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@@ -1377,3 +1377,4 @@ minigpt2/lib/python3.10/site-packages/pillow.libs/liblcms2-e69eef39.so.2.0.16 fi
 minigpt2/lib/python3.10/site-packages/idna/__pycache__/idnadata.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 minigpt2/lib/python3.10/site-packages/idna/__pycache__/uts46data.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 minigpt2/lib/python3.10/site-packages/pillow.libs/libbrotlicommon-3ecfe81c.so.1 filter=lfs diff=lfs merge=lfs -text
+videochat2/lib/python3.10/site-packages/torch/lib/libtorch_python.so filter=lfs diff=lfs merge=lfs -text

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/biconnected.py

@@ -0,0 +1,394 @@
+"""Biconnected components and articulation points."""
+
+from itertools import chain
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "biconnected_components",
+    "biconnected_component_edges",
+    "is_biconnected",
+    "articulation_points",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def is_biconnected(G):
+    """Returns True if the graph is biconnected, False otherwise.
+
+    A graph is biconnected if, and only if, it cannot be disconnected by
+    removing only one node (and all edges incident on that node).  If
+    removing a node increases the number of disconnected components
+    in the graph, that node is called an articulation point, or cut
+    vertex.  A biconnected graph has no articulation points.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    biconnected : bool
+        True if the graph is biconnected, False otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> G.add_edge(0, 3)
+    >>> print(nx.is_biconnected(G))
+    True
+
+    See Also
+    --------
+    biconnected_components
+    articulation_points
+    biconnected_component_edges
+    is_strongly_connected
+    is_weakly_connected
+    is_connected
+    is_semiconnected
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+       "Efficient algorithms for graph manipulation".
+       Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    bccs = biconnected_components(G)
+    try:
+        bcc = next(bccs)
+    except StopIteration:
+        # No bicomponents (empty graph?)
+        return False
+    try:
+        next(bccs)
+    except StopIteration:
+        # Only one bicomponent
+        return len(bcc) == len(G)
+    else:
+        # Multiple bicomponents
+        return False
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def biconnected_component_edges(G):
+    """Returns a generator of lists of edges, one list for each biconnected
+    component of the input graph.
+
+    Biconnected components are maximal subgraphs such that the removal of a
+    node (and all edges incident on that node) will not disconnect the
+    subgraph.  Note that nodes may be part of more than one biconnected
+    component.  Those nodes are articulation points, or cut vertices.
+    However, each edge belongs to one, and only one, biconnected component.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    edges : generator of lists
+        Generator of lists of edges, one list for each bicomponent.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.barbell_graph(4, 2)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> bicomponents_edges = list(nx.biconnected_component_edges(G))
+    >>> len(bicomponents_edges)
+    5
+    >>> G.add_edge(2, 8)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> bicomponents_edges = list(nx.biconnected_component_edges(G))
+    >>> len(bicomponents_edges)
+    1
+
+    See Also
+    --------
+    is_biconnected,
+    biconnected_components,
+    articulation_points,
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    yield from _biconnected_dfs(G, components=True)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def biconnected_components(G):
+    """Returns a generator of sets of nodes, one set for each biconnected
+    component of the graph
+
+    Biconnected components are maximal subgraphs such that the removal of a
+    node (and all edges incident on that node) will not disconnect the
+    subgraph. Note that nodes may be part of more than one biconnected
+    component.  Those nodes are articulation points, or cut vertices.  The
+    removal of articulation points will increase the number of connected
+    components of the graph.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Returns
+    -------
+    nodes : generator
+        Generator of sets of nodes, one set for each biconnected component.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+    >>> G = nx.lollipop_graph(5, 1)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> bicomponents = list(nx.biconnected_components(G))
+    >>> len(bicomponents)
+    2
+    >>> G.add_edge(0, 5)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> bicomponents = list(nx.biconnected_components(G))
+    >>> len(bicomponents)
+    1
+
+    You can generate a sorted list of biconnected components, largest
+    first, using sort.
+
+    >>> G.remove_edge(0, 5)
+    >>> [len(c) for c in sorted(nx.biconnected_components(G), key=len, reverse=True)]
+    [5, 2]
+
+    If you only want the largest connected component, it's more
+    efficient to use max instead of sort.
+
+    >>> Gc = max(nx.biconnected_components(G), key=len)
+
+    To create the components as subgraphs use:
+    ``(G.subgraph(c).copy() for c in biconnected_components(G))``
+
+    See Also
+    --------
+    is_biconnected
+    articulation_points
+    biconnected_component_edges
+    k_components : this function is a special case where k=2
+    bridge_components : similar to this function, but is defined using
+        2-edge-connectivity instead of 2-node-connectivity.
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    for comp in _biconnected_dfs(G, components=True):
+        yield set(chain.from_iterable(comp))
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def articulation_points(G):
+    """Yield the articulation points, or cut vertices, of a graph.
+
+    An articulation point or cut vertex is any node whose removal (along with
+    all its incident edges) increases the number of connected components of
+    a graph.  An undirected connected graph without articulation points is
+    biconnected. Articulation points belong to more than one biconnected
+    component of a graph.
+
+    Notice that by convention a dyad is considered a biconnected component.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        An undirected graph.
+
+    Yields
+    ------
+    node
+        An articulation point in the graph.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If the input graph is not undirected.
