+A k-edge-connected subgraph (k-edge-subgraph) is a maximal set of nodes in G,
+such that the subgraph of G defined by the nodes has an edge-connectivity at
+least k.
+"""
+
+import itertools as it
+from functools import partial
+
+import networkx as nx
+from networkx.utils import arbitrary_element, not_implemented_for
+
+__all__ = [
+    "k_edge_components",
+    "k_edge_subgraphs",
+    "bridge_components",
+    "EdgeComponentAuxGraph",
+]
+
+
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def k_edge_components(G, k):
+    """Generates nodes in each maximal k-edge-connected component in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    k : Integer
+        Desired edge connectivity
+
+    Returns
+    -------
+    k_edge_components : a generator of k-edge-ccs. Each set of returned nodes
+       will have k-edge-connectivity in the graph G.
+
+    See Also
+    --------
+    :func:`local_edge_connectivity`
+    :func:`k_edge_subgraphs` : similar to this function, but the subgraph
+        defined by the nodes must also have k-edge-connectivity.
+    :func:`k_components` : similar to this function, but uses node-connectivity
+        instead of edge-connectivity
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is a multigraph.
+
+    ValueError:
+        If k is less than 1
+
+    Notes
+    -----
+    Attempts to use the most efficient implementation available based on k.
+    If k=1, this is simply connected components for directed graphs and
+    connected components for undirected graphs.
+    If k=2 on an efficient bridge connected component algorithm from _[1] is
+    run based on the chain decomposition.
+    Otherwise, the algorithm from _[2] is used.
+
+    Examples
+    --------
+    >>> import itertools as it
+    >>> from networkx.utils import pairwise
+    >>> paths = [
+    ...     (1, 2, 4, 3, 1, 4),
+    ...     (5, 6, 7, 8, 5, 7, 8, 6),
+    ... ]
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from(it.chain(*paths))
+    >>> G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
+    >>> # note this returns {1, 4} unlike k_edge_subgraphs
+    >>> sorted(map(sorted, nx.k_edge_components(G, k=3)))
+    [[1, 4], [2], [3], [5, 6, 7, 8]]
+
+    References
+    ----------
+    .. [1] https://en.wikipedia.org/wiki/Bridge_%28graph_theory%29
+    .. [2] Wang, Tianhao, et al. (2015) A simple algorithm for finding all
+        k-edge-connected components.
+        http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
+    """
+    # Compute k-edge-ccs using the most efficient algorithms available.
+    if k < 1:
+        raise ValueError("k cannot be less than 1")
+    if G.is_directed():
+        if k == 1:
+            return nx.strongly_connected_components(G)
+        else:
+            # TODO: investigate https://arxiv.org/abs/1412.6466 for k=2
+            aux_graph = EdgeComponentAuxGraph.construct(G)
+            return aux_graph.k_edge_components(k)
+    else:
+        if k == 1:
+            return nx.connected_components(G)
+        elif k == 2:
+            return bridge_components(G)
+        else:
+            aux_graph = EdgeComponentAuxGraph.construct(G)
+            return aux_graph.k_edge_components(k)
+
+
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def k_edge_subgraphs(G, k):
+    """Generates nodes in each maximal k-edge-connected subgraph in G.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    k : Integer
+        Desired edge connectivity
+
+    Returns
+    -------
+    k_edge_subgraphs : a generator of k-edge-subgraphs
+        Each k-edge-subgraph is a maximal set of nodes that defines a subgraph
+        of G that is k-edge-connected.
+
+    See Also
+    --------
+    :func:`edge_connectivity`
+    :func:`k_edge_components` : similar to this function, but nodes only
+        need to have k-edge-connectivity within the graph G and the subgraphs
+        might not be k-edge-connected.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is a multigraph.
+
+    ValueError:
+        If k is less than 1
+
+    Notes
+    -----
+    Attempts to use the most efficient implementation available based on k.
+    If k=1, or k=2 and the graph is undirected, then this simply calls
+    `k_edge_components`.  Otherwise the algorithm from _[1] is used.
+
+    Examples
+    --------
+    >>> import itertools as it
+    >>> from networkx.utils import pairwise
+    >>> paths = [
+    ...     (1, 2, 4, 3, 1, 4),
+    ...     (5, 6, 7, 8, 5, 7, 8, 6),
+    ... ]
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from(it.chain(*paths))
+    >>> G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
+    >>> # note this does not return {1, 4} unlike k_edge_components
+    >>> sorted(map(sorted, nx.k_edge_subgraphs(G, k=3)))
+    [[1], [2], [3], [4], [5, 6, 7, 8]]
+
+    References
+    ----------
+    .. [1] Zhou, Liu, et al. (2012) Finding maximal k-edge-connected subgraphs
+        from a large graph.  ACM International Conference on Extending Database
+        Technology 2012 480-–491.
+        https://openproceedings.org/2012/conf/edbt/ZhouLYLCL12.pdf
+    """
+    if k < 1:
+        raise ValueError("k cannot be less than 1")
+    if G.is_directed():
+        if k <= 1:
+            # For directed graphs ,
+            # When k == 1, k-edge-ccs and k-edge-subgraphs are the same
+            return k_edge_components(G, k)
+        else:
+            return _k_edge_subgraphs_nodes(G, k)
+    else:
+        if k <= 2:
+            # For undirected graphs,
+            # when k <= 2, k-edge-ccs and k-edge-subgraphs are the same
+            return k_edge_components(G, k)
+        else:
+            return _k_edge_subgraphs_nodes(G, k)
+
+
+def _k_edge_subgraphs_nodes(G, k):
+    """Helper to get the nodes from the subgraphs.
+
+    This allows k_edge_subgraphs to return a generator.
+    """
+    for C in general_k_edge_subgraphs(G, k):
+        yield set(C.nodes())
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable
+def bridge_components(G):
+    """Finds all bridge-connected components G.
+
+    Parameters
+    ----------
+    G : NetworkX undirected graph
+
+    Returns
+    -------
+    bridge_components : a generator of 2-edge-connected components
+
+
+    See Also
+    --------
+    :func:`k_edge_subgraphs` : this function is a special case for an
+        undirected graph where k=2.
+    :func:`biconnected_components` : similar to this function, but is defined
+        using 2-node-connectivity instead of 2-edge-connectivity.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is directed or a multigraph.
+
+    Notes
+    -----
+    Bridge-connected components are also known as 2-edge-connected components.
+
+    Examples
+    --------
+    >>> # The barbell graph with parameter zero has a single bridge
+    >>> G = nx.barbell_graph(5, 0)
+    >>> from networkx.algorithms.connectivity.edge_kcomponents import bridge_components
+    >>> sorted(map(sorted, bridge_components(G)))
+    [[0, 1, 2, 3, 4], [5, 6, 7, 8, 9]]
+    """
+    H = G.copy()
+    H.remove_edges_from(nx.bridges(G))
+    yield from nx.connected_components(H)
+
+
+class EdgeComponentAuxGraph:
+    r"""A simple algorithm to find all k-edge-connected components in a graph.
+
+    Constructing the auxiliary graph (which may take some time) allows for the
+    k-edge-ccs to be found in linear time for arbitrary k.
+
+    Notes
+    -----
+    This implementation is based on [1]_. The idea is to construct an auxiliary
+    graph from which the k-edge-ccs can be extracted in linear time. The
+    auxiliary graph is constructed in $O(|V|\cdot F)$ operations, where F is the
+    complexity of max flow. Querying the components takes an additional $O(|V|)$
+    operations. This algorithm can be slow for large graphs, but it handles an
+    arbitrary k and works for both directed and undirected inputs.
+
+    The undirected case for k=1 is exactly connected components.
+    The undirected case for k=2 is exactly bridge connected components.
+    The directed case for k=1 is exactly strongly connected components.
+
+    References
+    ----------
+    .. [1] Wang, Tianhao, et al. (2015) A simple algorithm for finding all
+        k-edge-connected components.
+        http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0136264
+
+    Examples
+    --------
+    >>> import itertools as it
+    >>> from networkx.utils import pairwise
+    >>> from networkx.algorithms.connectivity import EdgeComponentAuxGraph
+    >>> # Build an interesting graph with multiple levels of k-edge-ccs
+    >>> paths = [
+    ...     (1, 2, 3, 4, 1, 3, 4, 2),  # a 3-edge-cc (a 4 clique)
+    ...     (5, 6, 7, 5),  # a 2-edge-cc (a 3 clique)
+    ...     (1, 5),  # combine first two ccs into a 1-edge-cc
+    ...     (0,),  # add an additional disconnected 1-edge-cc
+    ... ]
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from(it.chain(*paths))
+    >>> G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
+    >>> # Constructing the AuxGraph takes about O(n ** 4)
+    >>> aux_graph = EdgeComponentAuxGraph.construct(G)
+    >>> # Once constructed, querying takes O(n)
+    >>> sorted(map(sorted, aux_graph.k_edge_components(k=1)))
+    [[0], [1, 2, 3, 4, 5, 6, 7]]
+    >>> sorted(map(sorted, aux_graph.k_edge_components(k=2)))
+    [[0], [1, 2, 3, 4], [5, 6, 7]]
+    >>> sorted(map(sorted, aux_graph.k_edge_components(k=3)))
+    [[0], [1, 2, 3, 4], [5], [6], [7]]
+    >>> sorted(map(sorted, aux_graph.k_edge_components(k=4)))
+    [[0], [1], [2], [3], [4], [5], [6], [7]]
+
+    The auxiliary graph is primarily used for k-edge-ccs but it
+    can also speed up the queries of k-edge-subgraphs by refining the
+    search space.
+
+    >>> import itertools as it
+    >>> from networkx.utils import pairwise
+    >>> from networkx.algorithms.connectivity import EdgeComponentAuxGraph
+    >>> paths = [
+    ...     (1, 2, 4, 3, 1, 4),
+    ... ]
+    >>> G = nx.Graph()
+    >>> G.add_nodes_from(it.chain(*paths))
+    >>> G.add_edges_from(it.chain(*[pairwise(path) for path in paths]))
+    >>> aux_graph = EdgeComponentAuxGraph.construct(G)
+    >>> sorted(map(sorted, aux_graph.k_edge_subgraphs(k=3)))
+    [[1], [2], [3], [4]]
+    >>> sorted(map(sorted, aux_graph.k_edge_components(k=3)))
+    [[1, 4], [2], [3]]
+    """
+
+    # @not_implemented_for('multigraph')  # TODO: fix decor for classmethods
+    @classmethod
+    def construct(EdgeComponentAuxGraph, G):
+        """Builds an auxiliary graph encoding edge-connectivity between nodes.
+
+        Notes
+        -----
+        Given G=(V, E), initialize an empty auxiliary graph A.
+        Choose an arbitrary source node s.  Initialize a set N of available
+        nodes (that can be used as the sink). The algorithm picks an
+        arbitrary node t from N - {s}, and then computes the minimum st-cut
+        (S, T) with value w. If G is directed the minimum of the st-cut or
+        the ts-cut is used instead. Then, the edge (s, t) is added to the
+        auxiliary graph with weight w. The algorithm is called recursively
+        first using S as the available nodes and s as the source, and then
+        using T and t. Recursion stops when the source is the only available
+        node.
+
+        Parameters
+        ----------
+        G : NetworkX graph
+        """
+        # workaround for classmethod decorator
+        not_implemented_for("multigraph")(lambda G: G)(G)
+
+        def _recursive_build(H, A, source, avail):
+            # Terminate once the flow has been compute to every node.
+            if {source} == avail:
+                return
+            # pick an arbitrary node as the sink
+            sink = arbitrary_element(avail - {source})
+            # find the minimum cut and its weight
+            value, (S, T) = nx.minimum_cut(H, source, sink)
+            if H.is_directed():
+                # check if the reverse direction has a smaller cut
+                value_, (T_, S_) = nx.minimum_cut(H, sink, source)
+                if value_ < value:
+                    value, S, T = value_, S_, T_
+            # add edge with weight of cut to the aux graph
+            A.add_edge(source, sink, weight=value)
+            # recursively call until all but one node is used
+            _recursive_build(H, A, source, avail.intersection(S))
+            _recursive_build(H, A, sink, avail.intersection(T))
+
+        # Copy input to ensure all edges have unit capacity
+        H = G.__class__()
+        H.add_nodes_from(G.nodes())
+        H.add_edges_from(G.edges(), capacity=1)
+
+        # A is the auxiliary graph to be constructed
+        # It is a weighted undirected tree
+        A = nx.Graph()
+
+        # Pick an arbitrary node as the source
+        if H.number_of_nodes() > 0:
+            source = arbitrary_element(H.nodes())
+            # Initialize a set of elements that can be chosen as the sink
+            avail = set(H.nodes())
+
+            # This constructs A
+            _recursive_build(H, A, source, avail)
+
+        # This class is a container the holds the auxiliary graph A and
+        # provides access the k_edge_components function.
+        self = EdgeComponentAuxGraph()
+        self.A = A
+        self.H = H
+        return self
+
+    def k_edge_components(self, k):
+        """Queries the auxiliary graph for k-edge-connected components.
+
+        Parameters
+        ----------
+        k : Integer
+            Desired edge connectivity
+
+        Returns
+        -------
+        k_edge_components : a generator of k-edge-ccs
+
+        Notes
+        -----
+        Given the auxiliary graph, the k-edge-connected components can be
+        determined in linear time by removing all edges with weights less than
+        k from the auxiliary graph.  The resulting connected components are the
+        k-edge-ccs in the original graph.
+        """
+        if k < 1:
+            raise ValueError("k cannot be less than 1")
+        A = self.A
+        # "traverse the auxiliary graph A and delete all edges with weights less
+        # than k"
+        aux_weights = nx.get_edge_attributes(A, "weight")
+        # Create a relevant graph with the auxiliary edges with weights >= k
+        R = nx.Graph()
+        R.add_nodes_from(A.nodes())
+        R.add_edges_from(e for e, w in aux_weights.items() if w >= k)
+
+        # Return the nodes that are k-edge-connected in the original graph
+        yield from nx.connected_components(R)
+
+    def k_edge_subgraphs(self, k):
+        """Queries the auxiliary graph for k-edge-connected subgraphs.
+
+        Parameters
+        ----------
+        k : Integer
+            Desired edge connectivity
+
+        Returns
+        -------
+        k_edge_subgraphs : a generator of k-edge-subgraphs
+
+        Notes
+        -----
+        Refines the k-edge-ccs into k-edge-subgraphs. The running time is more
+        than $O(|V|)$.
+
+        For single values of k it is faster to use `nx.k_edge_subgraphs`.
+        But for multiple values of k, it can be faster to build AuxGraph and
+        then use this method.
+        """
+        if k < 1:
+            raise ValueError("k cannot be less than 1")
+        H = self.H
+        A = self.A
+        # "traverse the auxiliary graph A and delete all edges with weights less
+        # than k"
+        aux_weights = nx.get_edge_attributes(A, "weight")
+        # Create a relevant graph with the auxiliary edges with weights >= k
+        R = nx.Graph()
+        R.add_nodes_from(A.nodes())
+        R.add_edges_from(e for e, w in aux_weights.items() if w >= k)
+
+        # Return the components whose subgraphs are k-edge-connected
+        for cc in nx.connected_components(R):
+            if len(cc) < k:
+                # Early return optimization
+                for node in cc:
+                    yield {node}
+            else:
+                # Call subgraph solution to refine the results
+                C = H.subgraph(cc)
+                yield from k_edge_subgraphs(C, k)
+
+
+def _low_degree_nodes(G, k, nbunch=None):
+    """Helper for finding nodes with degree less than k."""
+    # Nodes with degree less than k cannot be k-edge-connected.
+    if G.is_directed():
+        # Consider both in and out degree in the directed case
+        seen = set()
+        for node, degree in G.out_degree(nbunch):
+            if degree < k:
+                seen.add(node)
+                yield node
+        for node, degree in G.in_degree(nbunch):
+            if node not in seen and degree < k:
+                seen.add(node)
+                yield node
+    else:
+        # Only the degree matters in the undirected case
+        for node, degree in G.degree(nbunch):
+            if degree < k:
+                yield node
+
+
+def _high_degree_components(G, k):
+    """Helper for filtering components that can't be k-edge-connected.
+
+    Removes and generates each node with degree less than k.  Then generates
+    remaining components where all nodes have degree at least k.
+    """
+    # Iteratively remove parts of the graph that are not k-edge-connected
+    H = G.copy()
+    singletons = set(_low_degree_nodes(H, k))
+    while singletons:
+        # Only search neighbors of removed nodes
+        nbunch = set(it.chain.from_iterable(map(H.neighbors, singletons)))
+        nbunch.difference_update(singletons)
+        H.remove_nodes_from(singletons)
+        for node in singletons:
+            yield {node}
+        singletons = set(_low_degree_nodes(H, k, nbunch))
+
+    # Note: remaining connected components may not be k-edge-connected
+    if G.is_directed():
+        yield from nx.strongly_connected_components(H)
+    else:
+        yield from nx.connected_components(H)
+
+
+@nx._dispatchable(returns_graph=True)
+def general_k_edge_subgraphs(G, k):
+    """General algorithm to find all maximal k-edge-connected subgraphs in `G`.
+
+    Parameters
+    ----------
+    G : nx.Graph
+       Graph in which all maximal k-edge-connected subgraphs will be found.
+
+    k : int
+
+    Yields
+    ------
+    k_edge_subgraphs : Graph instances that are k-edge-subgraphs
+        Each k-edge-subgraph contains a maximal set of nodes that defines a
+        subgraph of `G` that is k-edge-connected.
+
+    Notes
+    -----
+    Implementation of the basic algorithm from [1]_.  The basic idea is to find
+    a global minimum cut of the graph. If the cut value is at least k, then the
+    graph is a k-edge-connected subgraph and can be added to the results.
+    Otherwise, the cut is used to split the graph in two and the procedure is
+    applied recursively. If the graph is just a single node, then it is also
+    added to the results. At the end, each result is either guaranteed to be
+    a single node or a subgraph of G that is k-edge-connected.
+
+    This implementation contains optimizations for reducing the number of calls
+    to max-flow, but there are other optimizations in [1]_ that could be
+    implemented.
+
+    References
+    ----------
+    .. [1] Zhou, Liu, et al. (2012) Finding maximal k-edge-connected subgraphs
+        from a large graph.  ACM International Conference on Extending Database
+        Technology 2012 480-–491.
+        https://openproceedings.org/2012/conf/edbt/ZhouLYLCL12.pdf
+
+    Examples
+    --------
+    >>> from networkx.utils import pairwise
+    >>> paths = [
+    ...     (11, 12, 13, 14, 11, 13, 14, 12),  # a 4-clique
+    ...     (21, 22, 23, 24, 21, 23, 24, 22),  # another 4-clique
+    ...     # connect the cliques with high degree but low connectivity
+    ...     (50, 13),
+    ...     (12, 50, 22),
+    ...     (13, 102, 23),
+    ...     (14, 101, 24),
+    ... ]
+    >>> G = nx.Graph(it.chain(*[pairwise(path) for path in paths]))
+    >>> sorted(len(k_sg) for k_sg in k_edge_subgraphs(G, k=3))
+    [1, 1, 1, 4, 4]
+    """
+    if k < 1:
+        raise ValueError("k cannot be less than 1")
+
+    # Node pruning optimization (incorporates early return)
+    # find_ccs is either connected_components/strongly_connected_components
+    find_ccs = partial(_high_degree_components, k=k)
+
+    # Quick return optimization
+    if G.number_of_nodes() < k:
+        for node in G.nodes():
+            yield G.subgraph([node]).copy()
+        return
+
+    # Intermediate results
+    R0 = {G.subgraph(cc).copy() for cc in find_ccs(G)}
+    # Subdivide CCs in the intermediate results until they are k-conn
+    while R0:
+        G1 = R0.pop()
+        if G1.number_of_nodes() == 1:
+            yield G1
+        else:
+            # Find a global minimum cut
+            cut_edges = nx.minimum_edge_cut(G1)
+            cut_value = len(cut_edges)
+            if cut_value < k:
+                # G1 is not k-edge-connected, so subdivide it
+                G1.remove_edges_from(cut_edges)
+                for cc in find_ccs(G1):
+                    R0.add(G1.subgraph(cc).copy())
+            else:
+                # Otherwise we found a k-edge-connected subgraph
+                yield G1

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcomponents.py

@@ -0,0 +1,223 @@
+"""
+Moody and White algorithm for k-components
+"""
+
+from collections import defaultdict
+from itertools import combinations
+from operator import itemgetter
+
+import networkx as nx
+
+# Define the default maximum flow function.
+from networkx.algorithms.flow import edmonds_karp
+from networkx.utils import not_implemented_for
+
+default_flow_func = edmonds_karp
+
+__all__ = ["k_components"]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def k_components(G, flow_func=None):
+    r"""Returns the k-component structure of a graph G.
+
+    A `k`-component is a maximal subgraph of a graph G that has, at least,
+    node connectivity `k`: we need to remove at least `k` nodes to break it
+    into more components. `k`-components have an inherent hierarchical
+    structure because they are nested in terms of connectivity: a connected
+    graph can contain several 2-components, each of which can contain
+    one or more 3-components, and so forth.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+
+    flow_func : function
+        Function to perform the underlying flow computations. Default value
+        :meth:`edmonds_karp`. This function performs better in sparse graphs with
+        right tailed degree distributions. :meth:`shortest_augmenting_path` will
+        perform better in denser graphs.
+
+    Returns
+    -------
+    k_components : dict
+        Dictionary with all connectivity levels `k` in the input Graph as keys
+        and a list of sets of nodes that form a k-component of level `k` as
+        values.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is directed.
+
+    Examples
+    --------
+    >>> # Petersen graph has 10 nodes and it is triconnected, thus all
+    >>> # nodes are in a single component on all three connectivity levels
+    >>> G = nx.petersen_graph()
+    >>> k_components = nx.k_components(G)
+
+    Notes
+    -----
+    Moody and White [1]_ (appendix A) provide an algorithm for identifying
+    k-components in a graph, which is based on Kanevsky's algorithm [2]_
+    for finding all minimum-size node cut-sets of a graph (implemented in
+    :meth:`all_node_cuts` function):
+
+        1. Compute node connectivity, k, of the input graph G.
+
+        2. Identify all k-cutsets at the current level of connectivity using
+           Kanevsky's algorithm.
+
+        3. Generate new graph components based on the removal of
+           these cutsets. Nodes in a cutset belong to both sides
+           of the induced cut.
+
+        4. If the graph is neither complete nor trivial, return to 1;
+           else end.
+
+    This implementation also uses some heuristics (see [3]_ for details)
+    to speed up the computation.
+
+    See also
+    --------
+    node_connectivity
+    all_node_cuts
+    biconnected_components : special case of this function when k=2
+    k_edge_components : similar to this function, but uses edge-connectivity
+        instead of node-connectivity
+
+    References
+    ----------
+    .. [1]  Moody, J. and D. White (2003). Social cohesion and embeddedness:
+            A hierarchical conception of social groups.
+            American Sociological Review 68(1), 103--28.
+            http://www2.asanet.org/journals/ASRFeb03MoodyWhite.pdf
+
+    .. [2]  Kanevsky, A. (1993). Finding all minimum-size separating vertex
+            sets in a graph. Networks 23(6), 533--541.
+            http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract
+
+    .. [3]  Torrents, J. and F. Ferraro (2015). Structural Cohesion:
+            Visualization and Heuristics for Fast Computation.
+            https://arxiv.org/pdf/1503.04476v1
+
+    """
+    # Dictionary with connectivity level (k) as keys and a list of
+    # sets of nodes that form a k-component as values. Note that
+    # k-components can overlap (but only k - 1 nodes).
+    k_components = defaultdict(list)
+    # Define default flow function
+    if flow_func is None:
+        flow_func = default_flow_func
+    # Bicomponents as a base to check for higher order k-components
+    for component in nx.connected_components(G):
+        # isolated nodes have connectivity 0
+        comp = set(component)
+        if len(comp) > 1:
+            k_components[1].append(comp)
+    bicomponents = [G.subgraph(c) for c in nx.biconnected_components(G)]
+    for bicomponent in bicomponents:
+        bicomp = set(bicomponent)
+        # avoid considering dyads as bicomponents
+        if len(bicomp) > 2:
+            k_components[2].append(bicomp)
+    for B in bicomponents:
+        if len(B) <= 2:
+            continue
+        k = nx.node_connectivity(B, flow_func=flow_func)
+        if k > 2:
+            k_components[k].append(set(B))
+        # Perform cuts in a DFS like order.
+        cuts = list(nx.all_node_cuts(B, k=k, flow_func=flow_func))
+        stack = [(k, _generate_partition(B, cuts, k))]
+        while stack:
+            (parent_k, partition) = stack[-1]
+            try:
+                nodes = next(partition)
+                C = B.subgraph(nodes)
+                this_k = nx.node_connectivity(C, flow_func=flow_func)
+                if this_k > parent_k and this_k > 2:
+                    k_components[this_k].append(set(C))
+                cuts = list(nx.all_node_cuts(C, k=this_k, flow_func=flow_func))
+                if cuts:
+                    stack.append((this_k, _generate_partition(C, cuts, this_k)))
+            except StopIteration:
+                stack.pop()
+
+    # This is necessary because k-components may only be reported at their
+    # maximum k level. But we want to return a dictionary in which keys are
+    # connectivity levels and values list of sets of components, without
+    # skipping any connectivity level. Also, it's possible that subsets of
+    # an already detected k-component appear at a level k. Checking for this
+    # in the while loop above penalizes the common case. Thus we also have to
+    # _consolidate all connectivity levels in _reconstruct_k_components.
+    return _reconstruct_k_components(k_components)
+
+
+def _consolidate(sets, k):
+    """Merge sets that share k or more elements.
+
+    See: http://rosettacode.org/wiki/Set_consolidation
+
+    The iterative python implementation posted there is
+    faster than this because of the overhead of building a
+    Graph and calling nx.connected_components, but it's not
+    clear for us if we can use it in NetworkX because there
+    is no licence for the code.
+
+    """
+    G = nx.Graph()
+    nodes = dict(enumerate(sets))
+    G.add_nodes_from(nodes)
+    G.add_edges_from(
+        (u, v) for u, v in combinations(nodes, 2) if len(nodes[u] & nodes[v]) >= k
+    )
+    for component in nx.connected_components(G):
+        yield set.union(*[nodes[n] for n in component])
+
+
+def _generate_partition(G, cuts, k):
+    def has_nbrs_in_partition(G, node, partition):
+        return any(n in partition for n in G[node])
+
+    components = []
+    nodes = {n for n, d in G.degree() if d > k} - {n for cut in cuts for n in cut}
+    H = G.subgraph(nodes)
+    for cc in nx.connected_components(H):
+        component = set(cc)
+        for cut in cuts:
+            for node in cut:
+                if has_nbrs_in_partition(G, node, cc):
+                    component.add(node)
+        if len(component) < G.order():
+            components.append(component)
+    yield from _consolidate(components, k + 1)
+
+
+def _reconstruct_k_components(k_comps):
+    result = {}
+    max_k = max(k_comps)
+    for k in reversed(range(1, max_k + 1)):
+        if k == max_k:
+            result[k] = list(_consolidate(k_comps[k], k))
+        elif k not in k_comps:
+            result[k] = list(_consolidate(result[k + 1], k))
+        else:
+            nodes_at_k = set.union(*k_comps[k])
+            to_add = [c for c in result[k + 1] if any(n not in nodes_at_k for n in c)]
+            if to_add:
+                result[k] = list(_consolidate(k_comps[k] + to_add, k))
+            else:
+                result[k] = list(_consolidate(k_comps[k], k))
+    return result
+
+
+def build_k_number_dict(kcomps):
+    result = {}
+    for k, comps in sorted(kcomps.items(), key=itemgetter(0)):
+        for comp in comps:
+            for node in comp:
+                result[node] = k
+    return result

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/kcutsets.py

@@ -0,0 +1,235 @@
+"""
+Kanevsky all minimum node k cutsets algorithm.
+"""
+
+import copy
+from collections import defaultdict
+from itertools import combinations
+from operator import itemgetter
+
+import networkx as nx
+from networkx.algorithms.flow import (
+    build_residual_network,
+    edmonds_karp,
+    shortest_augmenting_path,
+)
+
+from .utils import build_auxiliary_node_connectivity
+
+default_flow_func = edmonds_karp
+
+
+__all__ = ["all_node_cuts"]
+
+
+@nx._dispatchable
+def all_node_cuts(G, k=None, flow_func=None):
+    r"""Returns all minimum k cutsets of an undirected graph G.
+
+    This implementation is based on Kanevsky's algorithm [1]_ for finding all
+    minimum-size node cut-sets of an undirected graph G; ie the set (or sets)
+    of nodes of cardinality equal to the node connectivity of G. Thus if
+    removed, would break G into two or more connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Undirected graph
+
+    k : Integer
+        Node connectivity of the input graph. If k is None, then it is
+        computed. Default value: None.
+
+    flow_func : function
+        Function to perform the underlying flow computations. Default value is
+        :func:`~networkx.algorithms.flow.edmonds_karp`. This function performs
+        better in sparse graphs with right tailed degree distributions.
+        :func:`~networkx.algorithms.flow.shortest_augmenting_path` will
+        perform better in denser graphs.
+
+
+    Returns
+    -------
+    cuts : a generator of node cutsets
+        Each node cutset has cardinality equal to the node connectivity of
+        the input graph.
+
+    Examples
+    --------
+    >>> # A two-dimensional grid graph has 4 cutsets of cardinality 2
+    >>> G = nx.grid_2d_graph(5, 5)
+    >>> cutsets = list(nx.all_node_cuts(G))
+    >>> len(cutsets)
+    4
+    >>> all(2 == len(cutset) for cutset in cutsets)
+    True
+    >>> nx.node_connectivity(G)
+    2
+
+    Notes
+    -----
+    This implementation is based on the sequential algorithm for finding all
+    minimum-size separating vertex sets in a graph [1]_. The main idea is to
+    compute minimum cuts using local maximum flow computations among a set
+    of nodes of highest degree and all other non-adjacent nodes in the Graph.
+    Once we find a minimum cut, we add an edge between the high degree
+    node and the target node of the local maximum flow computation to make
+    sure that we will not find that minimum cut again.
+
+    See also
+    --------
+    node_connectivity
+    edmonds_karp
+    shortest_augmenting_path
+
+    References
+    ----------
+    .. [1]  Kanevsky, A. (1993). Finding all minimum-size separating vertex
+            sets in a graph. Networks 23(6), 533--541.
+            http://onlinelibrary.wiley.com/doi/10.1002/net.3230230604/abstract
+
+    """
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("Input graph is disconnected.")
+
+    # Address some corner cases first.
+    # For complete Graphs
+
+    if nx.density(G) == 1:
+        yield from ()
+        return
+
+    # Initialize data structures.
+    # Keep track of the cuts already computed so we do not repeat them.
+    seen = []
+    # Even-Tarjan reduction is what we call auxiliary digraph
+    # for node connectivity.
+    H = build_auxiliary_node_connectivity(G)
+    H_nodes = H.nodes  # for speed
+    mapping = H.graph["mapping"]
+    # Keep a copy of original predecessors, H will be modified later.
+    # Shallow copy is enough.
+    original_H_pred = copy.copy(H._pred)
+    R = build_residual_network(H, "capacity")
+    kwargs = {"capacity": "capacity", "residual": R}
+    # Define default flow function
+    if flow_func is None:
+        flow_func = default_flow_func
+    if flow_func is shortest_augmenting_path:
+        kwargs["two_phase"] = True
+    # Begin the actual algorithm
+    # step 1: Find node connectivity k of G
+    if k is None:
+        k = nx.node_connectivity(G, flow_func=flow_func)
+    # step 2:
+    # Find k nodes with top degree, call it X:
+    X = {n for n, d in sorted(G.degree(), key=itemgetter(1), reverse=True)[:k]}
+    # Check if X is a k-node-cutset
+    if _is_separating_set(G, X):
+        seen.append(X)
+        yield X
+
+    for x in X:
+        # step 3: Compute local connectivity flow of x with all other
+        # non adjacent nodes in G
+        non_adjacent = set(G) - {x} - set(G[x])
+        for v in non_adjacent:
+            # step 4: compute maximum flow in an Even-Tarjan reduction H of G
+            # and step 5: build the associated residual network R
+            R = flow_func(H, f"{mapping[x]}B", f"{mapping[v]}A", **kwargs)
+            flow_value = R.graph["flow_value"]
+
+            if flow_value == k:
+                # Find the nodes incident to the flow.
+                E1 = flowed_edges = [
+                    (u, w) for (u, w, d) in R.edges(data=True) if d["flow"] != 0
+                ]
+                VE1 = incident_nodes = {n for edge in E1 for n in edge}
+                # Remove saturated edges form the residual network.
+                # Note that reversed edges are introduced with capacity 0
+                # in the residual graph and they need to be removed too.
+                saturated_edges = [
+                    (u, w, d)
+                    for (u, w, d) in R.edges(data=True)
+                    if d["capacity"] == d["flow"] or d["capacity"] == 0
+                ]
+                R.remove_edges_from(saturated_edges)
+                R_closure = nx.transitive_closure(R)
+                # step 6: shrink the strongly connected components of
+                # residual flow network R and call it L.
+                L = nx.condensation(R)
+                cmap = L.graph["mapping"]
+                inv_cmap = defaultdict(list)
+                for n, scc in cmap.items():
+                    inv_cmap[scc].append(n)
+                # Find the incident nodes in the condensed graph.
+                VE1 = {cmap[n] for n in VE1}
+                # step 7: Compute all antichains of L;
+                # they map to closed sets in H.
+                # Any edge in H that links a closed set is part of a cutset.
+                for antichain in nx.antichains(L):
+                    # Only antichains that are subsets of incident nodes counts.
+                    # Lemma 8 in reference.
+                    if not set(antichain).issubset(VE1):
+                        continue
+                    # Nodes in an antichain of the condensation graph of
+                    # the residual network map to a closed set of nodes that
+                    # define a node partition of the auxiliary digraph H
+                    # through taking all of antichain's predecessors in the
+                    # transitive closure.
+                    S = set()
+                    for scc in antichain:
+                        S.update(inv_cmap[scc])
+                    S_ancestors = set()
+                    for n in S:
+                        S_ancestors.update(R_closure._pred[n])
+                    S.update(S_ancestors)
+                    if f"{mapping[x]}B" not in S or f"{mapping[v]}A" in S:
+                        continue
+                    # Find the cutset that links the node partition (S,~S) in H
+                    cutset = set()
+                    for u in S:
+                        cutset.update((u, w) for w in original_H_pred[u] if w not in S)
+                    # The edges in H that form the cutset are internal edges
+                    # (ie edges that represent a node of the original graph G)
+                    if any(H_nodes[u]["id"] != H_nodes[w]["id"] for u, w in cutset):
+                        continue
+                    node_cut = {H_nodes[u]["id"] for u, _ in cutset}
+
+                    if len(node_cut) == k:
+                        # The cut is invalid if it includes internal edges of
+                        # end nodes. The other half of Lemma 8 in ref.
+                        if x in node_cut or v in node_cut:
+                            continue
+                        if node_cut not in seen:
+                            yield node_cut
+                            seen.append(node_cut)
+
+                # Add an edge (x, v) to make sure that we do not
+                # find this cutset again. This is equivalent
+                # of adding the edge in the input graph
+                # G.add_edge(x, v) and then regenerate H and R:
+                # Add edges to the auxiliary digraph.
+                # See build_residual_network for convention we used
+                # in residual graphs.
+                H.add_edge(f"{mapping[x]}B", f"{mapping[v]}A", capacity=1)
+                H.add_edge(f"{mapping[v]}B", f"{mapping[x]}A", capacity=1)
+                # Add edges to the residual network.
+                R.add_edge(f"{mapping[x]}B", f"{mapping[v]}A", capacity=1)
+                R.add_edge(f"{mapping[v]}A", f"{mapping[x]}B", capacity=0)
+                R.add_edge(f"{mapping[v]}B", f"{mapping[x]}A", capacity=1)
+                R.add_edge(f"{mapping[x]}A", f"{mapping[v]}B", capacity=0)
+
+                # Add again the saturated edges to reuse the residual network
+                R.add_edges_from(saturated_edges)
+
+
+def _is_separating_set(G, cut):
+    """Assumes that the input graph is connected"""
+    if len(cut) == len(G) - 1:
+        return True
+
+    H = nx.restricted_view(G, cut, [])
+    if nx.is_connected(H):
+        return False
+    return True