+
+    Examples
+    --------
+
+    >>> G = nx.barbell_graph(4, 2)
+    >>> print(nx.is_biconnected(G))
+    False
+    >>> len(list(nx.articulation_points(G)))
+    4
+    >>> G.add_edge(2, 8)
+    >>> print(nx.is_biconnected(G))
+    True
+    >>> len(list(nx.articulation_points(G)))
+    0
+
+    See Also
+    --------
+    is_biconnected
+    biconnected_components
+    biconnected_component_edges
+
+    Notes
+    -----
+    The algorithm to find articulation points and biconnected
+    components is implemented using a non-recursive depth-first-search
+    (DFS) that keeps track of the highest level that back edges reach
+    in the DFS tree.  A node `n` is an articulation point if, and only
+    if, there exists a subtree rooted at `n` such that there is no
+    back edge from any successor of `n` that links to a predecessor of
+    `n` in the DFS tree.  By keeping track of all the edges traversed
+    by the DFS we can obtain the biconnected components because all
+    edges of a bicomponent will be traversed consecutively between
+    articulation points.
+
+    References
+    ----------
+    .. [1] Hopcroft, J.; Tarjan, R. (1973).
+           "Efficient algorithms for graph manipulation".
+           Communications of the ACM 16: 372–378. doi:10.1145/362248.362272
+
+    """
+    seen = set()
+    for articulation in _biconnected_dfs(G, components=False):
+        if articulation not in seen:
+            seen.add(articulation)
+            yield articulation
+
+
+@not_implemented_for("directed")
+def _biconnected_dfs(G, components=True):
+    # depth-first search algorithm to generate articulation points
+    # and biconnected components
+    visited = set()
+    for start in G:
+        if start in visited:
+            continue
+        discovery = {start: 0}  # time of first discovery of node during search
+        low = {start: 0}
+        root_children = 0
+        visited.add(start)
+        edge_stack = []
+        stack = [(start, start, iter(G[start]))]
+        edge_index = {}
+        while stack:
+            grandparent, parent, children = stack[-1]
+            try:
+                child = next(children)
+                if grandparent == child:
+                    continue
+                if child in visited:
+                    if discovery[child] <= discovery[parent]:  # back edge
+                        low[parent] = min(low[parent], discovery[child])
+                        if components:
+                            edge_index[parent, child] = len(edge_stack)
+                            edge_stack.append((parent, child))
+                else:
+                    low[child] = discovery[child] = len(discovery)
+                    visited.add(child)
+                    stack.append((parent, child, iter(G[child])))
+                    if components:
+                        edge_index[parent, child] = len(edge_stack)
+                        edge_stack.append((parent, child))
+
+            except StopIteration:
+                stack.pop()
+                if len(stack) > 1:
+                    if low[parent] >= discovery[grandparent]:
+                        if components:
+                            ind = edge_index[grandparent, parent]
+                            yield edge_stack[ind:]
+                            del edge_stack[ind:]
+
+                        else:
+                            yield grandparent
+                    low[grandparent] = min(low[parent], low[grandparent])
+                elif stack:  # length 1 so grandparent is root
+                    root_children += 1
+                    if components:
+                        ind = edge_index[grandparent, parent]
+                        yield edge_stack[ind:]
+                        del edge_stack[ind:]
+        if not components:
+            # root node is articulation point if it has more than 1 child
+            if root_children > 1:
+                yield start

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/connected.py

@@ -0,0 +1,216 @@
+"""Connected components."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+from ...utils import arbitrary_element
+
+__all__ = [
+    "number_connected_components",
+    "connected_components",
+    "is_connected",
+    "node_connected_component",
+]
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def connected_components(G):
+    """Generate connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph
+
+    Returns
+    -------
+    comp : generator of sets
+       A generator of sets of nodes, one for each component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    Generate a sorted list of connected components, largest first.
+
+    >>> G = nx.path_graph(4)
+    >>> nx.add_path(G, [10, 11, 12])
+    >>> [len(c) for c in sorted(nx.connected_components(G), key=len, reverse=True)]
+    [4, 3]
+
+    If you only want the largest connected component, it's more
+    efficient to use max instead of sort.
+
+    >>> largest_cc = max(nx.connected_components(G), key=len)
+
+    To create the induced subgraph of each component use:
+
+    >>> S = [G.subgraph(c).copy() for c in nx.connected_components(G)]
+
+    See Also
+    --------
+    strongly_connected_components
+    weakly_connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    seen = set()
+    n = len(G)
+    for v in G:
+        if v not in seen:
+            c = _plain_bfs(G, n, v)
+            seen.update(c)
+            yield c
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def number_connected_components(G):
+    """Returns the number of connected components.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       An undirected graph.
+
+    Returns
+    -------
+    n : integer
+       Number of connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)])
+    >>> nx.number_connected_components(G)
+    3
+
+    See Also
+    --------
+    connected_components
+    number_weakly_connected_components
+    number_strongly_connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    return sum(1 for cc in connected_components(G))
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def is_connected(G):
+    """Returns True if the graph is connected, False otherwise.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph.
+
+    Returns
+    -------
+    connected : bool
+      True if the graph is connected, false otherwise.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> print(nx.is_connected(G))
+    True
+
+    See Also
+    --------
+    is_strongly_connected
+    is_weakly_connected
+    is_semiconnected
+    is_biconnected
+    connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    n = len(G)
+    if n == 0:
+        raise nx.NetworkXPointlessConcept(
+            "Connectivity is undefined for the null graph."
+        )
+    return sum(1 for node in _plain_bfs(G, n, arbitrary_element(G))) == len(G)
+
+
+@not_implemented_for("directed")
+@nx._dispatchable
+def node_connected_component(G, n):
+    """Returns the set of nodes in the component of graph containing node n.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       An undirected graph.
+
+    n : node label
+       A node in G
+
+    Returns
+    -------
+    comp : set
+       A set of nodes in the component of G containing node n.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is directed.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (1, 2), (5, 6), (3, 4)])
+    >>> nx.node_connected_component(G, 0)  # nodes of component that contains node 0
+    {0, 1, 2}
+
+    See Also
+    --------
+    connected_components
+
+    Notes
+    -----
+    For undirected graphs only.
+
+    """
+    return _plain_bfs(G, len(G), n)
+
+
+def _plain_bfs(G, n, source):
+    """A fast BFS node generator"""
+    adj = G._adj
+    seen = {source}
+    nextlevel = [source]
+    while nextlevel:
+        thislevel = nextlevel
+        nextlevel = []
+        for v in thislevel:
+            for w in adj[v]:
+                if w not in seen:
+                    seen.add(w)
+                    nextlevel.append(w)
+            if len(seen) == n:
+                return seen
+    return seen

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/strongly_connected.py

@@ -0,0 +1,351 @@
+"""Strongly connected components."""
+
+import networkx as nx
+from networkx.utils.decorators import not_implemented_for
+
+__all__ = [
+    "number_strongly_connected_components",
+    "strongly_connected_components",
+    "is_strongly_connected",
+    "kosaraju_strongly_connected_components",
+    "condensation",
+]
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def strongly_connected_components(G):
+    """Generate nodes in strongly connected components of graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(nx.strongly_connected_components(G), key=len, reverse=True)
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.strongly_connected_components(G), key=len)
+
+    See Also
+    --------
+    connected_components
+    weakly_connected_components
+    kosaraju_strongly_connected_components
+
+    Notes
+    -----
+    Uses Tarjan's algorithm[1]_ with Nuutila's modifications[2]_.
+    Nonrecursive version of algorithm.
+
+    References
+    ----------
+    .. [1] Depth-first search and linear graph algorithms, R. Tarjan
+       SIAM Journal of Computing 1(2):146-160, (1972).
+
+    .. [2] On finding the strongly connected components in a directed graph.
+       E. Nuutila and E. Soisalon-Soinen
+       Information Processing Letters 49(1): 9-14, (1994)..
+
+    """
+    preorder = {}
+    lowlink = {}
+    scc_found = set()
+    scc_queue = []
+    i = 0  # Preorder counter
+    neighbors = {v: iter(G[v]) for v in G}
+    for source in G:
+        if source not in scc_found:
+            queue = [source]
+            while queue:
+                v = queue[-1]
+                if v not in preorder:
+                    i = i + 1
+                    preorder[v] = i
+                done = True
+                for w in neighbors[v]:
+                    if w not in preorder:
+                        queue.append(w)
+                        done = False
+                        break
+                if done:
+                    lowlink[v] = preorder[v]
+                    for w in G[v]:
+                        if w not in scc_found:
+                            if preorder[w] > preorder[v]:
+                                lowlink[v] = min([lowlink[v], lowlink[w]])
+                            else:
+                                lowlink[v] = min([lowlink[v], preorder[w]])
+                    queue.pop()
+                    if lowlink[v] == preorder[v]:
+                        scc = {v}
+                        while scc_queue and preorder[scc_queue[-1]] > preorder[v]:
+                            k = scc_queue.pop()
+                            scc.add(k)
+                        scc_found.update(scc)
+                        yield scc
+                    else:
+                        scc_queue.append(v)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def kosaraju_strongly_connected_components(G, source=None):
+    """Generate nodes in strongly connected components of graph.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+        A directed graph.
+
+    Returns
+    -------
+    comp : generator of sets
+        A generator of sets of nodes, one for each strongly connected
+        component of G.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Generate a sorted list of strongly connected components, largest first.
+
+    >>> G = nx.cycle_graph(4, create_using=nx.DiGraph())
+    >>> nx.add_cycle(G, [10, 11, 12])
+    >>> [
+    ...     len(c)
+    ...     for c in sorted(
+    ...         nx.kosaraju_strongly_connected_components(G), key=len, reverse=True
+    ...     )
+    ... ]
+    [4, 3]
+
+    If you only want the largest component, it's more efficient to
+    use max instead of sort.
+
+    >>> largest = max(nx.kosaraju_strongly_connected_components(G), key=len)
+
+    See Also
+    --------
+    strongly_connected_components
+
+    Notes
+    -----
+    Uses Kosaraju's algorithm.
+
+    """
+    post = list(nx.dfs_postorder_nodes(G.reverse(copy=False), source=source))
+
+    seen = set()
+    while post:
+        r = post.pop()
+        if r in seen:
+            continue
+        c = nx.dfs_preorder_nodes(G, r)
+        new = {v for v in c if v not in seen}
+        seen.update(new)
+        yield new
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def number_strongly_connected_components(G):
+    """Returns number of strongly connected components in graph.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+       A directed graph.