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/stoerwagner.py

@@ -0,0 +1,152 @@
+"""
+Stoer-Wagner minimum cut algorithm.
+"""
+
+from itertools import islice
+
+import networkx as nx
+
+from ...utils import BinaryHeap, arbitrary_element, not_implemented_for
+
+__all__ = ["stoer_wagner"]
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(edge_attrs="weight")
+def stoer_wagner(G, weight="weight", heap=BinaryHeap):
+    r"""Returns the weighted minimum edge cut using the Stoer-Wagner algorithm.
+
+    Determine the minimum edge cut of a connected graph using the
+    Stoer-Wagner algorithm. In weighted cases, all weights must be
+    nonnegative.
+
+    The running time of the algorithm depends on the type of heaps used:
+
+    ============== =============================================
+    Type of heap   Running time
+    ============== =============================================
+    Binary heap    $O(n (m + n) \log n)$
+    Fibonacci heap $O(nm + n^2 \log n)$
+    Pairing heap   $O(2^{2 \sqrt{\log \log n}} nm + n^2 \log n)$
+    ============== =============================================
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        Edges of the graph are expected to have an attribute named by the
+        weight parameter below. If this attribute is not present, the edge is
+        considered to have unit weight.
+
+    weight : string
+        Name of the weight attribute of the edges. If the attribute is not
+        present, unit weight is assumed. Default value: 'weight'.
+
+    heap : class
+        Type of heap to be used in the algorithm. It should be a subclass of
+        :class:`MinHeap` or implement a compatible interface.
+
+        If a stock heap implementation is to be used, :class:`BinaryHeap` is
+        recommended over :class:`PairingHeap` for Python implementations without
+        optimized attribute accesses (e.g., CPython) despite a slower
+        asymptotic running time. For Python implementations with optimized
+        attribute accesses (e.g., PyPy), :class:`PairingHeap` provides better
+        performance. Default value: :class:`BinaryHeap`.
+
+    Returns
+    -------
+    cut_value : integer or float
+        The sum of weights of edges in a minimum cut.
+
+    partition : pair of node lists
+        A partitioning of the nodes that defines a minimum cut.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the graph is directed or a multigraph.
+
+    NetworkXError
+        If the graph has less than two nodes, is not connected or has a
+        negative-weighted edge.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> G.add_edge("x", "a", weight=3)
+    >>> G.add_edge("x", "b", weight=1)
+    >>> G.add_edge("a", "c", weight=3)
+    >>> G.add_edge("b", "c", weight=5)
+    >>> G.add_edge("b", "d", weight=4)
+    >>> G.add_edge("d", "e", weight=2)
+    >>> G.add_edge("c", "y", weight=2)
+    >>> G.add_edge("e", "y", weight=3)
+    >>> cut_value, partition = nx.stoer_wagner(G)
+    >>> cut_value
+    4
+    """
+    n = len(G)
+    if n < 2:
+        raise nx.NetworkXError("graph has less than two nodes.")
+    if not nx.is_connected(G):
+        raise nx.NetworkXError("graph is not connected.")
+
+    # Make a copy of the graph for internal use.
+    G = nx.Graph(
+        (u, v, {"weight": e.get(weight, 1)}) for u, v, e in G.edges(data=True) if u != v
+    )
+    G.__networkx_cache__ = None  # Disable caching
+
+    for u, v, e in G.edges(data=True):
+        if e["weight"] < 0:
+            raise nx.NetworkXError("graph has a negative-weighted edge.")
+
+    cut_value = float("inf")
+    nodes = set(G)
+    contractions = []  # contracted node pairs
+
+    # Repeatedly pick a pair of nodes to contract until only one node is left.
+    for i in range(n - 1):
+        # Pick an arbitrary node u and create a set A = {u}.
+        u = arbitrary_element(G)
+        A = {u}
+        # Repeatedly pick the node "most tightly connected" to A and add it to
+        # A. The tightness of connectivity of a node not in A is defined by the
+        # of edges connecting it to nodes in A.
+        h = heap()  # min-heap emulating a max-heap
+        for v, e in G[u].items():
+            h.insert(v, -e["weight"])
+        # Repeat until all but one node has been added to A.
+        for j in range(n - i - 2):
+            u = h.pop()[0]
+            A.add(u)
+            for v, e in G[u].items():
+                if v not in A:
+                    h.insert(v, h.get(v, 0) - e["weight"])
+        # A and the remaining node v define a "cut of the phase". There is a
+        # minimum cut of the original graph that is also a cut of the phase.
+        # Due to contractions in earlier phases, v may in fact represent
+        # multiple nodes in the original graph.
+        v, w = h.min()
+        w = -w
+        if w < cut_value:
+            cut_value = w
+            best_phase = i
+        # Contract v and the last node added to A.
+        contractions.append((u, v))
+        for w, e in G[v].items():
+            if w != u:
+                if w not in G[u]:
+                    G.add_edge(u, w, weight=e["weight"])
+                else:
+                    G[u][w]["weight"] += e["weight"]
+        G.remove_node(v)
+
+    # Recover the optimal partitioning from the contractions.
+    G = nx.Graph(islice(contractions, best_phase))
+    v = contractions[best_phase][1]
+    G.add_node(v)
+    reachable = set(nx.single_source_shortest_path_length(G, v))
+    partition = (list(reachable), list(nodes - reachable))
+
+    return cut_value, partition

evalkit_tf446/lib/python3.10/site-packages/networkx/algorithms/connectivity/utils.py

@@ -0,0 +1,88 @@
+"""
+Utilities for connectivity package
+"""
+
+import networkx as nx
+
+__all__ = ["build_auxiliary_node_connectivity", "build_auxiliary_edge_connectivity"]
+
+
+@nx._dispatchable(returns_graph=True)
+def build_auxiliary_node_connectivity(G):
+    r"""Creates a directed graph D from an undirected graph G to compute flow
+    based node connectivity.
+
+    For an undirected graph G having `n` nodes and `m` edges we derive a
+    directed graph D with `2n` nodes and `2m+n` arcs by replacing each
+    original node `v` with two nodes `vA`, `vB` linked by an (internal)
+    arc in D. Then for each edge (`u`, `v`) in G we add two arcs (`uB`, `vA`)
+    and (`vB`, `uA`) in D. Finally we set the attribute capacity = 1 for each
+    arc in D [1]_.
+
+    For a directed graph having `n` nodes and `m` arcs we derive a
+    directed graph D with `2n` nodes and `m+n` arcs by replacing each
+    original node `v` with two nodes `vA`, `vB` linked by an (internal)
+    arc (`vA`, `vB`) in D. Then for each arc (`u`, `v`) in G we add one
+    arc (`uB`, `vA`) in D. Finally we set the attribute capacity = 1 for
+    each arc in D.
+
+    A dictionary with a mapping between nodes in the original graph and the
+    auxiliary digraph is stored as a graph attribute: D.graph['mapping'].
+
+    References
+    ----------
+    .. [1] Kammer, Frank and Hanjo Taubig. Graph Connectivity. in Brandes and
+        Erlebach, 'Network Analysis: Methodological Foundations', Lecture
+        Notes in Computer Science, Volume 3418, Springer-Verlag, 2005.
+        https://doi.org/10.1007/978-3-540-31955-9_7
+
+    """
+    directed = G.is_directed()
+
+    mapping = {}
+    H = nx.DiGraph()
+
+    for i, node in enumerate(G):
+        mapping[node] = i
+        H.add_node(f"{i}A", id=node)
+        H.add_node(f"{i}B", id=node)
+        H.add_edge(f"{i}A", f"{i}B", capacity=1)
+
+    edges = []
+    for source, target in G.edges():
+        edges.append((f"{mapping[source]}B", f"{mapping[target]}A"))
+        if not directed:
+            edges.append((f"{mapping[target]}B", f"{mapping[source]}A"))
+    H.add_edges_from(edges, capacity=1)
+
+    # Store mapping as graph attribute
+    H.graph["mapping"] = mapping
+    return H
+
+
+@nx._dispatchable(returns_graph=True)
+def build_auxiliary_edge_connectivity(G):
+    """Auxiliary digraph for computing flow based edge connectivity
+
+    If the input graph is undirected, we replace each edge (`u`,`v`) with
+    two reciprocal arcs (`u`, `v`) and (`v`, `u`) and then we set the attribute
+    'capacity' for each arc to 1. If the input graph is directed we simply
+    add the 'capacity' attribute. Part of algorithm 1 in [1]_ .
+
+    References
+    ----------
+    .. [1] Abdol-Hossein Esfahanian. Connectivity Algorithms. (this is a
+        chapter, look for the reference of the book).
+        http://www.cse.msu.edu/~cse835/Papers/Graph_connectivity_revised.pdf
+    """
+    if G.is_directed():
+        H = nx.DiGraph()
+        H.add_nodes_from(G.nodes())
+        H.add_edges_from(G.edges(), capacity=1)
+        return H
+    else:
+        H = nx.DiGraph()
+        H.add_nodes_from(G.nodes())
+        for source, target in G.edges():
+            H.add_edges_from([(source, target), (target, source)], capacity=1)
+        return H

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/atlas.dat.gz

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:73fc416df0164923607751cb759f4ae81deb5f6550bf25be59c86de3b747e41d
+size 8887