+
+    Returns
+    -------
+    n : integer
+       Number of strongly connected components
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph(
+    ...     [(0, 1), (1, 2), (2, 0), (2, 3), (4, 5), (3, 4), (5, 6), (6, 3), (6, 7)]
+    ... )
+    >>> nx.number_strongly_connected_components(G)
+    3
+
+    See Also
+    --------
+    strongly_connected_components
+    number_connected_components
+    number_weakly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+    """
+    return sum(1 for scc in strongly_connected_components(G))
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable
+def is_strongly_connected(G):
+    """Test directed graph for strong connectivity.
+
+    A directed graph is strongly connected if and only if every vertex in
+    the graph is reachable from every other vertex.
+
+    Parameters
+    ----------
+    G : NetworkX Graph
+       A directed graph.
+
+    Returns
+    -------
+    connected : bool
+      True if the graph is strongly connected, False otherwise.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 2)])
+    >>> nx.is_strongly_connected(G)
+    True
+    >>> G.remove_edge(2, 3)
+    >>> nx.is_strongly_connected(G)
+    False
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    See Also
+    --------
+    is_weakly_connected
+    is_semiconnected
+    is_connected
+    is_biconnected
+    strongly_connected_components
+
+    Notes
+    -----
+    For directed graphs only.
+    """
+    if len(G) == 0:
+        raise nx.NetworkXPointlessConcept(
+            """Connectivity is undefined for the null graph."""
+        )
+
+    return len(next(strongly_connected_components(G))) == len(G)
+
+
+@not_implemented_for("undirected")
+@nx._dispatchable(returns_graph=True)
+def condensation(G, scc=None):
+    """Returns the condensation of G.
+
+    The condensation of G is the graph with each of the strongly connected
+    components contracted into a single node.
+
+    Parameters
+    ----------
+    G : NetworkX DiGraph
+       A directed graph.
+
+    scc:  list or generator (optional, default=None)
+       Strongly connected components. If provided, the elements in
+       `scc` must partition the nodes in `G`. If not provided, it will be
+       calculated as scc=nx.strongly_connected_components(G).
+
+    Returns
+    -------
+    C : NetworkX DiGraph
+       The condensation graph C of G.  The node labels are integers
+       corresponding to the index of the component in the list of
+       strongly connected components of G.  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 SCC that the node in C represents.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If G is undirected.
+
+    Examples
+    --------
+    Contracting two sets of strongly connected nodes into two distinct SCC
+    using the barbell graph.
+
+    >>> G = nx.barbell_graph(4, 0)
+    >>> G.remove_edge(3, 4)
+    >>> G = nx.DiGraph(G)
+    >>> H = nx.condensation(G)
+    >>> H.nodes.data()
+    NodeDataView({0: {'members': {0, 1, 2, 3}}, 1: {'members': {4, 5, 6, 7}}})
+    >>> H.graph["mapping"]
+    {0: 0, 1: 0, 2: 0, 3: 0, 4: 1, 5: 1, 6: 1, 7: 1}
+
+    Contracting a complete graph into one single SCC.
+
+    >>> G = nx.complete_graph(7, create_using=nx.DiGraph)
+    >>> H = nx.condensation(G)
+    >>> H.nodes
+    NodeView((0,))
+    >>> H.nodes.data()
+    NodeDataView({0: {'members': {0, 1, 2, 3, 4, 5, 6}}})
+
+    Notes
+    -----
+    After contracting all strongly connected components to a single node,
+    the resulting graph is a directed acyclic graph.
+
+    """
+    if scc is None:
+        scc = nx.strongly_connected_components(G)
+    mapping = {}
+    members = {}
+    C = nx.DiGraph()
+    # Add mapping dict as graph attribute
+    C.graph["mapping"] = mapping
+    if len(G) == 0:
+        return C
+    for i, component in enumerate(scc):
+        members[i] = component
+        mapping.update((n, i) for n in component)
+    number_of_components = i + 1
+    C.add_nodes_from(range(number_of_components))
+    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, members, "members")
+    return C

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_attracting.py

@@ -0,0 +1,70 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestAttractingComponents:
+    @classmethod
+    def setup_class(cls):
+        cls.G1 = nx.DiGraph()
+        cls.G1.add_edges_from(
+            [
+                (5, 11),
+                (11, 2),
+                (11, 9),
+                (11, 10),
+                (7, 11),
+                (7, 8),
+                (8, 9),
+                (3, 8),
+                (3, 10),
+            ]
+        )
+        cls.G2 = nx.DiGraph()
+        cls.G2.add_edges_from([(0, 1), (0, 2), (1, 1), (1, 2), (2, 1)])
+
+        cls.G3 = nx.DiGraph()
+        cls.G3.add_edges_from([(0, 1), (1, 2), (2, 1), (0, 3), (3, 4), (4, 3)])
+
+        cls.G4 = nx.DiGraph()
+
+    def test_attracting_components(self):
+        ac = list(nx.attracting_components(self.G1))