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/classic.py

@@ -0,0 +1,1068 @@
+"""Generators for some classic graphs.
+
+The typical graph builder function is called as follows:
+
+>>> G = nx.complete_graph(100)
+
+returning the complete graph on n nodes labeled 0, .., 99
+as a simple graph. Except for `empty_graph`, all the functions
+in this module return a Graph class (i.e. a simple, undirected graph).
+
+"""
+
+import itertools
+import numbers
+
+import networkx as nx
+from networkx.classes import Graph
+from networkx.exception import NetworkXError
+from networkx.utils import nodes_or_number, pairwise
+
+__all__ = [
+    "balanced_tree",
+    "barbell_graph",
+    "binomial_tree",
+    "complete_graph",
+    "complete_multipartite_graph",
+    "circular_ladder_graph",
+    "circulant_graph",
+    "cycle_graph",
+    "dorogovtsev_goltsev_mendes_graph",
+    "empty_graph",
+    "full_rary_tree",
+    "kneser_graph",
+    "ladder_graph",
+    "lollipop_graph",
+    "null_graph",
+    "path_graph",
+    "star_graph",
+    "tadpole_graph",
+    "trivial_graph",
+    "turan_graph",
+    "wheel_graph",
+]
+
+
+# -------------------------------------------------------------------
+#   Some Classic Graphs
+# -------------------------------------------------------------------
+
+
+def _tree_edges(n, r):
+    if n == 0:
+        return
+    # helper function for trees
+    # yields edges in rooted tree at 0 with n nodes and branching ratio r
+    nodes = iter(range(n))
+    parents = [next(nodes)]  # stack of max length r
+    while parents:
+        source = parents.pop(0)
+        for i in range(r):
+            try:
+                target = next(nodes)
+                parents.append(target)
+                yield source, target
+            except StopIteration:
+                break
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def full_rary_tree(r, n, create_using=None):
+    """Creates a full r-ary tree of `n` nodes.
+
+    Sometimes called a k-ary, n-ary, or m-ary tree.
+    "... all non-leaf nodes have exactly r children and all levels
+    are full except for some rightmost position of the bottom level
+    (if a leaf at the bottom level is missing, then so are all of the
+    leaves to its right." [1]_
+
+    .. plot::
+
+        >>> nx.draw(nx.full_rary_tree(2, 10))
+
+    Parameters
+    ----------
+    r : int
+        branching factor of the tree
+    n : int
+        Number of nodes in the tree
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    G : networkx Graph
+        An r-ary tree with n nodes
+
+    References
+    ----------
+    .. [1] An introduction to data structures and algorithms,
+           James Andrew Storer,  Birkhauser Boston 2001, (page 225).
+    """
+    G = empty_graph(n, create_using)
+    G.add_edges_from(_tree_edges(n, r))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def kneser_graph(n, k):
+    """Returns the Kneser Graph with parameters `n` and `k`.
+
+    The Kneser Graph has nodes that are k-tuples (subsets) of the integers
+    between 0 and ``n-1``. Nodes are adjacent if their corresponding sets are disjoint.
+
+    Parameters
+    ----------
+    n: int
+        Number of integers from which to make node subsets.
+        Subsets are drawn from ``set(range(n))``.
+    k: int
+        Size of the subsets.
+
+    Returns
+    -------
+    G : NetworkX Graph
+
+    Examples
+    --------
+    >>> G = nx.kneser_graph(5, 2)
+    >>> G.number_of_nodes()
+    10
+    >>> G.number_of_edges()
+    15
+    >>> nx.is_isomorphic(G, nx.petersen_graph())
+    True
+    """
+    if n <= 0:
+        raise NetworkXError("n should be greater than zero")
+    if k <= 0 or k > n:
+        raise NetworkXError("k should be greater than zero and smaller than n")
+
+    G = nx.Graph()
+    # Create all k-subsets of [0, 1, ..., n-1]
+    subsets = list(itertools.combinations(range(n), k))
+
+    if 2 * k > n:
+        G.add_nodes_from(subsets)
+
+    universe = set(range(n))
+    comb = itertools.combinations  # only to make it all fit on one line
+    G.add_edges_from((s, t) for s in subsets for t in comb(universe - set(s), k))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def balanced_tree(r, h, create_using=None):
+    """Returns the perfectly balanced `r`-ary tree of height `h`.
+
+    .. plot::
+
+        >>> nx.draw(nx.balanced_tree(2, 3))
+
+    Parameters
+    ----------
+    r : int
+        Branching factor of the tree; each node will have `r`
+        children.
+
+    h : int
+        Height of the tree.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    G : NetworkX graph
+        A balanced `r`-ary tree of height `h`.
+
+    Notes
+    -----
+    This is the rooted tree where all leaves are at distance `h` from
+    the root. The root has degree `r` and all other internal nodes
+    have degree `r + 1`.
+
+    Node labels are integers, starting from zero.
+
+    A balanced tree is also known as a *complete r-ary tree*.
+
+    """
+    # The number of nodes in the balanced tree is `1 + r + ... + r^h`,
+    # which is computed by using the closed-form formula for a geometric
+    # sum with ratio `r`. In the special case that `r` is 1, the number
+    # of nodes is simply `h + 1` (since the tree is actually a path
+    # graph).
+    if r == 1:
+        n = h + 1
+    else:
+        # This must be an integer if both `r` and `h` are integers. If
+        # they are not, we force integer division anyway.
+        n = (1 - r ** (h + 1)) // (1 - r)
+    return full_rary_tree(r, n, create_using=create_using)
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def barbell_graph(m1, m2, create_using=None):
+    """Returns the Barbell Graph: two complete graphs connected by a path.
+
+    .. plot::
+
+        >>> nx.draw(nx.barbell_graph(4, 2))
+
+    Parameters
+    ----------
+    m1 : int
+        Size of the left and right barbells, must be greater than 2.
+
+    m2 : int
+        Length of the path connecting the barbells.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+       Only undirected Graphs are supported.
+
+    Returns
+    -------
+    G : NetworkX graph
+        A barbell graph.
+
+    Notes
+    -----
+
+
+    Two identical complete graphs $K_{m1}$ form the left and right bells,
+    and are connected by a path $P_{m2}$.
+
+    The `2*m1+m2`  nodes are numbered
+        `0, ..., m1-1` for the left barbell,
+        `m1, ..., m1+m2-1` for the path,
+        and `m1+m2, ..., 2*m1+m2-1` for the right barbell.
+
+    The 3 subgraphs are joined via the edges `(m1-1, m1)` and
+    `(m1+m2-1, m1+m2)`. If `m2=0`, this is merely two complete
+    graphs joined together.
+
+    This graph is an extremal example in David Aldous
+    and Jim Fill's e-text on Random Walks on Graphs.
+
+    """
+    if m1 < 2:
+        raise NetworkXError("Invalid graph description, m1 should be >=2")
+    if m2 < 0:
+        raise NetworkXError("Invalid graph description, m2 should be >=0")
+
+    # left barbell
+    G = complete_graph(m1, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    # connecting path
+    G.add_nodes_from(range(m1, m1 + m2 - 1))
+    if m2 > 1:
+        G.add_edges_from(pairwise(range(m1, m1 + m2)))
+
+    # right barbell
+    G.add_edges_from(
+        (u, v) for u in range(m1 + m2, 2 * m1 + m2) for v in range(u + 1, 2 * m1 + m2)
+    )
+
+    # connect it up
+    G.add_edge(m1 - 1, m1)
+    if m2 > 0:
+        G.add_edge(m1 + m2 - 1, m1 + m2)
+
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def binomial_tree(n, create_using=None):
+    """Returns the Binomial Tree of order n.
+
+    The binomial tree of order 0 consists of a single node. A binomial tree of order k
+    is defined recursively by linking two binomial trees of order k-1: the root of one is
+    the leftmost child of the root of the other.
+
+    .. plot::
+
+        >>> nx.draw(nx.binomial_tree(3))
+
+    Parameters
+    ----------
+    n : int
+        Order of the binomial tree.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    G : NetworkX graph
+        A binomial tree of $2^n$ nodes and $2^n - 1$ edges.
+
+    """
+    G = nx.empty_graph(1, create_using)
+
+    N = 1
+    for i in range(n):
+        # Use G.edges() to ensure 2-tuples. G.edges is 3-tuple for MultiGraph
+        edges = [(u + N, v + N) for (u, v) in G.edges()]
+        G.add_edges_from(edges)
+        G.add_edge(0, N)
+        N *= 2
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def complete_graph(n, create_using=None):
+    """Return the complete graph `K_n` with n nodes.
+
+    A complete graph on `n` nodes means that all pairs
+    of distinct nodes have an edge connecting them.
+
+    .. plot::
+
+        >>> nx.draw(nx.complete_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable container of nodes
+        If n is an integer, nodes are from range(n).
+        If n is a container of nodes, those nodes appear in the graph.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Examples
+    --------
+    >>> G = nx.complete_graph(9)
+    >>> len(G)
+    9
+    >>> G.size()
+    36
+    >>> G = nx.complete_graph(range(11, 14))
+    >>> list(G.nodes())
+    [11, 12, 13]
+    >>> G = nx.complete_graph(4, nx.DiGraph())
+    >>> G.is_directed()
+    True
+
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    if len(nodes) > 1:
+        if G.is_directed():
+            edges = itertools.permutations(nodes, 2)
+        else:
+            edges = itertools.combinations(nodes, 2)
+        G.add_edges_from(edges)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def circular_ladder_graph(n, create_using=None):
+    """Returns the circular ladder graph $CL_n$ of length n.
+
+    $CL_n$ consists of two concentric n-cycles in which
+    each of the n pairs of concentric nodes are joined by an edge.
+
+    Node labels are the integers 0 to n-1
+
+    .. plot::
+
+        >>> nx.draw(nx.circular_ladder_graph(5))
+
+    """
+    G = ladder_graph(n, create_using)
+    G.add_edge(0, n - 1)
+    G.add_edge(n, 2 * n - 1)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def circulant_graph(n, offsets, create_using=None):
+    r"""Returns the circulant graph $Ci_n(x_1, x_2, ..., x_m)$ with $n$ nodes.
+
+    The circulant graph $Ci_n(x_1, ..., x_m)$ consists of $n$ nodes $0, ..., n-1$
+    such that node $i$ is connected to nodes $(i + x) \mod n$ and $(i - x) \mod n$
+    for all $x$ in $x_1, ..., x_m$. Thus $Ci_n(1)$ is a cycle graph.
+
+    .. plot::
+
+        >>> nx.draw(nx.circulant_graph(10, [1]))
+
+    Parameters
+    ----------
+    n : integer
+        The number of nodes in the graph.
+    offsets : list of integers
+        A list of node offsets, $x_1$ up to $x_m$, as described above.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    NetworkX Graph of type create_using
+
+    Examples
+    --------
+    Many well-known graph families are subfamilies of the circulant graphs;
+    for example, to create the cycle graph on n points, we connect every
+    node to nodes on either side (with offset plus or minus one). For n = 10,
+
+    >>> G = nx.circulant_graph(10, [1])
+    >>> edges = [
+    ...     (0, 9),
+    ...     (0, 1),
+    ...     (1, 2),
+    ...     (2, 3),
+    ...     (3, 4),
+    ...     (4, 5),
+    ...     (5, 6),
+    ...     (6, 7),
+    ...     (7, 8),
+    ...     (8, 9),
+    ... ]
+    >>> sorted(edges) == sorted(G.edges())
+    True
+
+    Similarly, we can create the complete graph
+    on 5 points with the set of offsets [1, 2]:
+
+    >>> G = nx.circulant_graph(5, [1, 2])
+    >>> edges = [
+    ...     (0, 1),
+    ...     (0, 2),
+    ...     (0, 3),
+    ...     (0, 4),
+    ...     (1, 2),
+    ...     (1, 3),
+    ...     (1, 4),
+    ...     (2, 3),
+    ...     (2, 4),
+    ...     (3, 4),
+    ... ]
+    >>> sorted(edges) == sorted(G.edges())
+    True
+
+    """
+    G = empty_graph(n, create_using)
+    for i in range(n):
+        for j in offsets:
+            G.add_edge(i, (i - j) % n)
+            G.add_edge(i, (i + j) % n)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def cycle_graph(n, create_using=None):
+    """Returns the cycle graph $C_n$ of cyclically connected nodes.
+
+    $C_n$ is a path with its two end-nodes connected.
+
+    .. plot::
+
+        >>> nx.draw(nx.cycle_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable container of nodes
+        If n is an integer, nodes are from `range(n)`.
+        If n is a container of nodes, those nodes appear in the graph.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Notes
+    -----
+    If create_using is directed, the direction is in increasing order.
+
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    G.add_edges_from(pairwise(nodes, cyclic=True))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def dorogovtsev_goltsev_mendes_graph(n, create_using=None):
+    """Returns the hierarchically constructed Dorogovtsev--Goltsev--Mendes graph.
+
+    The Dorogovtsev--Goltsev--Mendes [1]_ procedure deterministically produces a
+    scale-free graph with ``3/2 * (3**(n-1) + 1)`` nodes
+    and ``3**n`` edges for a given `n`.
+
+    Note that `n` denotes the number of times the state transition is applied,
+    starting from the base graph with ``n = 0`` (no transitions), as in [2]_.
+    This is different from the parameter ``t = n - 1`` in [1]_.
+
+    .. plot::
+
+        >>> nx.draw(nx.dorogovtsev_goltsev_mendes_graph(3))
+
+    Parameters
+    ----------
+    n : integer
+        The generation number.
+
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+        Graph type to create. Directed graphs and multigraphs are not supported.
+
+    Returns
+    -------
+    G : NetworkX `Graph`
+
+    Raises
+    ------
+    NetworkXError
+        If `n` is less than zero.
+
+        If `create_using` is a directed graph or multigraph.
+
+    Examples
+    --------
+    >>> G = nx.dorogovtsev_goltsev_mendes_graph(3)
+    >>> G.number_of_nodes()
+    15
+    >>> G.number_of_edges()
+    27
+    >>> nx.is_planar(G)
+    True
+
+    References
+    ----------
+    .. [1] S. N. Dorogovtsev, A. V. Goltsev and J. F. F. Mendes,
+        "Pseudofractal scale-free web", Physical Review E 65, 066122, 2002.
+        https://arxiv.org/pdf/cond-mat/0112143.pdf
+    .. [2] Weisstein, Eric W. "Dorogovtsev--Goltsev--Mendes Graph".
+        From MathWorld--A Wolfram Web Resource.
+        https://mathworld.wolfram.com/Dorogovtsev-Goltsev-MendesGraph.html
+    """
+    if n < 0:
+        raise NetworkXError("n must be greater than or equal to 0")
+
+    G = empty_graph(0, create_using)
+    if G.is_directed():
+        raise NetworkXError("directed graph not supported")
+    if G.is_multigraph():
+        raise NetworkXError("multigraph not supported")
+
+    G.add_edge(0, 1)
+    new_node = 2  # next node to be added
+    for _ in range(n):  # iterate over number of generations.
+        new_edges = []
+        for u, v in G.edges():
+            new_edges.append((u, new_node))
+            new_edges.append((v, new_node))
+            new_node += 1
+
+        G.add_edges_from(new_edges)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def empty_graph(n=0, create_using=None, default=Graph):
+    """Returns the empty graph with n nodes and zero edges.
+
+    .. plot::
+
+        >>> nx.draw(nx.empty_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable container of nodes (default = 0)
+        If n is an integer, nodes are from `range(n)`.
+        If n is a container of nodes, those nodes appear in the graph.
+    create_using : Graph Instance, Constructor or None
+        Indicator of type of graph to return.
+        If a Graph-type instance, then clear and use it.
+        If None, use the `default` constructor.
+        If a constructor, call it to create an empty graph.
+    default : Graph constructor (optional, default = nx.Graph)
+        The constructor to use if create_using is None.
+        If None, then nx.Graph is used.
+        This is used when passing an unknown `create_using` value
+        through your home-grown function to `empty_graph` and
+        you want a default constructor other than nx.Graph.
+
+    Examples
+    --------
+    >>> G = nx.empty_graph(10)
+    >>> G.number_of_nodes()
+    10
+    >>> G.number_of_edges()
+    0
+    >>> G = nx.empty_graph("ABC")
+    >>> G.number_of_nodes()
+    3
+    >>> sorted(G)
+    ['A', 'B', 'C']
+
+    Notes
+    -----
+    The variable create_using should be a Graph Constructor or a
+    "graph"-like object. Constructors, e.g. `nx.Graph` or `nx.MultiGraph`
+    will be used to create the returned graph. "graph"-like objects
+    will be cleared (nodes and edges will be removed) and refitted as
+    an empty "graph" with nodes specified in n. This capability
+    is useful for specifying the class-nature of the resulting empty
+    "graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.).
+
+    The variable create_using has three main uses:
+    Firstly, the variable create_using can be used to create an
+    empty digraph, multigraph, etc.  For example,
+
+    >>> n = 10
+    >>> G = nx.empty_graph(n, create_using=nx.DiGraph)
+
+    will create an empty digraph on n nodes.
+
+    Secondly, one can pass an existing graph (digraph, multigraph,
+    etc.) via create_using. For example, if G is an existing graph
+    (resp. digraph, multigraph, etc.), then empty_graph(n, create_using=G)
+    will empty G (i.e. delete all nodes and edges using G.clear())
+    and then add n nodes and zero edges, and return the modified graph.
+
+    Thirdly, when constructing your home-grown graph creation function
+    you can use empty_graph to construct the graph by passing a user
+    defined create_using to empty_graph. In this case, if you want the
+    default constructor to be other than nx.Graph, specify `default`.
+
+    >>> def mygraph(n, create_using=None):
+    ...     G = nx.empty_graph(n, create_using, nx.MultiGraph)
+    ...     G.add_edges_from([(0, 1), (0, 1)])
+    ...     return G
+    >>> G = mygraph(3)
+    >>> G.is_multigraph()
+    True
+    >>> G = mygraph(3, nx.Graph)
+    >>> G.is_multigraph()
+    False
+
+    See also create_empty_copy(G).
+
+    """
+    if create_using is None:
+        G = default()
+    elif isinstance(create_using, type):
+        G = create_using()
+    elif not hasattr(create_using, "adj"):
+        raise TypeError("create_using is not a valid NetworkX graph type or instance")
+    else:
+        # create_using is a NetworkX style Graph
+        create_using.clear()
+        G = create_using
+
+    _, nodes = n
+    G.add_nodes_from(nodes)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def ladder_graph(n, create_using=None):
+    """Returns the Ladder graph of length n.
+
+    This is two paths of n nodes, with
+    each pair connected by a single edge.
+
+    Node labels are the integers 0 to 2*n - 1.
+
+    .. plot::
+
+        >>> nx.draw(nx.ladder_graph(5))
+
+    """
+    G = empty_graph(2 * n, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+    G.add_edges_from(pairwise(range(n)))
+    G.add_edges_from(pairwise(range(n, 2 * n)))
+    G.add_edges_from((v, v + n) for v in range(n))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number([0, 1])
+def lollipop_graph(m, n, create_using=None):
+    """Returns the Lollipop Graph; ``K_m`` connected to ``P_n``.
+
+    This is the Barbell Graph without the right barbell.
+
+    .. plot::
+
+        >>> nx.draw(nx.lollipop_graph(3, 4))
+
+    Parameters
+    ----------
+    m, n : int or iterable container of nodes
+        If an integer, nodes are from ``range(m)`` and ``range(m, m+n)``.
+        If a container of nodes, those nodes appear in the graph.
+        Warning: `m` and `n` are not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+
+        The nodes for `m` appear in the complete graph $K_m$ and the nodes
+        for `n` appear in the path $P_n$
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    Networkx graph
+       A complete graph with `m` nodes connected to a path of length `n`.
+
+    Notes
+    -----
+    The 2 subgraphs are joined via an edge ``(m-1, m)``.
+    If ``n=0``, this is merely a complete graph.
+
+    (This graph is an extremal example in David Aldous and Jim
+    Fill's etext on Random Walks on Graphs.)
+
+    """
+    m, m_nodes = m
+    M = len(m_nodes)
+    if M < 2:
+        raise NetworkXError("Invalid description: m should indicate at least 2 nodes")
+
+    n, n_nodes = n
+    if isinstance(m, numbers.Integral) and isinstance(n, numbers.Integral):
+        n_nodes = list(range(M, M + n))
+    N = len(n_nodes)
+
+    # the ball
+    G = complete_graph(m_nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    # the stick
+    G.add_nodes_from(n_nodes)
+    if N > 1:
+        G.add_edges_from(pairwise(n_nodes))
+
+    if len(G) != M + N:
+        raise NetworkXError("Nodes must be distinct in containers m and n")
+
+    # connect ball to stick
+    if M > 0 and N > 0:
+        G.add_edge(m_nodes[-1], n_nodes[0])
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def null_graph(create_using=None):
+    """Returns the Null graph with no nodes or edges.
+
+    See empty_graph for the use of create_using.
+
+    """
+    G = empty_graph(0, create_using)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def path_graph(n, create_using=None):
+    """Returns the Path graph `P_n` of linearly connected nodes.
+
+    .. plot::
+
+        >>> nx.draw(nx.path_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable
+        If an integer, nodes are 0 to n - 1.
+        If an iterable of nodes, in the order they appear in the path.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    G.add_edges_from(pairwise(nodes))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def star_graph(n, create_using=None):
+    """Return the star graph
+
+    The star graph consists of one center node connected to n outer nodes.
+
+    .. plot::
+
+        >>> nx.draw(nx.star_graph(6))
+
+    Parameters
+    ----------
+    n : int or iterable
+        If an integer, node labels are 0 to n with center 0.
+        If an iterable of nodes, the center is the first.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Notes
+    -----
+    The graph has n+1 nodes for integer n.
+    So star_graph(3) is the same as star_graph(range(4)).
+    """
+    n, nodes = n
+    if isinstance(n, numbers.Integral):
+        nodes.append(int(n))  # there should be n+1 nodes
+    G = empty_graph(nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    if len(nodes) > 1:
+        hub, *spokes = nodes
+        G.add_edges_from((hub, node) for node in spokes)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number([0, 1])
+def tadpole_graph(m, n, create_using=None):
+    """Returns the (m,n)-tadpole graph; ``C_m`` connected to ``P_n``.
+
+    This graph on m+n nodes connects a cycle of size `m` to a path of length `n`.
+    It looks like a tadpole. It is also called a kite graph or a dragon graph.
+
+    .. plot::
+
+        >>> nx.draw(nx.tadpole_graph(3, 5))
+
+    Parameters
+    ----------
+    m, n : int or iterable container of nodes
+        If an integer, nodes are from ``range(m)`` and ``range(m,m+n)``.
+        If a container of nodes, those nodes appear in the graph.
+        Warning: `m` and `n` are not checked for duplicates and if present the
+        resulting graph may not be as desired.
+
+        The nodes for `m` appear in the cycle graph $C_m$ and the nodes
+        for `n` appear in the path $P_n$.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Returns
+    -------
+    Networkx graph
+       A cycle of size `m` connected to a path of length `n`.
+
+    Raises
+    ------
+    NetworkXError
+        If ``m < 2``. The tadpole graph is undefined for ``m<2``.
+
+    Notes
+    -----
+    The 2 subgraphs are joined via an edge ``(m-1, m)``.
+    If ``n=0``, this is a cycle graph.
+    `m` and/or `n` can be a container of nodes instead of an integer.
+
+    """
+    m, m_nodes = m
+    M = len(m_nodes)
+    if M < 2:
+        raise NetworkXError("Invalid description: m should indicate at least 2 nodes")
+
+    n, n_nodes = n
+    if isinstance(m, numbers.Integral) and isinstance(n, numbers.Integral):
+        n_nodes = list(range(M, M + n))
+
+    # the circle
+    G = cycle_graph(m_nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    # the stick
+    nx.add_path(G, [m_nodes[-1]] + list(n_nodes))
+
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def trivial_graph(create_using=None):
+    """Return the Trivial graph with one node (with label 0) and no edges.
+
+    .. plot::
+
+        >>> nx.draw(nx.trivial_graph(), with_labels=True)
+
+    """
+    G = empty_graph(1, create_using)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def turan_graph(n, r):
+    r"""Return the Turan Graph
+
+    The Turan Graph is a complete multipartite graph on $n$ nodes
+    with $r$ disjoint subsets. That is, edges connect each node to
+    every node not in its subset.
+
+    Given $n$ and $r$, we create a complete multipartite graph with
+    $r-(n \mod r)$ partitions of size $n/r$, rounded down, and
+    $n \mod r$ partitions of size $n/r+1$, rounded down.
+
+    .. plot::
+
+        >>> nx.draw(nx.turan_graph(6, 2))
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes.
+    r : int
+        The number of partitions.
+        Must be less than or equal to n.
+
+    Notes
+    -----
+    Must satisfy $1 <= r <= n$.
+    The graph has $(r-1)(n^2)/(2r)$ edges, rounded down.
+    """
+
+    if not 1 <= r <= n:
+        raise NetworkXError("Must satisfy 1 <= r <= n")
+
+    partitions = [n // r] * (r - (n % r)) + [n // r + 1] * (n % r)
+    G = complete_multipartite_graph(*partitions)
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+@nodes_or_number(0)
+def wheel_graph(n, create_using=None):
+    """Return the wheel graph
+
+    The wheel graph consists of a hub node connected to a cycle of (n-1) nodes.
+
+    .. plot::
+
+        >>> nx.draw(nx.wheel_graph(5))
+
+    Parameters
+    ----------
+    n : int or iterable
+        If an integer, node labels are 0 to n with center 0.
+        If an iterable of nodes, the center is the first.
+        Warning: n is not checked for duplicates and if present the
+        resulting graph may not be as desired. Make sure you have no duplicates.
+    create_using : NetworkX graph constructor, optional (default=nx.Graph)
+       Graph type to create. If graph instance, then cleared before populated.
+
+    Node labels are the integers 0 to n - 1.
+    """
+    _, nodes = n
+    G = empty_graph(nodes, create_using)
+    if G.is_directed():
+        raise NetworkXError("Directed Graph not supported")
+
+    if len(nodes) > 1:
+        hub, *rim = nodes
+        G.add_edges_from((hub, node) for node in rim)
+        if len(rim) > 1:
+            G.add_edges_from(pairwise(rim, cyclic=True))
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def complete_multipartite_graph(*subset_sizes):
+    """Returns the complete multipartite graph with the specified subset sizes.
+
+    .. plot::
+
+        >>> nx.draw(nx.complete_multipartite_graph(1, 2, 3))
+
+    Parameters
+    ----------
+    subset_sizes : tuple of integers or tuple of node iterables
+       The arguments can either all be integer number of nodes or they
+       can all be iterables of nodes. If integers, they represent the
+       number of nodes in each subset of the multipartite graph.
+       If iterables, each is used to create the nodes for that subset.
+       The length of subset_sizes is the number of subsets.
+
+    Returns
+    -------
+    G : NetworkX Graph
+       Returns the complete multipartite graph with the specified subsets.
+
+       For each node, the node attribute 'subset' is an integer
+       indicating which subset contains the node.
+
+    Examples
+    --------
+    Creating a complete tripartite graph, with subsets of one, two, and three
+    nodes, respectively.
+
+        >>> G = nx.complete_multipartite_graph(1, 2, 3)
+        >>> [G.nodes[u]["subset"] for u in G]
+        [0, 1, 1, 2, 2, 2]
+        >>> list(G.edges(0))
+        [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5)]
+        >>> list(G.edges(2))
+        [(2, 0), (2, 3), (2, 4), (2, 5)]
+        >>> list(G.edges(4))
+        [(4, 0), (4, 1), (4, 2)]
+
+        >>> G = nx.complete_multipartite_graph("a", "bc", "def")
+        >>> [G.nodes[u]["subset"] for u in sorted(G)]
+        [0, 1, 1, 2, 2, 2]
+
+    Notes
+    -----
+    This function generalizes several other graph builder functions.
+
+    - If no subset sizes are given, this returns the null graph.
+    - If a single subset size `n` is given, this returns the empty graph on
+      `n` nodes.
+    - If two subset sizes `m` and `n` are given, this returns the complete
+      bipartite graph on `m + n` nodes.
+    - If subset sizes `1` and `n` are given, this returns the star graph on
+      `n + 1` nodes.
+
+    See also
+    --------
+    complete_bipartite_graph
+    """
+    # The complete multipartite graph is an undirected simple graph.
+    G = Graph()
+
+    if len(subset_sizes) == 0:
+        return G
+
+    # set up subsets of nodes
+    try:
+        extents = pairwise(itertools.accumulate((0,) + subset_sizes))
+        subsets = [range(start, end) for start, end in extents]
+    except TypeError:
+        subsets = subset_sizes
+    else:
+        if any(size < 0 for size in subset_sizes):
+            raise NetworkXError(f"Negative number of nodes not valid: {subset_sizes}")
+
+    # add nodes with subset attribute
+    # while checking that ints are not mixed with iterables
+    try:
+        for i, subset in enumerate(subsets):
+            G.add_nodes_from(subset, subset=i)
+    except TypeError as err:
+        raise NetworkXError("Arguments must be all ints or all iterables") from err
+
+    # Across subsets, all nodes should be adjacent.
+    # We can use itertools.combinations() because undirected.
+    for subset1, subset2 in itertools.combinations(subsets, 2):
+        G.add_edges_from(itertools.product(subset1, subset2))
+    return G