+        assert {2} in ac
+        assert {9} in ac
+        assert {10} in ac
+
+        ac = list(nx.attracting_components(self.G2))
+        ac = [tuple(sorted(x)) for x in ac]
+        assert ac == [(1, 2)]
+
+        ac = list(nx.attracting_components(self.G3))
+        ac = [tuple(sorted(x)) for x in ac]
+        assert (1, 2) in ac
+        assert (3, 4) in ac
+        assert len(ac) == 2
+
+        ac = list(nx.attracting_components(self.G4))
+        assert ac == []
+
+    def test_number_attacting_components(self):
+        assert nx.number_attracting_components(self.G1) == 3
+        assert nx.number_attracting_components(self.G2) == 1
+        assert nx.number_attracting_components(self.G3) == 2
+        assert nx.number_attracting_components(self.G4) == 0
+
+    def test_is_attracting_component(self):
+        assert not nx.is_attracting_component(self.G1)
+        assert not nx.is_attracting_component(self.G2)
+        assert not nx.is_attracting_component(self.G3)
+        g2 = self.G3.subgraph([1, 2])
+        assert nx.is_attracting_component(g2)
+        assert not nx.is_attracting_component(self.G4)
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.attracting_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.number_attracting_components, G)
+        pytest.raises(NetworkXNotImplemented, nx.is_attracting_component, G)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_biconnected.py

@@ -0,0 +1,248 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+def assert_components_edges_equal(x, y):
+    sx = {frozenset(frozenset(e) for e in c) for c in x}
+    sy = {frozenset(frozenset(e) for e in c) for c in y}
+    assert sx == sy
+
+
+def assert_components_equal(x, y):
+    sx = {frozenset(c) for c in x}
+    sy = {frozenset(c) for c in y}
+    assert sx == sy
+
+
+def test_barbell():
+    G = nx.barbell_graph(8, 4)
+    nx.add_path(G, [7, 20, 21, 22])
+    nx.add_cycle(G, [22, 23, 24, 25])
+    pts = set(nx.articulation_points(G))
+    assert pts == {7, 8, 9, 10, 11, 12, 20, 21, 22}
+
+    answer = [
+        {12, 13, 14, 15, 16, 17, 18, 19},
+        {0, 1, 2, 3, 4, 5, 6, 7},
+        {22, 23, 24, 25},
+        {11, 12},
+        {10, 11},
+        {9, 10},
+        {8, 9},
+        {7, 8},
+        {21, 22},
+        {20, 21},
+        {7, 20},
+    ]
+    assert_components_equal(list(nx.biconnected_components(G)), answer)
+
+    G.add_edge(2, 17)
+    pts = set(nx.articulation_points(G))
+    assert pts == {7, 20, 21, 22}
+
+
+def test_articulation_points_repetitions():
+    G = nx.Graph()
+    G.add_edges_from([(0, 1), (1, 2), (1, 3)])
+    assert list(nx.articulation_points(G)) == [1]
+
+
+def test_articulation_points_cycle():
+    G = nx.cycle_graph(3)
+    nx.add_cycle(G, [1, 3, 4])
+    pts = set(nx.articulation_points(G))
+    assert pts == {1}
+
+
+def test_is_biconnected():
+    G = nx.cycle_graph(3)
+    assert nx.is_biconnected(G)
+    nx.add_cycle(G, [1, 3, 4])
+    assert not nx.is_biconnected(G)
+
+
+def test_empty_is_biconnected():
+    G = nx.empty_graph(5)
+    assert not nx.is_biconnected(G)
+    G.add_edge(0, 1)
+    assert not nx.is_biconnected(G)
+
+
+def test_biconnected_components_cycle():
+    G = nx.cycle_graph(3)
+    nx.add_cycle(G, [1, 3, 4])
+    answer = [{0, 1, 2}, {1, 3, 4}]
+    assert_components_equal(list(nx.biconnected_components(G)), answer)
+
+
+def test_biconnected_components1():
+    # graph example from
+    # https://web.archive.org/web/20121229123447/http://www.ibluemojo.com/school/articul_algorithm.html
+    edges = [
+        (0, 1),
+        (0, 5),
+        (0, 6),
+        (0, 14),
+        (1, 5),
+        (1, 6),
+        (1, 14),
+        (2, 4),
+        (2, 10),
+        (3, 4),
+        (3, 15),
+        (4, 6),
+        (4, 7),
+        (4, 10),
+        (5, 14),
+        (6, 14),
+        (7, 9),
+        (8, 9),
+        (8, 12),
+        (8, 13),
+        (10, 15),
+        (11, 12),
+        (11, 13),
+        (12, 13),
+    ]
+    G = nx.Graph(edges)
+    pts = set(nx.articulation_points(G))
+    assert pts == {4, 6, 7, 8, 9}
+    comps = list(nx.biconnected_component_edges(G))
+    answer = [
+        [(3, 4), (15, 3), (10, 15), (10, 4), (2, 10), (4, 2)],
+        [(13, 12), (13, 8), (11, 13), (12, 11), (8, 12)],
+        [(9, 8)],
+        [(7, 9)],
+        [(4, 7)],
+        [(6, 4)],
+        [(14, 0), (5, 1), (5, 0), (14, 5), (14, 1), (6, 14), (6, 0), (1, 6), (0, 1)],
+    ]
+    assert_components_edges_equal(comps, answer)
+
+
+def test_biconnected_components2():
+    G = nx.Graph()
+    nx.add_cycle(G, "ABC")
+    nx.add_cycle(G, "CDE")
+    nx.add_cycle(G, "FIJHG")
+    nx.add_cycle(G, "GIJ")
+    G.add_edge("E", "G")
+    comps = list(nx.biconnected_component_edges(G))
+    answer = [
+        [
+            tuple("GF"),
+            tuple("FI"),
+            tuple("IG"),
+            tuple("IJ"),
+            tuple("JG"),
+            tuple("JH"),
+            tuple("HG"),
+        ],
+        [tuple("EG")],
+        [tuple("CD"), tuple("DE"), tuple("CE")],
+        [tuple("AB"), tuple("BC"), tuple("AC")],
+    ]
+    assert_components_edges_equal(comps, answer)
+
+
+def test_biconnected_davis():
+    D = nx.davis_southern_women_graph()
+    bcc = list(nx.biconnected_components(D))[0]
+    assert set(D) == bcc  # All nodes in a giant bicomponent
+    # So no articulation points
+    assert len(list(nx.articulation_points(D))) == 0
+
+
+def test_biconnected_karate():
+    K = nx.karate_club_graph()
+    answer = [
+        {
+            0,
+            1,
+            2,
+            3,
+            7,
+            8,
+            9,
+            12,
+            13,
+            14,
+            15,
+            17,
+            18,
+            19,
+            20,
+            21,
+            22,
+            23,
+            24,
+            25,
+            26,
+            27,
+            28,
+            29,
+            30,
+            31,
+            32,
+            33,
+        },
+        {0, 4, 5, 6, 10, 16},
+        {0, 11},
+    ]
+    bcc = list(nx.biconnected_components(K))
+    assert_components_equal(bcc, answer)
+    assert set(nx.articulation_points(K)) == {0}
+
+
+def test_biconnected_eppstein():
+    # tests from http://www.ics.uci.edu/~eppstein/PADS/Biconnectivity.py
+    G1 = nx.Graph(
+        {
+            0: [1, 2, 5],
+            1: [0, 5],
+            2: [0, 3, 4],
+            3: [2, 4, 5, 6],
+            4: [2, 3, 5, 6],
+            5: [0, 1, 3, 4],
+            6: [3, 4],
+        }
+    )
+    G2 = nx.Graph(
+        {
+            0: [2, 5],
+            1: [3, 8],
+            2: [0, 3, 5],
+            3: [1, 2, 6, 8],
+            4: [7],
+            5: [0, 2],
+            6: [3, 8],
+            7: [4],
+            8: [1, 3, 6],
+        }
+    )
+    assert nx.is_biconnected(G1)
+    assert not nx.is_biconnected(G2)
+    answer_G2 = [{1, 3, 6, 8}, {0, 2, 5}, {2, 3}, {4, 7}]
+    bcc = list(nx.biconnected_components(G2))
+    assert_components_equal(bcc, answer_G2)
+
+
+def test_null_graph():
+    G = nx.Graph()
+    assert not nx.is_biconnected(G)
+    assert list(nx.biconnected_components(G)) == []
+    assert list(nx.biconnected_component_edges(G)) == []
+    assert list(nx.articulation_points(G)) == []
+
+
+def test_connected_raise():
+    DG = nx.DiGraph()
+    with pytest.raises(NetworkXNotImplemented):
+        next(nx.biconnected_components(DG))
+    with pytest.raises(NetworkXNotImplemented):
+        next(nx.biconnected_component_edges(DG))
+    with pytest.raises(NetworkXNotImplemented):
+        next(nx.articulation_points(DG))
+    pytest.raises(NetworkXNotImplemented, nx.is_biconnected, DG)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_connected.py

@@ -0,0 +1,138 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+from networkx import convert_node_labels_to_integers as cnlti
+from networkx.classes.tests import dispatch_interface
+
+
+class TestConnected:
+    @classmethod
+    def setup_class(cls):
+        G1 = cnlti(nx.grid_2d_graph(2, 2), first_label=0, ordering="sorted")
+        G2 = cnlti(nx.lollipop_graph(3, 3), first_label=4, ordering="sorted")
+        G3 = cnlti(nx.house_graph(), first_label=10, ordering="sorted")
+        cls.G = nx.union(G1, G2)
+        cls.G = nx.union(cls.G, G3)
+        cls.DG = nx.DiGraph([(1, 2), (1, 3), (2, 3)])
+        cls.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1)
+
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = [[3, 4, 5, 7], [1, 2, 8], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = [[2, 3, 4], [1]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = [[1, 2, 3]]
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = [[0], [1], [2], [3], [4], [5], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = [[0, 1, 2], [3, 4]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        C = []
+        cls.gc.append((G, C))
+
+    def test_connected_components(self):
+        # Test duplicated below
+        cc = nx.connected_components
+        G = self.G
+        C = {
+            frozenset([0, 1, 2, 3]),
+            frozenset([4, 5, 6, 7, 8, 9]),
+            frozenset([10, 11, 12, 13, 14]),
+        }
+        assert {frozenset(g) for g in cc(G)} == C
+
+    def test_connected_components_nx_loopback(self):
+        # This tests the @nx._dispatchable mechanism, treating nx.connected_components
+        # as if it were a re-implementation from another package.
+        # Test duplicated from above
+        cc = nx.connected_components
+        G = dispatch_interface.convert(self.G)
+        C = {
+            frozenset([0, 1, 2, 3]),
+            frozenset([4, 5, 6, 7, 8, 9]),
+            frozenset([10, 11, 12, 13, 14]),
+        }
+        if "nx_loopback" in nx.config.backends or not nx.config.backends:
+            # If `nx.config.backends` is empty, then `_dispatchable.__call__` takes a
+            # "fast path" and does not check graph inputs, so using an unknown backend
+            # here will still work.