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/directed.py

@@ -0,0 +1,501 @@
+"""
+Generators for some directed graphs, including growing network (GN) graphs and
+scale-free graphs.
+
+"""
+
+import numbers
+from collections import Counter
+
+import networkx as nx
+from networkx.generators.classic import empty_graph
+from networkx.utils import discrete_sequence, py_random_state, weighted_choice
+
+__all__ = [
+    "gn_graph",
+    "gnc_graph",
+    "gnr_graph",
+    "random_k_out_graph",
+    "scale_free_graph",
+]
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def gn_graph(n, kernel=None, create_using=None, seed=None):
+    """Returns the growing network (GN) digraph with `n` nodes.
+
+    The GN graph is built by adding nodes one at a time with a link to one
+    previously added node.  The target node for the link is chosen with
+    probability based on degree.  The default attachment kernel is a linear
+    function of the degree of a node.
+
+    The graph is always a (directed) tree.
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes for the generated graph.
+    kernel : function
+        The attachment kernel.
+    create_using : NetworkX graph constructor, optional (default DiGraph)
+        Graph type to create. If graph instance, then cleared before populated.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Examples
+    --------
+    To create the undirected GN graph, use the :meth:`~DiGraph.to_directed`
+    method::
+
+    >>> D = nx.gn_graph(10)  # the GN graph
+    >>> G = D.to_undirected()  # the undirected version
+
+    To specify an attachment kernel, use the `kernel` keyword argument::
+
+    >>> D = nx.gn_graph(10, kernel=lambda x: x**1.5)  # A_k = k^1.5
+
+    References
+    ----------
+    .. [1] P. L. Krapivsky and S. Redner,
+           Organization of Growing Random Networks,
+           Phys. Rev. E, 63, 066123, 2001.
+    """
+    G = empty_graph(1, create_using, default=nx.DiGraph)
+    if not G.is_directed():
+        raise nx.NetworkXError("create_using must indicate a Directed Graph")
+
+    if kernel is None:
+
+        def kernel(x):
+            return x
+
+    if n == 1:
+        return G
+
+    G.add_edge(1, 0)  # get started
+    ds = [1, 1]  # degree sequence
+
+    for source in range(2, n):
+        # compute distribution from kernel and degree
+        dist = [kernel(d) for d in ds]
+        # choose target from discrete distribution
+        target = discrete_sequence(1, distribution=dist, seed=seed)[0]
+        G.add_edge(source, target)
+        ds.append(1)  # the source has only one link (degree one)
+        ds[target] += 1  # add one to the target link degree
+    return G
+
+
+@py_random_state(3)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def gnr_graph(n, p, create_using=None, seed=None):
+    """Returns the growing network with redirection (GNR) digraph with `n`
+    nodes and redirection probability `p`.
+
+    The GNR graph is built by adding nodes one at a time with a link to one
+    previously added node.  The previous target node is chosen uniformly at
+    random.  With probability `p` the link is instead "redirected" to the
+    successor node of the target.
+
+    The graph is always a (directed) tree.
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes for the generated graph.
+    p : float
+        The redirection probability.
+    create_using : NetworkX graph constructor, optional (default DiGraph)
+        Graph type to create. If graph instance, then cleared before populated.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Examples
+    --------
+    To create the undirected GNR graph, use the :meth:`~DiGraph.to_directed`
+    method::
+
+    >>> D = nx.gnr_graph(10, 0.5)  # the GNR graph
+    >>> G = D.to_undirected()  # the undirected version
+
+    References
+    ----------
+    .. [1] P. L. Krapivsky and S. Redner,
+           Organization of Growing Random Networks,
+           Phys. Rev. E, 63, 066123, 2001.
+    """
+    G = empty_graph(1, create_using, default=nx.DiGraph)
+    if not G.is_directed():
+        raise nx.NetworkXError("create_using must indicate a Directed Graph")
+
+    if n == 1:
+        return G
+
+    for source in range(1, n):
+        target = seed.randrange(0, source)
+        if seed.random() < p and target != 0:
+            target = next(G.successors(target))
+        G.add_edge(source, target)
+    return G
+
+
+@py_random_state(2)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def gnc_graph(n, create_using=None, seed=None):
+    """Returns the growing network with copying (GNC) digraph with `n` nodes.
+
+    The GNC graph is built by adding nodes one at a time with a link to one
+    previously added node (chosen uniformly at random) and to all of that
+    node's successors.
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes for the generated graph.
+    create_using : NetworkX graph constructor, optional (default DiGraph)
+        Graph type to create. If graph instance, then cleared before populated.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    References
+    ----------
+    .. [1] P. L. Krapivsky and S. Redner,
+           Network Growth by Copying,
+           Phys. Rev. E, 71, 036118, 2005k.},
+    """
+    G = empty_graph(1, create_using, default=nx.DiGraph)
+    if not G.is_directed():
+        raise nx.NetworkXError("create_using must indicate a Directed Graph")
+
+    if n == 1:
+        return G
+
+    for source in range(1, n):
+        target = seed.randrange(0, source)
+        for succ in G.successors(target):
+            G.add_edge(source, succ)
+        G.add_edge(source, target)
+    return G
+
+
+@py_random_state(6)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def scale_free_graph(
+    n,
+    alpha=0.41,
+    beta=0.54,
+    gamma=0.05,
+    delta_in=0.2,
+    delta_out=0,
+    seed=None,
+    initial_graph=None,
+):
+    """Returns a scale-free directed graph.
+
+    Parameters
+    ----------
+    n : integer
+        Number of nodes in graph
+    alpha : float
+        Probability for adding a new node connected to an existing node
+        chosen randomly according to the in-degree distribution.
+    beta : float
+        Probability for adding an edge between two existing nodes.
+        One existing node is chosen randomly according the in-degree
+        distribution and the other chosen randomly according to the out-degree
+        distribution.
+    gamma : float
+        Probability for adding a new node connected to an existing node
+        chosen randomly according to the out-degree distribution.
+    delta_in : float
+        Bias for choosing nodes from in-degree distribution.
+    delta_out : float
+        Bias for choosing nodes from out-degree distribution.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    initial_graph : MultiDiGraph instance, optional
+        Build the scale-free graph starting from this initial MultiDiGraph,
+        if provided.
+
+    Returns
+    -------
+    MultiDiGraph
+
+    Examples
+    --------
+    Create a scale-free graph on one hundred nodes::
+
+    >>> G = nx.scale_free_graph(100)
+
+    Notes
+    -----
+    The sum of `alpha`, `beta`, and `gamma` must be 1.
+
+    References
+    ----------
+    .. [1] B. Bollobás, C. Borgs, J. Chayes, and O. Riordan,
+           Directed scale-free graphs,
+           Proceedings of the fourteenth annual ACM-SIAM Symposium on
+           Discrete Algorithms, 132--139, 2003.
+    """
+
+    def _choose_node(candidates, node_list, delta):
+        if delta > 0:
+            bias_sum = len(node_list) * delta
+            p_delta = bias_sum / (bias_sum + len(candidates))
+            if seed.random() < p_delta:
+                return seed.choice(node_list)
+        return seed.choice(candidates)
+
+    if initial_graph is not None and hasattr(initial_graph, "_adj"):
+        if not isinstance(initial_graph, nx.MultiDiGraph):
+            raise nx.NetworkXError("initial_graph must be a MultiDiGraph.")
+        G = initial_graph
+    else:
+        # Start with 3-cycle
+        G = nx.MultiDiGraph([(0, 1), (1, 2), (2, 0)])
+
+    if alpha <= 0:
+        raise ValueError("alpha must be > 0.")
+    if beta <= 0:
+        raise ValueError("beta must be > 0.")
+    if gamma <= 0:
+        raise ValueError("gamma must be > 0.")
+
+    if abs(alpha + beta + gamma - 1.0) >= 1e-9:
+        raise ValueError("alpha+beta+gamma must equal 1.")
+
+    if delta_in < 0:
+        raise ValueError("delta_in must be >= 0.")
+
+    if delta_out < 0:
+        raise ValueError("delta_out must be >= 0.")
+
+    # pre-populate degree states
+    vs = sum((count * [idx] for idx, count in G.out_degree()), [])
+    ws = sum((count * [idx] for idx, count in G.in_degree()), [])
+
+    # pre-populate node state
+    node_list = list(G.nodes())
+
+    # see if there already are number-based nodes
+    numeric_nodes = [n for n in node_list if isinstance(n, numbers.Number)]
+    if len(numeric_nodes) > 0:
+        # set cursor for new nodes appropriately
+        cursor = max(int(n.real) for n in numeric_nodes) + 1
+    else:
+        # or start at zero
+        cursor = 0
+
+    while len(G) < n:
+        r = seed.random()
+
+        # random choice in alpha,beta,gamma ranges
+        if r < alpha:
+            # alpha
+            # add new node v
+            v = cursor
+            cursor += 1
+            # also add to node state
+            node_list.append(v)
+            # choose w according to in-degree and delta_in
+            w = _choose_node(ws, node_list, delta_in)
+
+        elif r < alpha + beta:
+            # beta
+            # choose v according to out-degree and delta_out
+            v = _choose_node(vs, node_list, delta_out)
+            # choose w according to in-degree and delta_in
+            w = _choose_node(ws, node_list, delta_in)
+
+        else:
+            # gamma
+            # choose v according to out-degree and delta_out
+            v = _choose_node(vs, node_list, delta_out)
+            # add new node w
+            w = cursor
+            cursor += 1
+            # also add to node state
+            node_list.append(w)
+
+        # add edge to graph
+        G.add_edge(v, w)
+
+        # update degree states
+        vs.append(v)
+        ws.append(w)
+
+    return G
+
+
+@py_random_state(4)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def random_uniform_k_out_graph(n, k, self_loops=True, with_replacement=True, seed=None):
+    """Returns a random `k`-out graph with uniform attachment.
+
+    A random `k`-out graph with uniform attachment is a multidigraph
+    generated by the following algorithm. For each node *u*, choose
+    `k` nodes *v* uniformly at random (with replacement). Add a
+    directed edge joining *u* to *v*.
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes in the returned graph.
+
+    k : int
+        The out-degree of each node in the returned graph.
+
+    self_loops : bool
+        If True, self-loops are allowed when generating the graph.
+
+    with_replacement : bool
+        If True, neighbors are chosen with replacement and the
+        returned graph will be a directed multigraph. Otherwise,
+        neighbors are chosen without replacement and the returned graph
+        will be a directed graph.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    NetworkX graph
+        A `k`-out-regular directed graph generated according to the
+        above algorithm. It will be a multigraph if and only if
+        `with_replacement` is True.
+
+    Raises
+    ------
+    ValueError
+        If `with_replacement` is False and `k` is greater than
+        `n`.
+
+    See also
+    --------
+    random_k_out_graph
+
+    Notes
+    -----
+    The return digraph or multidigraph may not be strongly connected, or
+    even weakly connected.
+
+    If `with_replacement` is True, this function is similar to
+    :func:`random_k_out_graph`, if that function had parameter `alpha`
+    set to positive infinity.
+
+    """
+    if with_replacement:
+        create_using = nx.MultiDiGraph()
+
+        def sample(v, nodes):
+            if not self_loops:
+                nodes = nodes - {v}
+            return (seed.choice(list(nodes)) for i in range(k))
+
+    else:
+        create_using = nx.DiGraph()
+
+        def sample(v, nodes):
+            if not self_loops:
+                nodes = nodes - {v}
+            return seed.sample(list(nodes), k)
+
+    G = nx.empty_graph(n, create_using)
+    nodes = set(G)
+    for u in G:
+        G.add_edges_from((u, v) for v in sample(u, nodes))
+    return G
+
+
+@py_random_state(4)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def random_k_out_graph(n, k, alpha, self_loops=True, seed=None):
+    """Returns a random `k`-out graph with preferential attachment.
+
+    A random `k`-out graph with preferential attachment is a
+    multidigraph generated by the following algorithm.
+
+    1. Begin with an empty digraph, and initially set each node to have
+       weight `alpha`.
+    2. Choose a node `u` with out-degree less than `k` uniformly at
+       random.
+    3. Choose a node `v` from with probability proportional to its
+       weight.
+    4. Add a directed edge from `u` to `v`, and increase the weight
+       of `v` by one.
+    5. If each node has out-degree `k`, halt, otherwise repeat from
+       step 2.
+
+    For more information on this model of random graph, see [1].
+
+    Parameters
+    ----------
+    n : int
+        The number of nodes in the returned graph.
+
+    k : int
+        The out-degree of each node in the returned graph.
+
+    alpha : float
+        A positive :class:`float` representing the initial weight of
+        each vertex. A higher number means that in step 3 above, nodes
+        will be chosen more like a true uniformly random sample, and a
+        lower number means that nodes are more likely to be chosen as
+        their in-degree increases. If this parameter is not positive, a
+        :exc:`ValueError` is raised.
+
+    self_loops : bool
+        If True, self-loops are allowed when generating the graph.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    :class:`~networkx.classes.MultiDiGraph`
+        A `k`-out-regular multidigraph generated according to the above
+        algorithm.
+
+    Raises
+    ------
+    ValueError
+        If `alpha` is not positive.
+
+    Notes
+    -----
+    The returned multidigraph may not be strongly connected, or even
+    weakly connected.
+
+    References
+    ----------
+    [1]: Peterson, Nicholas R., and Boris Pittel.
+         "Distance between two random `k`-out digraphs, with and without
+         preferential attachment."
+         arXiv preprint arXiv:1311.5961 (2013).
+         <https://arxiv.org/abs/1311.5961>
+
+    """
+    if alpha < 0:
+        raise ValueError("alpha must be positive")
+    G = nx.empty_graph(n, create_using=nx.MultiDiGraph)
+    weights = Counter({v: alpha for v in G})
+    for i in range(k * n):
+        u = seed.choice([v for v, d in G.out_degree() if d < k])
+        # If self-loops are not allowed, make the source node `u` have
+        # weight zero.
+        if not self_loops:
+            adjustment = Counter({u: weights[u]})
+        else:
+            adjustment = Counter()
+        v = weighted_choice(weights - adjustment, seed=seed)
+        G.add_edge(u, v)
+        weights[v] += 1
+    return G

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/duplication.py

@@ -0,0 +1,174 @@
+"""Functions for generating graphs based on the "duplication" method.
+
+These graph generators start with a small initial graph then duplicate
+nodes and (partially) duplicate their edges. These functions are
+generally inspired by biological networks.
+
+"""
+
+import networkx as nx
+from networkx.exception import NetworkXError
+from networkx.utils import py_random_state
+from networkx.utils.misc import check_create_using
+
+__all__ = ["partial_duplication_graph", "duplication_divergence_graph"]
+
+
+@py_random_state(4)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def partial_duplication_graph(N, n, p, q, seed=None, *, create_using=None):
+    """Returns a random graph using the partial duplication model.
+
+    Parameters
+    ----------
+    N : int
+        The total number of nodes in the final graph.
+
+    n : int
+        The number of nodes in the initial clique.
+
+    p : float
+        The probability of joining each neighbor of a node to the
+        duplicate node. Must be a number in the between zero and one,
+        inclusive.
+
+    q : float
+        The probability of joining the source node to the duplicate
+        node. Must be a number in the between zero and one, inclusive.
+
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    create_using : Graph constructor, optional (default=nx.Graph)
+        Graph type to create. If graph instance, then cleared before populated.
+        Multigraph and directed types are not supported and raise a ``NetworkXError``.
+
+    Notes
+    -----
+    A graph of nodes is grown by creating a fully connected graph
+    of size `n`. The following procedure is then repeated until
+    a total of `N` nodes have been reached.
+
+    1. A random node, *u*, is picked and a new node, *v*, is created.
+    2. For each neighbor of *u* an edge from the neighbor to *v* is created
+       with probability `p`.
+    3. An edge from *u* to *v* is created with probability `q`.
+
+    This algorithm appears in [1].
+
+    This implementation allows the possibility of generating
+    disconnected graphs.
+
+    References
+    ----------
+    .. [1] Knudsen Michael, and Carsten Wiuf. "A Markov chain approach to
+           randomly grown graphs." Journal of Applied Mathematics 2008.
+           <https://doi.org/10.1155/2008/190836>
+
+    """
+    create_using = check_create_using(create_using, directed=False, multigraph=False)
+    if p < 0 or p > 1 or q < 0 or q > 1:
+        msg = "partial duplication graph must have 0 <= p, q <= 1."
+        raise NetworkXError(msg)
+    if n > N:
+        raise NetworkXError("partial duplication graph must have n <= N.")
+
+    G = nx.complete_graph(n, create_using)
+    for new_node in range(n, N):
+        # Pick a random vertex, u, already in the graph.
+        src_node = seed.randint(0, new_node - 1)
+
+        # Add a new vertex, v, to the graph.
+        G.add_node(new_node)
+
+        # For each neighbor of u...
+        for nbr_node in list(nx.all_neighbors(G, src_node)):
+            # Add the neighbor to v with probability p.
+            if seed.random() < p:
+                G.add_edge(new_node, nbr_node)
+
+        # Join v and u with probability q.
+        if seed.random() < q:
+            G.add_edge(new_node, src_node)
+    return G
+
+
+@py_random_state(2)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def duplication_divergence_graph(n, p, seed=None, *, create_using=None):
+    """Returns an undirected graph using the duplication-divergence model.
+
+    A graph of `n` nodes is created by duplicating the initial nodes
+    and retaining edges incident to the original nodes with a retention
+    probability `p`.
+
+    Parameters
+    ----------
+    n : int
+        The desired number of nodes in the graph.
+    p : float
+        The probability for retaining the edge of the replicated node.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+    create_using : Graph constructor, optional (default=nx.Graph)
+        Graph type to create. If graph instance, then cleared before populated.
+        Multigraph and directed types are not supported and raise a ``NetworkXError``.
+
+    Returns
+    -------
+    G : Graph
+
+    Raises
+    ------
+    NetworkXError
+        If `p` is not a valid probability.
+        If `n` is less than 2.
+
+    Notes
+    -----
+    This algorithm appears in [1].
+
+    This implementation disallows the possibility of generating
+    disconnected graphs.
+
+    References
+    ----------
+    .. [1] I. Ispolatov, P. L. Krapivsky, A. Yuryev,
+       "Duplication-divergence model of protein interaction network",
+       Phys. Rev. E, 71, 061911, 2005.
+
+    """
+    if p > 1 or p < 0:
+        msg = f"NetworkXError p={p} is not in [0,1]."
+        raise nx.NetworkXError(msg)
+    if n < 2:
+        msg = "n must be greater than or equal to 2"
+        raise nx.NetworkXError(msg)
+
+    create_using = check_create_using(create_using, directed=False, multigraph=False)
+    G = nx.empty_graph(create_using=create_using)
+
+    # Initialize the graph with two connected nodes.
+    G.add_edge(0, 1)
+    i = 2
+    while i < n:
+        # Choose a random node from current graph to duplicate.
+        random_node = seed.choice(list(G))
+        # Make the replica.
+        G.add_node(i)
+        # flag indicates whether at least one edge is connected on the replica.
+        flag = False
+        for nbr in G.neighbors(random_node):
+            if seed.random() < p:
+                # Link retention step.
+                G.add_edge(i, nbr)
+                flag = True
+        if not flag:
+            # Delete replica if no edges retained.
+            G.remove_node(i)
+        else:
+            # Successful duplication.
+            i += 1
+    return G

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/harary_graph.py

@@ -0,0 +1,199 @@
+"""Generators for Harary graphs
+
+This module gives two generators for the Harary graph, which was
+introduced by the famous mathematician Frank Harary in his 1962 work [H]_.
+The first generator gives the Harary graph that maximizes the node
+connectivity with given number of nodes and given number of edges.
+The second generator gives the Harary graph that minimizes
+the number of edges in the graph with given node connectivity and
+number of nodes.
+
+References
+----------
+.. [H] Harary, F. "The Maximum Connectivity of a Graph."
+       Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.
+
+"""
+
+import networkx as nx
+from networkx.exception import NetworkXError
+
+__all__ = ["hnm_harary_graph", "hkn_harary_graph"]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def hnm_harary_graph(n, m, create_using=None):
+    """Returns the Harary graph with given numbers of nodes and edges.
+
+    The Harary graph $H_{n,m}$ is the graph that maximizes node connectivity
+    with $n$ nodes and $m$ edges.
+
+    This maximum node connectivity is known to be floor($2m/n$). [1]_
+
+    Parameters
+    ----------
+    n: integer
+       The number of nodes the generated graph is to contain
+
+    m: integer
+       The number of edges the generated graph is to contain
+
+    create_using : NetworkX graph constructor, optional Graph type
+     to create (default=nx.Graph). If graph instance, then cleared
+     before populated.
+
+    Returns
+    -------
+    NetworkX graph
+        The Harary graph $H_{n,m}$.
+
+    See Also
+    --------
+    hkn_harary_graph
+
+    Notes
+    -----
+    This algorithm runs in $O(m)$ time.
+    It is implemented by following the Reference [2]_.
+
+    References
+    ----------
+    .. [1] F. T. Boesch, A. Satyanarayana, and C. L. Suffel,
+       "A Survey of Some Network Reliability Analysis and Synthesis Results,"
+       Networks, pp. 99-107, 2009.
+
+    .. [2] Harary, F. "The Maximum Connectivity of a Graph."
+       Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.
+    """
+
+    if n < 1:
+        raise NetworkXError("The number of nodes must be >= 1!")
+    if m < n - 1:
+        raise NetworkXError("The number of edges must be >= n - 1 !")
+    if m > n * (n - 1) // 2:
+        raise NetworkXError("The number of edges must be <= n(n-1)/2")
+
+    # Construct an empty graph with n nodes first
+    H = nx.empty_graph(n, create_using)
+    # Get the floor of average node degree
+    d = 2 * m // n
+
+    # Test the parity of n and d
+    if (n % 2 == 0) or (d % 2 == 0):
+        # Start with a regular graph of d degrees
+        offset = d // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        if d & 1:
+            # in case d is odd; n must be even in this case
+            half = n // 2
+            for i in range(half):
+                # add edges diagonally
+                H.add_edge(i, i + half)
+        # Get the remainder of 2*m modulo n
+        r = 2 * m % n
+        if r > 0:
+            # add remaining edges at offset+1
+            for i in range(r // 2):
+                H.add_edge(i, i + offset + 1)
+    else:
+        # Start with a regular graph of (d - 1) degrees
+        offset = (d - 1) // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        half = n // 2
+        for i in range(m - n * offset):
+            # add the remaining m - n*offset edges between i and i+half
+            H.add_edge(i, (i + half) % n)
+
+    return H
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def hkn_harary_graph(k, n, create_using=None):
+    """Returns the Harary graph with given node connectivity and node number.
+
+    The Harary graph $H_{k,n}$ is the graph that minimizes the number of
+    edges needed with given node connectivity $k$ and node number $n$.
+
+    This smallest number of edges is known to be ceil($kn/2$) [1]_.
+
+    Parameters
+    ----------
+    k: integer
+       The node connectivity of the generated graph
+
+    n: integer
+       The number of nodes the generated graph is to contain
+
+    create_using : NetworkX graph constructor, optional Graph type
+     to create (default=nx.Graph). If graph instance, then cleared
+     before populated.
+
+    Returns
+    -------
+    NetworkX graph
+        The Harary graph $H_{k,n}$.
+
+    See Also
+    --------
+    hnm_harary_graph
+
+    Notes
+    -----
+    This algorithm runs in $O(kn)$ time.
+    It is implemented by following the Reference [2]_.
+
+    References
+    ----------
+    .. [1] Weisstein, Eric W. "Harary Graph." From MathWorld--A Wolfram Web
+     Resource. http://mathworld.wolfram.com/HararyGraph.html.
+
+    .. [2] Harary, F. "The Maximum Connectivity of a Graph."
+      Proc. Nat. Acad. Sci. USA 48, 1142-1146, 1962.
+    """
+
+    if k < 1:
+        raise NetworkXError("The node connectivity must be >= 1!")
+    if n < k + 1:
+        raise NetworkXError("The number of nodes must be >= k+1 !")
+
+    # in case of connectivity 1, simply return the path graph
+    if k == 1:
+        H = nx.path_graph(n, create_using)
+        return H
+
+    # Construct an empty graph with n nodes first
+    H = nx.empty_graph(n, create_using)
+
+    # Test the parity of k and n
+    if (k % 2 == 0) or (n % 2 == 0):
+        # Construct a regular graph with k degrees
+        offset = k // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        if k & 1:
+            # odd degree; n must be even in this case
+            half = n // 2
+            for i in range(half):
+                # add edges diagonally
+                H.add_edge(i, i + half)
+    else:
+        # Construct a regular graph with (k - 1) degrees
+        offset = (k - 1) // 2
+        for i in range(n):
+            for j in range(1, offset + 1):
+                H.add_edge(i, (i - j) % n)
+                H.add_edge(i, (i + j) % n)
+        half = n // 2
+        for i in range(half + 1):
+            # add half+1 edges between i and i+half
+            H.add_edge(i, (i + half) % n)
+
+    return H

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/interval_graph.py

@@ -0,0 +1,70 @@
+"""
+Generators for interval graph.
+"""
+
+from collections.abc import Sequence
+
+import networkx as nx
+
+__all__ = ["interval_graph"]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def interval_graph(intervals):
+    """Generates an interval graph for a list of intervals given.
+
+    In graph theory, an interval graph is an undirected graph formed from a set
+    of closed intervals on the real line, with a vertex for each interval
+    and an edge between vertices whose intervals intersect.
+    It is the intersection graph of the intervals.
+
+    More information can be found at:
+    https://en.wikipedia.org/wiki/Interval_graph
+
+    Parameters
+    ----------
+    intervals : a sequence of intervals, say (l, r) where l is the left end,
+    and r is the right end of the closed interval.
+
+    Returns
+    -------
+    G : networkx graph
+
+    Examples
+    --------
+    >>> intervals = [(-2, 3), [1, 4], (2, 3), (4, 6)]
+    >>> G = nx.interval_graph(intervals)
+    >>> sorted(G.edges)
+    [((-2, 3), (1, 4)), ((-2, 3), (2, 3)), ((1, 4), (2, 3)), ((1, 4), (4, 6))]
+
+    Raises
+    ------
+    :exc:`TypeError`
+        if `intervals` contains None or an element which is not
+        collections.abc.Sequence or not a length of 2.
+    :exc:`ValueError`
+        if `intervals` contains an interval such that min1 > max1
+        where min1,max1 = interval
+    """
+    intervals = list(intervals)
+    for interval in intervals:
+        if not (isinstance(interval, Sequence) and len(interval) == 2):
+            raise TypeError(
+                "Each interval must have length 2, and be a "
+                "collections.abc.Sequence such as tuple or list."
+            )
+        if interval[0] > interval[1]:
+            raise ValueError(f"Interval must have lower value first. Got {interval}")
+
+    graph = nx.Graph()
+
+    tupled_intervals = [tuple(interval) for interval in intervals]
+    graph.add_nodes_from(tupled_intervals)
+
+    while tupled_intervals:
+        min1, max1 = interval1 = tupled_intervals.pop()
+        for interval2 in tupled_intervals:
+            min2, max2 = interval2
+            if max1 >= min2 and max2 >= min1:
+                graph.add_edge(interval1, interval2)
+    return graph

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/nonisomorphic_trees.py

@@ -0,0 +1,212 @@
+"""
+Implementation of the Wright, Richmond, Odlyzko and McKay (WROM)
+algorithm for the enumeration of all non-isomorphic free trees of a
+given order.  Rooted trees are represented by level sequences, i.e.,
+lists in which the i-th element specifies the distance of vertex i to
+the root.
+
+"""
+
+__all__ = ["nonisomorphic_trees", "number_of_nonisomorphic_trees"]
+
+import networkx as nx
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def nonisomorphic_trees(order, create="graph"):
+    """Generates lists of nonisomorphic trees
+
+    Parameters
+    ----------
+    order : int
+       order of the desired tree(s)
+
+    create : one of {"graph", "matrix"} (default="graph")
+       If ``"graph"`` is selected a list of ``Graph`` instances will be returned,
+       if matrix is selected a list of adjacency matrices will be returned.
+
+       .. deprecated:: 3.3
+
+          The `create` argument is deprecated and will be removed in NetworkX
+          version 3.5. In the future, `nonisomorphic_trees` will yield graph
+          instances by default. To generate adjacency matrices, call
+          ``nx.to_numpy_array`` on the output, e.g.::
+
+             [nx.to_numpy_array(G) for G in nx.nonisomorphic_trees(N)]
+
+    Yields
+    ------
+    list
+       A list of nonisomorphic trees, in one of two formats depending on the
+       value of the `create` parameter:
+       - ``create="graph"``: yields a list of `networkx.Graph` instances
+       - ``create="matrix"``: yields a list of list-of-lists representing adjacency matrices
+    """
+
+    if order < 2:
+        raise ValueError
+    # start at the path graph rooted at its center
+    layout = list(range(order // 2 + 1)) + list(range(1, (order + 1) // 2))
+
+    while layout is not None:
+        layout = _next_tree(layout)
+        if layout is not None:
+            if create == "graph":
+                yield _layout_to_graph(layout)
+            elif create == "matrix":
+                import warnings
+
+                warnings.warn(
+                    (
+                        "\n\nThe 'create=matrix' argument of nonisomorphic_trees\n"
+                        "is deprecated and will be removed in version 3.5.\n"
+                        "Use ``nx.to_numpy_array`` to convert graphs to adjacency "
+                        "matrices, e.g.::\n\n"
+                        "   [nx.to_numpy_array(G) for G in nx.nonisomorphic_trees(N)]"
+                    ),
+                    category=DeprecationWarning,
+                    stacklevel=2,
+                )
+
+                yield _layout_to_matrix(layout)
+            layout = _next_rooted_tree(layout)
+
+
+@nx._dispatchable(graphs=None)
+def number_of_nonisomorphic_trees(order):
+    """Returns the number of nonisomorphic trees
+
+    Parameters
+    ----------
+    order : int
+      order of the desired tree(s)
+
+    Returns
+    -------
+    length : Number of nonisomorphic graphs for the given order
+
+    References
+    ----------
+
+    """
+    return sum(1 for _ in nonisomorphic_trees(order))
+
+
+def _next_rooted_tree(predecessor, p=None):
+    """One iteration of the Beyer-Hedetniemi algorithm."""
+
+    if p is None:
+        p = len(predecessor) - 1
+        while predecessor[p] == 1:
+            p -= 1
+    if p == 0:
+        return None
+
+    q = p - 1
+    while predecessor[q] != predecessor[p] - 1:
+        q -= 1
+    result = list(predecessor)
+    for i in range(p, len(result)):
+        result[i] = result[i - p + q]
+    return result
+
+
+def _next_tree(candidate):
+    """One iteration of the Wright, Richmond, Odlyzko and McKay
+    algorithm."""
+
+    # valid representation of a free tree if:
+    # there are at least two vertices at layer 1
+    # (this is always the case because we start at the path graph)
+    left, rest = _split_tree(candidate)
+
+    # and the left subtree of the root
+    # is less high than the tree with the left subtree removed
+    left_height = max(left)
+    rest_height = max(rest)
+    valid = rest_height >= left_height
+
+    if valid and rest_height == left_height:
+        # and, if left and rest are of the same height,
+        # if left does not encompass more vertices
+        if len(left) > len(rest):
+            valid = False
+        # and, if they have the same number or vertices,
+        # if left does not come after rest lexicographically
+        elif len(left) == len(rest) and left > rest:
+            valid = False
+
+    if valid:
+        return candidate
+    else:
+        # jump to the next valid free tree
+        p = len(left)
+        new_candidate = _next_rooted_tree(candidate, p)
+        if candidate[p] > 2:
+            new_left, new_rest = _split_tree(new_candidate)
+            new_left_height = max(new_left)
+            suffix = range(1, new_left_height + 2)
+            new_candidate[-len(suffix) :] = suffix
+        return new_candidate
+
+
+def _split_tree(layout):
+    """Returns a tuple of two layouts, one containing the left
+    subtree of the root vertex, and one containing the original tree
+    with the left subtree removed."""
+
+    one_found = False
+    m = None
+    for i in range(len(layout)):
+        if layout[i] == 1:
+            if one_found:
+                m = i
+                break
+            else:
+                one_found = True
+
+    if m is None:
+        m = len(layout)
+
+    left = [layout[i] - 1 for i in range(1, m)]
+    rest = [0] + [layout[i] for i in range(m, len(layout))]
+    return (left, rest)
+
+
+def _layout_to_matrix(layout):
+    """Create the adjacency matrix for the tree specified by the
+    given layout (level sequence)."""
+
+    result = [[0] * len(layout) for i in range(len(layout))]
+    stack = []
+    for i in range(len(layout)):
+        i_level = layout[i]
+        if stack:
+            j = stack[-1]
+            j_level = layout[j]
+            while j_level >= i_level:
+                stack.pop()
+                j = stack[-1]
+                j_level = layout[j]
+            result[i][j] = result[j][i] = 1
+        stack.append(i)
+    return result
+
+
+def _layout_to_graph(layout):
+    """Create a NetworkX Graph for the tree specified by the
+    given layout(level sequence)"""
+    G = nx.Graph()
+    stack = []
+    for i in range(len(layout)):
+        i_level = layout[i]
+        if stack:
+            j = stack[-1]
+            j_level = layout[j]
+            while j_level >= i_level:
+                stack.pop()
+                j = stack[-1]
+                j_level = layout[j]
+            G.add_edge(i, j)
+        stack.append(i)
+    return G

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/random_clustered.py

@@ -0,0 +1,117 @@
+"""Generate graphs with given degree and triangle sequence."""
+
+import networkx as nx
+from networkx.utils import py_random_state
+
+__all__ = ["random_clustered_graph"]
+
+
+@py_random_state(2)
+@nx._dispatchable(graphs=None, returns_graph=True)
+def random_clustered_graph(joint_degree_sequence, create_using=None, seed=None):
+    r"""Generate a random graph with the given joint independent edge degree and
+    triangle degree sequence.
+
+    This uses a configuration model-like approach to generate a random graph
+    (with parallel edges and self-loops) by randomly assigning edges to match
+    the given joint degree sequence.
+
+    The joint degree sequence is a list of pairs of integers of the form
+    $[(d_{1,i}, d_{1,t}), \dotsc, (d_{n,i}, d_{n,t})]$. According to this list,
+    vertex $u$ is a member of $d_{u,t}$ triangles and has $d_{u, i}$ other
+    edges. The number $d_{u,t}$ is the *triangle degree* of $u$ and the number
+    $d_{u,i}$ is the *independent edge degree*.
+
+    Parameters
+    ----------
+    joint_degree_sequence : list of integer pairs
+        Each list entry corresponds to the independent edge degree and
+        triangle degree of a node.
+    create_using : NetworkX graph constructor, optional (default MultiGraph)
+       Graph type to create. If graph instance, then cleared before populated.
+    seed : integer, random_state, or None (default)
+        Indicator of random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    G : MultiGraph
+        A graph with the specified degree sequence. Nodes are labeled
+        starting at 0 with an index corresponding to the position in
+        deg_sequence.
+
+    Raises
+    ------
+    NetworkXError
+        If the independent edge degree sequence sum is not even
+        or the triangle degree sequence sum is not divisible by 3.
+
+    Notes
+    -----
+    As described by Miller [1]_ (see also Newman [2]_ for an equivalent
+    description).
+
+    A non-graphical degree sequence (not realizable by some simple
+    graph) is allowed since this function returns graphs with self
+    loops and parallel edges.  An exception is raised if the
+    independent degree sequence does not have an even sum or the
+    triangle degree sequence sum is not divisible by 3.
+
+    This configuration model-like construction process can lead to
+    duplicate edges and loops.  You can remove the self-loops and
+    parallel edges (see below) which will likely result in a graph
+    that doesn't have the exact degree sequence specified.  This
+    "finite-size effect" decreases as the size of the graph increases.
+
+    References
+    ----------
+    .. [1] Joel C. Miller. "Percolation and epidemics in random clustered
+           networks". In: Physical review. E, Statistical, nonlinear, and soft
+           matter physics 80 (2 Part 1 August 2009).
+    .. [2] M. E. J. Newman. "Random Graphs with Clustering".
+           In: Physical Review Letters 103 (5 July 2009)
+
+    Examples
+    --------
+    >>> deg = [(1, 0), (1, 0), (1, 0), (2, 0), (1, 0), (2, 1), (0, 1), (0, 1)]
+    >>> G = nx.random_clustered_graph(deg)
+
+    To remove parallel edges:
+
+    >>> G = nx.Graph(G)
+
+    To remove self loops:
+
+    >>> G.remove_edges_from(nx.selfloop_edges(G))
+
+    """
+    # In Python 3, zip() returns an iterator. Make this into a list.
+    joint_degree_sequence = list(joint_degree_sequence)
+
+    N = len(joint_degree_sequence)
+    G = nx.empty_graph(N, create_using, default=nx.MultiGraph)
+    if G.is_directed():
+        raise nx.NetworkXError("Directed Graph not supported")
+
+    ilist = []
+    tlist = []
+    for n in G:
+        degrees = joint_degree_sequence[n]
+        for icount in range(degrees[0]):
+            ilist.append(n)
+        for tcount in range(degrees[1]):
+            tlist.append(n)
+
+    if len(ilist) % 2 != 0 or len(tlist) % 3 != 0:
+        raise nx.NetworkXError("Invalid degree sequence")
+
+    seed.shuffle(ilist)
+    seed.shuffle(tlist)
+    while ilist:
+        G.add_edge(ilist.pop(), ilist.pop())
+    while tlist:
+        n1 = tlist.pop()
+        n2 = tlist.pop()
+        n3 = tlist.pop()
+        G.add_edges_from([(n1, n2), (n1, n3), (n2, n3)])
+    return G