+            assert {frozenset(g) for g in cc(G)} == C
+        else:
+            # This raises, because "nx_loopback" is not registered as a backend.
+            with pytest.raises(
+                ImportError, match="'nx_loopback' backend is not installed"
+            ):
+                cc(G)
+
+    def test_number_connected_components(self):
+        ncc = nx.number_connected_components
+        assert ncc(self.G) == 3
+
+    def test_number_connected_components2(self):
+        ncc = nx.number_connected_components
+        assert ncc(self.grid) == 1
+
+    def test_connected_components2(self):
+        cc = nx.connected_components
+        G = self.grid
+        C = {frozenset([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16])}
+        assert {frozenset(g) for g in cc(G)} == C
+
+    def test_node_connected_components(self):
+        ncc = nx.node_connected_component
+        G = self.grid
+        C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}
+        assert ncc(G, 1) == C
+
+    def test_is_connected(self):
+        assert nx.is_connected(self.grid)
+        G = nx.Graph()
+        G.add_nodes_from([1, 2])
+        assert not nx.is_connected(G)
+
+    def test_connected_raise(self):
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.connected_components(self.DG))
+        pytest.raises(NetworkXNotImplemented, nx.number_connected_components, self.DG)
+        pytest.raises(NetworkXNotImplemented, nx.node_connected_component, self.DG, 1)
+        pytest.raises(NetworkXNotImplemented, nx.is_connected, self.DG)
+        pytest.raises(nx.NetworkXPointlessConcept, nx.is_connected, nx.Graph())
+
+    def test_connected_mutability(self):
+        G = self.grid
+        seen = set()
+        for component in nx.connected_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_semiconnected.py

@@ -0,0 +1,55 @@
+from itertools import chain
+
+import pytest
+
+import networkx as nx
+
+
+class TestIsSemiconnected:
+    def test_undirected(self):
+        pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.Graph())
+        pytest.raises(nx.NetworkXNotImplemented, nx.is_semiconnected, nx.MultiGraph())
+
+    def test_empty(self):
+        pytest.raises(nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.DiGraph())
+        pytest.raises(
+            nx.NetworkXPointlessConcept, nx.is_semiconnected, nx.MultiDiGraph()
+        )
+
+    def test_single_node_graph(self):
+        G = nx.DiGraph()
+        G.add_node(0)
+        assert nx.is_semiconnected(G)
+
+    def test_path(self):
+        G = nx.path_graph(100, create_using=nx.DiGraph())
+        assert nx.is_semiconnected(G)
+        G.add_edge(100, 99)
+        assert not nx.is_semiconnected(G)
+
+    def test_cycle(self):
+        G = nx.cycle_graph(100, create_using=nx.DiGraph())
+        assert nx.is_semiconnected(G)
+        G = nx.path_graph(100, create_using=nx.DiGraph())
+        G.add_edge(0, 99)
+        assert nx.is_semiconnected(G)
+
+    def test_tree(self):
+        G = nx.DiGraph()
+        G.add_edges_from(
+            chain.from_iterable([(i, 2 * i + 1), (i, 2 * i + 2)] for i in range(100))
+        )
+        assert not nx.is_semiconnected(G)
+
+    def test_dumbbell(self):
+        G = nx.cycle_graph(100, create_using=nx.DiGraph())
+        G.add_edges_from((i + 100, (i + 1) % 100 + 100) for i in range(100))
+        assert not nx.is_semiconnected(G)  # G is disconnected.
+        G.add_edge(100, 99)
+        assert nx.is_semiconnected(G)
+
+    def test_alternating_path(self):
+        G = nx.DiGraph(
+            chain.from_iterable([(i, i - 1), (i, i + 1)] for i in range(0, 100, 2))
+        )
+        assert not nx.is_semiconnected(G)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_strongly_connected.py

@@ -0,0 +1,193 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestStronglyConnected:
+    @classmethod
+    def setup_class(cls):
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = {frozenset([3, 4, 5, 7]), frozenset([1, 2, 8]), frozenset([6])}
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = {frozenset([2, 3, 4]), frozenset([1])}
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = {frozenset([1, 2, 3])}
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = {
+            frozenset([0]),
+            frozenset([1]),
+            frozenset([2]),
+            frozenset([3]),
+            frozenset([4]),
+            frozenset([5]),
+            frozenset([6]),
+        }
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = {frozenset([0, 1, 2]), frozenset([3, 4])}
+        cls.gc.append((G, C))
+
+    def test_tarjan(self):
+        scc = nx.strongly_connected_components
+        for G, C in self.gc:
+            assert {frozenset(g) for g in scc(G)} == C
+
+    def test_kosaraju(self):
+        scc = nx.kosaraju_strongly_connected_components
+        for G, C in self.gc:
+            assert {frozenset(g) for g in scc(G)} == C
+
+    def test_number_strongly_connected_components(self):
+        ncc = nx.number_strongly_connected_components
+        for G, C in self.gc:
+            assert ncc(G) == len(C)
+
+    def test_is_strongly_connected(self):
+        for G, C in self.gc:
+            if len(C) == 1:
+                assert nx.is_strongly_connected(G)
+            else:
+                assert not nx.is_strongly_connected(G)
+
+    def test_contract_scc1(self):
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 11),
+                (2, 12),
+                (3, 4),
+                (4, 3),
+                (4, 5),
+                (5, 6),
+                (6, 5),
+                (6, 7),
+                (7, 8),
+                (7, 9),
+                (7, 10),
+                (8, 9),
+                (9, 7),
+                (10, 6),
+                (11, 2),
+                (11, 4),
+                (11, 6),
+                (12, 6),
+                (12, 11),
+            ]
+        )
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        # DAG
+        assert nx.is_directed_acyclic_graph(cG)
+        # nodes
+        assert sorted(cG.nodes()) == [0, 1, 2, 3]
+        # edges
+        mapping = {}
+        for i, component in enumerate(scc):
+            for n in component:
+                mapping[n] = i
+        edge = (mapping[2], mapping[3])
+        assert cG.has_edge(*edge)
+        edge = (mapping[2], mapping[5])
+        assert cG.has_edge(*edge)
+        edge = (mapping[3], mapping[5])
+        assert cG.has_edge(*edge)
+
+    def test_contract_scc_isolate(self):
+        # Bug found and fixed in [1687].