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/social.py

@@ -0,0 +1,554 @@
+"""
+Famous social networks.
+"""
+
+import networkx as nx
+
+__all__ = [
+    "karate_club_graph",
+    "davis_southern_women_graph",
+    "florentine_families_graph",
+    "les_miserables_graph",
+]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def karate_club_graph():
+    """Returns Zachary's Karate Club graph.
+
+    Each node in the returned graph has a node attribute 'club' that
+    indicates the name of the club to which the member represented by that node
+    belongs, either 'Mr. Hi' or 'Officer'. Each edge has a weight based on the
+    number of contexts in which that edge's incident node members interacted.
+
+    The dataset is derived from the 'Club After Split From Data' column of Table 3 in [1]_.
+    This was in turn derived from the 'Club After Fission' column of Table 1 in the
+    same paper. Note that the nodes are 0-indexed in NetworkX, but 1-indexed in the
+    paper (the 'Individual Number in Matrix C' column of Table 3 starts at 1). This
+    means, for example, that ``G.nodes[9]["club"]`` returns 'Officer', which
+    corresponds to row 10 of Table 3 in the paper.
+
+    Examples
+    --------
+    To get the name of the club to which a node belongs::
+
+        >>> G = nx.karate_club_graph()
+        >>> G.nodes[5]["club"]
+        'Mr. Hi'
+        >>> G.nodes[9]["club"]
+        'Officer'
+
+    References
+    ----------
+    .. [1] Zachary, Wayne W.
+       "An Information Flow Model for Conflict and Fission in Small Groups."
+       *Journal of Anthropological Research*, 33, 452--473, (1977).
+    """
+    # Create the set of all members, and the members of each club.
+    all_members = set(range(34))
+    club1 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 16, 17, 19, 21}
+    # club2 = all_members - club1
+
+    G = nx.Graph()
+    G.add_nodes_from(all_members)
+    G.name = "Zachary's Karate Club"
+
+    zacharydat = """\
+0 4 5 3 3 3 3 2 2 0 2 3 2 3 0 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0
+4 0 6 3 0 0 0 4 0 0 0 0 0 5 0 0 0 1 0 2 0 2 0 0 0 0 0 0 0 0 2 0 0 0
+5 6 0 3 0 0 0 4 5 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 3 0
+3 3 3 0 0 0 0 3 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+3 0 0 0 0 0 2 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+3 0 0 0 0 0 5 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+3 0 0 0 2 5 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+2 4 4 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+2 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 4 3
+0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
+2 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+1 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+3 5 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 2
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 4
+0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2
+2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 1
+2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 4 0 2 0 0 5 4
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 0 0 2 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 0 0 0 0 0 0 7 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 2
+0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3 0 0 0 0 0 0 0 0 4
+0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 4 0 0 0 0 0 3 2
+0 2 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3
+2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 7 0 0 2 0 0 0 4 4
+0 0 2 0 0 0 0 0 3 0 0 0 0 0 3 3 0 0 1 0 3 0 2 5 0 0 0 0 0 4 3 4 0 5
+0 0 0 0 0 0 0 0 4 2 0 0 0 3 2 4 0 0 2 1 1 0 3 4 0 0 2 4 2 2 3 4 5 0"""
+
+    for row, line in enumerate(zacharydat.split("\n")):
+        thisrow = [int(b) for b in line.split()]
+        for col, entry in enumerate(thisrow):
+            if entry >= 1:
+                G.add_edge(row, col, weight=entry)
+
+    # Add the name of each member's club as a node attribute.
+    for v in G:
+        G.nodes[v]["club"] = "Mr. Hi" if v in club1 else "Officer"
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def davis_southern_women_graph():
+    """Returns Davis Southern women social network.
+
+    This is a bipartite graph.
+
+    References
+    ----------
+    .. [1] A. Davis, Gardner, B. B., Gardner, M. R., 1941. Deep South.
+        University of Chicago Press, Chicago, IL.
+    """
+    G = nx.Graph()
+    # Top nodes
+    women = [
+        "Evelyn Jefferson",
+        "Laura Mandeville",
+        "Theresa Anderson",
+        "Brenda Rogers",
+        "Charlotte McDowd",
+        "Frances Anderson",
+        "Eleanor Nye",
+        "Pearl Oglethorpe",
+        "Ruth DeSand",
+        "Verne Sanderson",
+        "Myra Liddel",
+        "Katherina Rogers",
+        "Sylvia Avondale",
+        "Nora Fayette",
+        "Helen Lloyd",
+        "Dorothy Murchison",
+        "Olivia Carleton",
+        "Flora Price",
+    ]
+    G.add_nodes_from(women, bipartite=0)
+    # Bottom nodes
+    events = [
+        "E1",
+        "E2",
+        "E3",
+        "E4",
+        "E5",
+        "E6",
+        "E7",
+        "E8",
+        "E9",
+        "E10",
+        "E11",
+        "E12",
+        "E13",
+        "E14",
+    ]
+    G.add_nodes_from(events, bipartite=1)
+
+    G.add_edges_from(
+        [
+            ("Evelyn Jefferson", "E1"),
+            ("Evelyn Jefferson", "E2"),
+            ("Evelyn Jefferson", "E3"),
+            ("Evelyn Jefferson", "E4"),
+            ("Evelyn Jefferson", "E5"),
+            ("Evelyn Jefferson", "E6"),
+            ("Evelyn Jefferson", "E8"),
+            ("Evelyn Jefferson", "E9"),
+            ("Laura Mandeville", "E1"),
+            ("Laura Mandeville", "E2"),
+            ("Laura Mandeville", "E3"),
+            ("Laura Mandeville", "E5"),
+            ("Laura Mandeville", "E6"),
+            ("Laura Mandeville", "E7"),
+            ("Laura Mandeville", "E8"),
+            ("Theresa Anderson", "E2"),
+            ("Theresa Anderson", "E3"),
+            ("Theresa Anderson", "E4"),
+            ("Theresa Anderson", "E5"),
+            ("Theresa Anderson", "E6"),
+            ("Theresa Anderson", "E7"),
+            ("Theresa Anderson", "E8"),
+            ("Theresa Anderson", "E9"),
+            ("Brenda Rogers", "E1"),
+            ("Brenda Rogers", "E3"),
+            ("Brenda Rogers", "E4"),
+            ("Brenda Rogers", "E5"),
+            ("Brenda Rogers", "E6"),
+            ("Brenda Rogers", "E7"),
+            ("Brenda Rogers", "E8"),
+            ("Charlotte McDowd", "E3"),
+            ("Charlotte McDowd", "E4"),
+            ("Charlotte McDowd", "E5"),
+            ("Charlotte McDowd", "E7"),
+            ("Frances Anderson", "E3"),
+            ("Frances Anderson", "E5"),
+            ("Frances Anderson", "E6"),
+            ("Frances Anderson", "E8"),
+            ("Eleanor Nye", "E5"),
+            ("Eleanor Nye", "E6"),
+            ("Eleanor Nye", "E7"),
+            ("Eleanor Nye", "E8"),
+            ("Pearl Oglethorpe", "E6"),
+            ("Pearl Oglethorpe", "E8"),
+            ("Pearl Oglethorpe", "E9"),
+            ("Ruth DeSand", "E5"),
+            ("Ruth DeSand", "E7"),
+            ("Ruth DeSand", "E8"),
+            ("Ruth DeSand", "E9"),
+            ("Verne Sanderson", "E7"),
+            ("Verne Sanderson", "E8"),
+            ("Verne Sanderson", "E9"),
+            ("Verne Sanderson", "E12"),
+            ("Myra Liddel", "E8"),
+            ("Myra Liddel", "E9"),
+            ("Myra Liddel", "E10"),
+            ("Myra Liddel", "E12"),
+            ("Katherina Rogers", "E8"),
+            ("Katherina Rogers", "E9"),
+            ("Katherina Rogers", "E10"),
+            ("Katherina Rogers", "E12"),
+            ("Katherina Rogers", "E13"),
+            ("Katherina Rogers", "E14"),
+            ("Sylvia Avondale", "E7"),
+            ("Sylvia Avondale", "E8"),
+            ("Sylvia Avondale", "E9"),
+            ("Sylvia Avondale", "E10"),
+            ("Sylvia Avondale", "E12"),
+            ("Sylvia Avondale", "E13"),
+            ("Sylvia Avondale", "E14"),
+            ("Nora Fayette", "E6"),
+            ("Nora Fayette", "E7"),
+            ("Nora Fayette", "E9"),
+            ("Nora Fayette", "E10"),
+            ("Nora Fayette", "E11"),
+            ("Nora Fayette", "E12"),
+            ("Nora Fayette", "E13"),
+            ("Nora Fayette", "E14"),
+            ("Helen Lloyd", "E7"),
+            ("Helen Lloyd", "E8"),
+            ("Helen Lloyd", "E10"),
+            ("Helen Lloyd", "E11"),
+            ("Helen Lloyd", "E12"),
+            ("Dorothy Murchison", "E8"),
+            ("Dorothy Murchison", "E9"),
+            ("Olivia Carleton", "E9"),
+            ("Olivia Carleton", "E11"),
+            ("Flora Price", "E9"),
+            ("Flora Price", "E11"),
+        ]
+    )
+    G.graph["top"] = women
+    G.graph["bottom"] = events
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def florentine_families_graph():
+    """Returns Florentine families graph.
+
+    References
+    ----------
+    .. [1] Ronald L. Breiger and Philippa E. Pattison
+       Cumulated social roles: The duality of persons and their algebras,1
+       Social Networks, Volume 8, Issue 3, September 1986, Pages 215-256
+    """
+    G = nx.Graph()
+    G.add_edge("Acciaiuoli", "Medici")
+    G.add_edge("Castellani", "Peruzzi")
+    G.add_edge("Castellani", "Strozzi")
+    G.add_edge("Castellani", "Barbadori")
+    G.add_edge("Medici", "Barbadori")
+    G.add_edge("Medici", "Ridolfi")
+    G.add_edge("Medici", "Tornabuoni")
+    G.add_edge("Medici", "Albizzi")
+    G.add_edge("Medici", "Salviati")
+    G.add_edge("Salviati", "Pazzi")
+    G.add_edge("Peruzzi", "Strozzi")
+    G.add_edge("Peruzzi", "Bischeri")
+    G.add_edge("Strozzi", "Ridolfi")
+    G.add_edge("Strozzi", "Bischeri")
+    G.add_edge("Ridolfi", "Tornabuoni")
+    G.add_edge("Tornabuoni", "Guadagni")
+    G.add_edge("Albizzi", "Ginori")
+    G.add_edge("Albizzi", "Guadagni")
+    G.add_edge("Bischeri", "Guadagni")
+    G.add_edge("Guadagni", "Lamberteschi")
+    return G
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def les_miserables_graph():
+    """Returns coappearance network of characters in the novel Les Miserables.
+
+    References
+    ----------
+    .. [1] D. E. Knuth, 1993.
+       The Stanford GraphBase: a platform for combinatorial computing,
+       pp. 74-87. New York: AcM Press.
+    """
+    G = nx.Graph()
+    G.add_edge("Napoleon", "Myriel", weight=1)
+    G.add_edge("MlleBaptistine", "Myriel", weight=8)
+    G.add_edge("MmeMagloire", "Myriel", weight=10)
+    G.add_edge("MmeMagloire", "MlleBaptistine", weight=6)
+    G.add_edge("CountessDeLo", "Myriel", weight=1)
+    G.add_edge("Geborand", "Myriel", weight=1)
+    G.add_edge("Champtercier", "Myriel", weight=1)
+    G.add_edge("Cravatte", "Myriel", weight=1)
+    G.add_edge("Count", "Myriel", weight=2)
+    G.add_edge("OldMan", "Myriel", weight=1)
+    G.add_edge("Valjean", "Labarre", weight=1)
+    G.add_edge("Valjean", "MmeMagloire", weight=3)
+    G.add_edge("Valjean", "MlleBaptistine", weight=3)
+    G.add_edge("Valjean", "Myriel", weight=5)
+    G.add_edge("Marguerite", "Valjean", weight=1)
+    G.add_edge("MmeDeR", "Valjean", weight=1)
+    G.add_edge("Isabeau", "Valjean", weight=1)
+    G.add_edge("Gervais", "Valjean", weight=1)
+    G.add_edge("Listolier", "Tholomyes", weight=4)
+    G.add_edge("Fameuil", "Tholomyes", weight=4)
+    G.add_edge("Fameuil", "Listolier", weight=4)
+    G.add_edge("Blacheville", "Tholomyes", weight=4)
+    G.add_edge("Blacheville", "Listolier", weight=4)
+    G.add_edge("Blacheville", "Fameuil", weight=4)
+    G.add_edge("Favourite", "Tholomyes", weight=3)
+    G.add_edge("Favourite", "Listolier", weight=3)
+    G.add_edge("Favourite", "Fameuil", weight=3)
+    G.add_edge("Favourite", "Blacheville", weight=4)
+    G.add_edge("Dahlia", "Tholomyes", weight=3)
+    G.add_edge("Dahlia", "Listolier", weight=3)
+    G.add_edge("Dahlia", "Fameuil", weight=3)
+    G.add_edge("Dahlia", "Blacheville", weight=3)
+    G.add_edge("Dahlia", "Favourite", weight=5)
+    G.add_edge("Zephine", "Tholomyes", weight=3)
+    G.add_edge("Zephine", "Listolier", weight=3)
+    G.add_edge("Zephine", "Fameuil", weight=3)
+    G.add_edge("Zephine", "Blacheville", weight=3)
+    G.add_edge("Zephine", "Favourite", weight=4)
+    G.add_edge("Zephine", "Dahlia", weight=4)
+    G.add_edge("Fantine", "Tholomyes", weight=3)
+    G.add_edge("Fantine", "Listolier", weight=3)
+    G.add_edge("Fantine", "Fameuil", weight=3)
+    G.add_edge("Fantine", "Blacheville", weight=3)
+    G.add_edge("Fantine", "Favourite", weight=4)
+    G.add_edge("Fantine", "Dahlia", weight=4)
+    G.add_edge("Fantine", "Zephine", weight=4)
+    G.add_edge("Fantine", "Marguerite", weight=2)
+    G.add_edge("Fantine", "Valjean", weight=9)
+    G.add_edge("MmeThenardier", "Fantine", weight=2)
+    G.add_edge("MmeThenardier", "Valjean", weight=7)
+    G.add_edge("Thenardier", "MmeThenardier", weight=13)
+    G.add_edge("Thenardier", "Fantine", weight=1)
+    G.add_edge("Thenardier", "Valjean", weight=12)
+    G.add_edge("Cosette", "MmeThenardier", weight=4)
+    G.add_edge("Cosette", "Valjean", weight=31)
+    G.add_edge("Cosette", "Tholomyes", weight=1)
+    G.add_edge("Cosette", "Thenardier", weight=1)
+    G.add_edge("Javert", "Valjean", weight=17)
+    G.add_edge("Javert", "Fantine", weight=5)
+    G.add_edge("Javert", "Thenardier", weight=5)
+    G.add_edge("Javert", "MmeThenardier", weight=1)
+    G.add_edge("Javert", "Cosette", weight=1)
+    G.add_edge("Fauchelevent", "Valjean", weight=8)
+    G.add_edge("Fauchelevent", "Javert", weight=1)
+    G.add_edge("Bamatabois", "Fantine", weight=1)
+    G.add_edge("Bamatabois", "Javert", weight=1)
+    G.add_edge("Bamatabois", "Valjean", weight=2)
+    G.add_edge("Perpetue", "Fantine", weight=1)
+    G.add_edge("Simplice", "Perpetue", weight=2)
+    G.add_edge("Simplice", "Valjean", weight=3)
+    G.add_edge("Simplice", "Fantine", weight=2)
+    G.add_edge("Simplice", "Javert", weight=1)
+    G.add_edge("Scaufflaire", "Valjean", weight=1)
+    G.add_edge("Woman1", "Valjean", weight=2)
+    G.add_edge("Woman1", "Javert", weight=1)
+    G.add_edge("Judge", "Valjean", weight=3)
+    G.add_edge("Judge", "Bamatabois", weight=2)
+    G.add_edge("Champmathieu", "Valjean", weight=3)
+    G.add_edge("Champmathieu", "Judge", weight=3)
+    G.add_edge("Champmathieu", "Bamatabois", weight=2)
+    G.add_edge("Brevet", "Judge", weight=2)
+    G.add_edge("Brevet", "Champmathieu", weight=2)
+    G.add_edge("Brevet", "Valjean", weight=2)
+    G.add_edge("Brevet", "Bamatabois", weight=1)
+    G.add_edge("Chenildieu", "Judge", weight=2)
+    G.add_edge("Chenildieu", "Champmathieu", weight=2)
+    G.add_edge("Chenildieu", "Brevet", weight=2)
+    G.add_edge("Chenildieu", "Valjean", weight=2)
+    G.add_edge("Chenildieu", "Bamatabois", weight=1)
+    G.add_edge("Cochepaille", "Judge", weight=2)
+    G.add_edge("Cochepaille", "Champmathieu", weight=2)
+    G.add_edge("Cochepaille", "Brevet", weight=2)
+    G.add_edge("Cochepaille", "Chenildieu", weight=2)
+    G.add_edge("Cochepaille", "Valjean", weight=2)
+    G.add_edge("Cochepaille", "Bamatabois", weight=1)
+    G.add_edge("Pontmercy", "Thenardier", weight=1)
+    G.add_edge("Boulatruelle", "Thenardier", weight=1)
+    G.add_edge("Eponine", "MmeThenardier", weight=2)
+    G.add_edge("Eponine", "Thenardier", weight=3)
+    G.add_edge("Anzelma", "Eponine", weight=2)
+    G.add_edge("Anzelma", "Thenardier", weight=2)
+    G.add_edge("Anzelma", "MmeThenardier", weight=1)
+    G.add_edge("Woman2", "Valjean", weight=3)
+    G.add_edge("Woman2", "Cosette", weight=1)
+    G.add_edge("Woman2", "Javert", weight=1)
+    G.add_edge("MotherInnocent", "Fauchelevent", weight=3)
+    G.add_edge("MotherInnocent", "Valjean", weight=1)
+    G.add_edge("Gribier", "Fauchelevent", weight=2)
+    G.add_edge("MmeBurgon", "Jondrette", weight=1)
+    G.add_edge("Gavroche", "MmeBurgon", weight=2)
+    G.add_edge("Gavroche", "Thenardier", weight=1)
+    G.add_edge("Gavroche", "Javert", weight=1)
+    G.add_edge("Gavroche", "Valjean", weight=1)
+    G.add_edge("Gillenormand", "Cosette", weight=3)
+    G.add_edge("Gillenormand", "Valjean", weight=2)
+    G.add_edge("Magnon", "Gillenormand", weight=1)
+    G.add_edge("Magnon", "MmeThenardier", weight=1)
+    G.add_edge("MlleGillenormand", "Gillenormand", weight=9)
+    G.add_edge("MlleGillenormand", "Cosette", weight=2)
+    G.add_edge("MlleGillenormand", "Valjean", weight=2)
+    G.add_edge("MmePontmercy", "MlleGillenormand", weight=1)
+    G.add_edge("MmePontmercy", "Pontmercy", weight=1)
+    G.add_edge("MlleVaubois", "MlleGillenormand", weight=1)
+    G.add_edge("LtGillenormand", "MlleGillenormand", weight=2)
+    G.add_edge("LtGillenormand", "Gillenormand", weight=1)
+    G.add_edge("LtGillenormand", "Cosette", weight=1)
+    G.add_edge("Marius", "MlleGillenormand", weight=6)
+    G.add_edge("Marius", "Gillenormand", weight=12)
+    G.add_edge("Marius", "Pontmercy", weight=1)
+    G.add_edge("Marius", "LtGillenormand", weight=1)
+    G.add_edge("Marius", "Cosette", weight=21)
+    G.add_edge("Marius", "Valjean", weight=19)
+    G.add_edge("Marius", "Tholomyes", weight=1)
+    G.add_edge("Marius", "Thenardier", weight=2)
+    G.add_edge("Marius", "Eponine", weight=5)
+    G.add_edge("Marius", "Gavroche", weight=4)
+    G.add_edge("BaronessT", "Gillenormand", weight=1)
+    G.add_edge("BaronessT", "Marius", weight=1)
+    G.add_edge("Mabeuf", "Marius", weight=1)
+    G.add_edge("Mabeuf", "Eponine", weight=1)
+    G.add_edge("Mabeuf", "Gavroche", weight=1)
+    G.add_edge("Enjolras", "Marius", weight=7)
+    G.add_edge("Enjolras", "Gavroche", weight=7)
+    G.add_edge("Enjolras", "Javert", weight=6)
+    G.add_edge("Enjolras", "Mabeuf", weight=1)
+    G.add_edge("Enjolras", "Valjean", weight=4)
+    G.add_edge("Combeferre", "Enjolras", weight=15)
+    G.add_edge("Combeferre", "Marius", weight=5)
+    G.add_edge("Combeferre", "Gavroche", weight=6)
+    G.add_edge("Combeferre", "Mabeuf", weight=2)
+    G.add_edge("Prouvaire", "Gavroche", weight=1)
+    G.add_edge("Prouvaire", "Enjolras", weight=4)
+    G.add_edge("Prouvaire", "Combeferre", weight=2)
+    G.add_edge("Feuilly", "Gavroche", weight=2)
+    G.add_edge("Feuilly", "Enjolras", weight=6)
+    G.add_edge("Feuilly", "Prouvaire", weight=2)
+    G.add_edge("Feuilly", "Combeferre", weight=5)
+    G.add_edge("Feuilly", "Mabeuf", weight=1)
+    G.add_edge("Feuilly", "Marius", weight=1)
+    G.add_edge("Courfeyrac", "Marius", weight=9)
+    G.add_edge("Courfeyrac", "Enjolras", weight=17)
+    G.add_edge("Courfeyrac", "Combeferre", weight=13)
+    G.add_edge("Courfeyrac", "Gavroche", weight=7)
+    G.add_edge("Courfeyrac", "Mabeuf", weight=2)
+    G.add_edge("Courfeyrac", "Eponine", weight=1)
+    G.add_edge("Courfeyrac", "Feuilly", weight=6)
+    G.add_edge("Courfeyrac", "Prouvaire", weight=3)
+    G.add_edge("Bahorel", "Combeferre", weight=5)
+    G.add_edge("Bahorel", "Gavroche", weight=5)
+    G.add_edge("Bahorel", "Courfeyrac", weight=6)
+    G.add_edge("Bahorel", "Mabeuf", weight=2)
+    G.add_edge("Bahorel", "Enjolras", weight=4)
+    G.add_edge("Bahorel", "Feuilly", weight=3)
+    G.add_edge("Bahorel", "Prouvaire", weight=2)
+    G.add_edge("Bahorel", "Marius", weight=1)
+    G.add_edge("Bossuet", "Marius", weight=5)
+    G.add_edge("Bossuet", "Courfeyrac", weight=12)
+    G.add_edge("Bossuet", "Gavroche", weight=5)
+    G.add_edge("Bossuet", "Bahorel", weight=4)
+    G.add_edge("Bossuet", "Enjolras", weight=10)
+    G.add_edge("Bossuet", "Feuilly", weight=6)
+    G.add_edge("Bossuet", "Prouvaire", weight=2)
+    G.add_edge("Bossuet", "Combeferre", weight=9)
+    G.add_edge("Bossuet", "Mabeuf", weight=1)
+    G.add_edge("Bossuet", "Valjean", weight=1)
+    G.add_edge("Joly", "Bahorel", weight=5)
+    G.add_edge("Joly", "Bossuet", weight=7)
+    G.add_edge("Joly", "Gavroche", weight=3)
+    G.add_edge("Joly", "Courfeyrac", weight=5)
+    G.add_edge("Joly", "Enjolras", weight=5)
+    G.add_edge("Joly", "Feuilly", weight=5)
+    G.add_edge("Joly", "Prouvaire", weight=2)
+    G.add_edge("Joly", "Combeferre", weight=5)
+    G.add_edge("Joly", "Mabeuf", weight=1)
+    G.add_edge("Joly", "Marius", weight=2)
+    G.add_edge("Grantaire", "Bossuet", weight=3)
+    G.add_edge("Grantaire", "Enjolras", weight=3)
+    G.add_edge("Grantaire", "Combeferre", weight=1)
+    G.add_edge("Grantaire", "Courfeyrac", weight=2)
+    G.add_edge("Grantaire", "Joly", weight=2)
+    G.add_edge("Grantaire", "Gavroche", weight=1)
+    G.add_edge("Grantaire", "Bahorel", weight=1)
+    G.add_edge("Grantaire", "Feuilly", weight=1)
+    G.add_edge("Grantaire", "Prouvaire", weight=1)
+    G.add_edge("MotherPlutarch", "Mabeuf", weight=3)
+    G.add_edge("Gueulemer", "Thenardier", weight=5)
+    G.add_edge("Gueulemer", "Valjean", weight=1)
+    G.add_edge("Gueulemer", "MmeThenardier", weight=1)
+    G.add_edge("Gueulemer", "Javert", weight=1)
+    G.add_edge("Gueulemer", "Gavroche", weight=1)
+    G.add_edge("Gueulemer", "Eponine", weight=1)
+    G.add_edge("Babet", "Thenardier", weight=6)
+    G.add_edge("Babet", "Gueulemer", weight=6)
+    G.add_edge("Babet", "Valjean", weight=1)
+    G.add_edge("Babet", "MmeThenardier", weight=1)
+    G.add_edge("Babet", "Javert", weight=2)
+    G.add_edge("Babet", "Gavroche", weight=1)
+    G.add_edge("Babet", "Eponine", weight=1)
+    G.add_edge("Claquesous", "Thenardier", weight=4)
+    G.add_edge("Claquesous", "Babet", weight=4)
+    G.add_edge("Claquesous", "Gueulemer", weight=4)
+    G.add_edge("Claquesous", "Valjean", weight=1)
+    G.add_edge("Claquesous", "MmeThenardier", weight=1)
+    G.add_edge("Claquesous", "Javert", weight=1)
+    G.add_edge("Claquesous", "Eponine", weight=1)
+    G.add_edge("Claquesous", "Enjolras", weight=1)
+    G.add_edge("Montparnasse", "Javert", weight=1)
+    G.add_edge("Montparnasse", "Babet", weight=2)
+    G.add_edge("Montparnasse", "Gueulemer", weight=2)
+    G.add_edge("Montparnasse", "Claquesous", weight=2)
+    G.add_edge("Montparnasse", "Valjean", weight=1)
+    G.add_edge("Montparnasse", "Gavroche", weight=1)
+    G.add_edge("Montparnasse", "Eponine", weight=1)
+    G.add_edge("Montparnasse", "Thenardier", weight=1)
+    G.add_edge("Toussaint", "Cosette", weight=2)
+    G.add_edge("Toussaint", "Javert", weight=1)
+    G.add_edge("Toussaint", "Valjean", weight=1)
+    G.add_edge("Child1", "Gavroche", weight=2)
+    G.add_edge("Child2", "Gavroche", weight=2)
+    G.add_edge("Child2", "Child1", weight=3)
+    G.add_edge("Brujon", "Babet", weight=3)
+    G.add_edge("Brujon", "Gueulemer", weight=3)
+    G.add_edge("Brujon", "Thenardier", weight=3)
+    G.add_edge("Brujon", "Gavroche", weight=1)
+    G.add_edge("Brujon", "Eponine", weight=1)
+    G.add_edge("Brujon", "Claquesous", weight=1)
+    G.add_edge("Brujon", "Montparnasse", weight=1)
+    G.add_edge("MmeHucheloup", "Bossuet", weight=1)
+    G.add_edge("MmeHucheloup", "Joly", weight=1)
+    G.add_edge("MmeHucheloup", "Grantaire", weight=1)
+    G.add_edge("MmeHucheloup", "Bahorel", weight=1)
+    G.add_edge("MmeHucheloup", "Courfeyrac", weight=1)
+    G.add_edge("MmeHucheloup", "Gavroche", weight=1)
+    G.add_edge("MmeHucheloup", "Enjolras", weight=1)
+    return G

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/spectral_graph_forge.py

@@ -0,0 +1,120 @@
+"""Generates graphs with a given eigenvector structure"""
+
+import networkx as nx
+from networkx.utils import np_random_state
+
+__all__ = ["spectral_graph_forge"]
+
+
+@np_random_state(3)
+@nx._dispatchable(returns_graph=True)
+def spectral_graph_forge(G, alpha, transformation="identity", seed=None):
+    """Returns a random simple graph with spectrum resembling that of `G`
+
+    This algorithm, called Spectral Graph Forge (SGF), computes the
+    eigenvectors of a given graph adjacency matrix, filters them and
+    builds a random graph with a similar eigenstructure.
+    SGF has been proved to be particularly useful for synthesizing
+    realistic social networks and it can also be used to anonymize
+    graph sensitive data.
+
+    Parameters
+    ----------
+    G : Graph
+    alpha :  float
+        Ratio representing the percentage of eigenvectors of G to consider,
+        values in [0,1].
+    transformation : string, optional
+        Represents the intended matrix linear transformation, possible values
+        are 'identity' and 'modularity'
+    seed : integer, random_state, or None (default)
+        Indicator of numpy random number generation state.
+        See :ref:`Randomness<randomness>`.
+
+    Returns
+    -------
+    H : Graph
+        A graph with a similar eigenvector structure of the input one.
+
+    Raises
+    ------
+    NetworkXError
+        If transformation has a value different from 'identity' or 'modularity'
+
+    Notes
+    -----
+    Spectral Graph Forge (SGF) generates a random simple graph resembling the
+    global properties of the given one.
+    It leverages the low-rank approximation of the associated adjacency matrix
+    driven by the *alpha* precision parameter.
+    SGF preserves the number of nodes of the input graph and their ordering.
+    This way, nodes of output graphs resemble the properties of the input one
+    and attributes can be directly mapped.
+
+    It considers the graph adjacency matrices which can optionally be
+    transformed to other symmetric real matrices (currently transformation
+    options include *identity* and *modularity*).
+    The *modularity* transformation, in the sense of Newman's modularity matrix
+    allows the focusing on community structure related properties of the graph.
+
+    SGF applies a low-rank approximation whose fixed rank is computed from the
+    ratio *alpha* of the input graph adjacency matrix dimension.
+    This step performs a filtering on the input eigenvectors similar to the low
+    pass filtering common in telecommunications.
+
+    The filtered values (after truncation) are used as input to a Bernoulli
+    sampling for constructing a random adjacency matrix.
+
+    References
+    ----------
+    ..  [1] L. Baldesi, C. T. Butts, A. Markopoulou, "Spectral Graph Forge:
+        Graph Generation Targeting Modularity", IEEE Infocom, '18.
+        https://arxiv.org/abs/1801.01715
+    ..  [2] M. Newman, "Networks: an introduction", Oxford university press,
+        2010
+
+    Examples
+    --------
+    >>> G = nx.karate_club_graph()
+    >>> H = nx.spectral_graph_forge(G, 0.3)
+    >>>
+    """
+    import numpy as np
+    import scipy as sp
+
+    available_transformations = ["identity", "modularity"]
+    alpha = np.clip(alpha, 0, 1)
+    A = nx.to_numpy_array(G)
+    n = A.shape[1]
+    level = round(n * alpha)
+
+    if transformation not in available_transformations:
+        msg = f"{transformation!r} is not a valid transformation. "
+        msg += f"Transformations: {available_transformations}"
+        raise nx.NetworkXError(msg)
+
+    K = np.ones((1, n)) @ A
+
+    B = A
+    if transformation == "modularity":
+        B -= K.T @ K / K.sum()
+
+    # Compute low-rank approximation of B
+    evals, evecs = np.linalg.eigh(B)
+    k = np.argsort(np.abs(evals))[::-1]  # indices of evals in descending order
+    evecs[:, k[np.arange(level, n)]] = 0  # set smallest eigenvectors to 0
+    B = evecs @ np.diag(evals) @ evecs.T
+
+    if transformation == "modularity":
+        B += K.T @ K / K.sum()
+
+    B = np.clip(B, 0, 1)
+    np.fill_diagonal(B, 0)
+
+    for i in range(n - 1):
+        B[i, i + 1 :] = sp.stats.bernoulli.rvs(B[i, i + 1 :], random_state=seed)
+        B[i + 1 :, i] = np.transpose(B[i, i + 1 :])
+
+    H = nx.from_numpy_array(B)
+
+    return H

evalkit_tf446/lib/python3.10/site-packages/networkx/generators/sudoku.py

@@ -0,0 +1,131 @@
+"""Generator for Sudoku graphs
+
+This module gives a generator for n-Sudoku graphs. It can be used to develop
+algorithms for solving or generating Sudoku puzzles.
+
+A completed Sudoku grid is a 9x9 array of integers between 1 and 9, with no
+number appearing twice in the same row, column, or 3x3 box.
+
++---------+---------+---------+
+| | 8 6 4 | | 3 7 1 | | 2 5 9 |
+| | 3 2 5 | | 8 4 9 | | 7 6 1 |
+| | 9 7 1 | | 2 6 5 | | 8 4 3 |
++---------+---------+---------+
+| | 4 3 6 | | 1 9 2 | | 5 8 7 |
+| | 1 9 8 | | 6 5 7 | | 4 3 2 |
+| | 2 5 7 | | 4 8 3 | | 9 1 6 |
++---------+---------+---------+
+| | 6 8 9 | | 7 3 4 | | 1 2 5 |
+| | 7 1 3 | | 5 2 8 | | 6 9 4 |
+| | 5 4 2 | | 9 1 6 | | 3 7 8 |
++---------+---------+---------+
+
+
+The Sudoku graph is an undirected graph with 81 vertices, corresponding to
+the cells of a Sudoku grid. It is a regular graph of degree 20. Two distinct
+vertices are adjacent if and only if the corresponding cells belong to the
+same row, column, or box. A completed Sudoku grid corresponds to a vertex
+coloring of the Sudoku graph with nine colors.
+
+More generally, the n-Sudoku graph is a graph with n^4 vertices, corresponding
+to the cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and
+only if they belong to the same row, column, or n by n box.
+
+References
+----------
+.. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic
+    polynomials. Notices of the AMS, 54(6), 708-717.
+.. [2] Sander, Torsten (2009), "Sudoku graphs are integral",
+    Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816
+.. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free
+    Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019.
+"""
+
+import networkx as nx
+from networkx.exception import NetworkXError
+
+__all__ = ["sudoku_graph"]
+
+
+@nx._dispatchable(graphs=None, returns_graph=True)
+def sudoku_graph(n=3):
+    """Returns the n-Sudoku graph. The default value of n is 3.
+
+    The n-Sudoku graph is a graph with n^4 vertices, corresponding to the
+    cells of an n^2 by n^2 grid. Two distinct vertices are adjacent if and
+    only if they belong to the same row, column, or n-by-n box.
+
+    Parameters
+    ----------
+    n: integer
+       The order of the Sudoku graph, equal to the square root of the
+       number of rows. The default is 3.
+
+    Returns
+    -------
+    NetworkX graph
+        The n-Sudoku graph Sud(n).
+
+    Examples
+    --------
+    >>> G = nx.sudoku_graph()
+    >>> G.number_of_nodes()
+    81
+    >>> G.number_of_edges()
+    810
+    >>> sorted(G.neighbors(42))
+    [6, 15, 24, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 51, 52, 53, 60, 69, 78]
+    >>> G = nx.sudoku_graph(2)
+    >>> G.number_of_nodes()
+    16
+    >>> G.number_of_edges()
+    56
+
+    References
+    ----------
+    .. [1] Herzberg, A. M., & Murty, M. R. (2007). Sudoku squares and chromatic
+       polynomials. Notices of the AMS, 54(6), 708-717.
+    .. [2] Sander, Torsten (2009), "Sudoku graphs are integral",
+       Electronic Journal of Combinatorics, 16 (1): Note 25, 7pp, MR 2529816
+    .. [3] Wikipedia contributors. "Glossary of Sudoku." Wikipedia, The Free
+       Encyclopedia, 3 Dec. 2019. Web. 22 Dec. 2019.
+    """
+
+    if n < 0:
+        raise NetworkXError("The order must be greater than or equal to zero.")
+
+    n2 = n * n
+    n3 = n2 * n
+    n4 = n3 * n
+
+    # Construct an empty graph with n^4 nodes
+    G = nx.empty_graph(n4)
+
+    # A Sudoku graph of order 0 or 1 has no edges
+    if n < 2:
+        return G
+
+    # Add edges for cells in the same row
+    for row_no in range(n2):
+        row_start = row_no * n2
+        for j in range(1, n2):
+            for i in range(j):
+                G.add_edge(row_start + i, row_start + j)
+
+    # Add edges for cells in the same column
+    for col_no in range(n2):
+        for j in range(col_no, n4, n2):
+            for i in range(col_no, j, n2):
+                G.add_edge(i, j)
+
+    # Add edges for cells in the same box
+    for band_no in range(n):
+        for stack_no in range(n):
+            box_start = n3 * band_no + n * stack_no
+            for j in range(1, n2):
+                for i in range(j):
+                    u = box_start + (i % n) + n2 * (i // n)
+                    v = box_start + (j % n) + n2 * (j // n)
+                    G.add_edge(u, v)
+
+    return G