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        assert list(cG.nodes()) == [0]
+        assert list(cG.edges()) == []
+
+    def test_contract_scc_edge(self):
+        G = nx.DiGraph()
+        G.add_edge(1, 2)
+        G.add_edge(2, 1)
+        G.add_edge(2, 3)
+        G.add_edge(3, 4)
+        G.add_edge(4, 3)
+        scc = list(nx.strongly_connected_components(G))
+        cG = nx.condensation(G, scc)
+        assert sorted(cG.nodes()) == [0, 1]
+        if 1 in scc[0]:
+            edge = (0, 1)
+        else:
+            edge = (1, 0)
+        assert list(cG.edges()) == [edge]
+
+    def test_condensation_mapping_and_members(self):
+        G, C = self.gc[1]
+        C = sorted(C, key=len, reverse=True)
+        cG = nx.condensation(G)
+        mapping = cG.graph["mapping"]
+        assert all(n in G for n in mapping)
+        assert all(0 == cN for n, cN in mapping.items() if n in C[0])
+        assert all(1 == cN for n, cN in mapping.items() if n in C[1])
+        for n, d in cG.nodes(data=True):
+            assert set(C[n]) == cG.nodes[n]["members"]
+
+    def test_null_graph(self):
+        G = nx.DiGraph()
+        assert list(nx.strongly_connected_components(G)) == []
+        assert list(nx.kosaraju_strongly_connected_components(G)) == []
+        assert len(nx.condensation(G)) == 0
+        pytest.raises(
+            nx.NetworkXPointlessConcept, nx.is_strongly_connected, nx.DiGraph()
+        )
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.strongly_connected_components(G))
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.kosaraju_strongly_connected_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.is_strongly_connected, G)
+        pytest.raises(NetworkXNotImplemented, nx.condensation, G)
+
+    strong_cc_methods = (
+        nx.strongly_connected_components,
+        nx.kosaraju_strongly_connected_components,
+    )
+
+    @pytest.mark.parametrize("get_components", strong_cc_methods)
+    def test_connected_mutability(self, get_components):
+        DG = nx.path_graph(5, create_using=nx.DiGraph)
+        G = nx.disjoint_union(DG, DG)
+        seen = set()
+        for component in get_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()

minigpt2/lib/python3.10/site-packages/networkx/algorithms/components/tests/test_weakly_connected.py

@@ -0,0 +1,96 @@
+import pytest
+
+import networkx as nx
+from networkx import NetworkXNotImplemented
+
+
+class TestWeaklyConnected:
+    @classmethod
+    def setup_class(cls):
+        cls.gc = []
+        G = nx.DiGraph()
+        G.add_edges_from(
+            [
+                (1, 2),
+                (2, 3),
+                (2, 8),
+                (3, 4),
+                (3, 7),
+                (4, 5),
+                (5, 3),
+                (5, 6),
+                (7, 4),
+                (7, 6),
+                (8, 1),
+                (8, 7),
+            ]
+        )
+        C = [[3, 4, 5, 7], [1, 2, 8], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (1, 3), (1, 4), (4, 2), (3, 4), (2, 3)])
+        C = [[2, 3, 4], [1]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph()
+        G.add_edges_from([(1, 2), (2, 3), (3, 2), (2, 1)])
+        C = [[1, 2, 3]]
+        cls.gc.append((G, C))
+
+        # Eppstein's tests
+        G = nx.DiGraph({0: [1], 1: [2, 3], 2: [4, 5], 3: [4, 5], 4: [6], 5: [], 6: []})
+        C = [[0], [1], [2], [3], [4], [5], [6]]
+        cls.gc.append((G, C))
+
+        G = nx.DiGraph({0: [1], 1: [2, 3, 4], 2: [0, 3], 3: [4], 4: [3]})
+        C = [[0, 1, 2], [3, 4]]
+        cls.gc.append((G, C))
+
+    def test_weakly_connected_components(self):
+        for G, C in self.gc:
+            U = G.to_undirected()
+            w = {frozenset(g) for g in nx.weakly_connected_components(G)}
+            c = {frozenset(g) for g in nx.connected_components(U)}
+            assert w == c
+
+    def test_number_weakly_connected_components(self):
+        for G, C in self.gc:
+            U = G.to_undirected()
+            w = nx.number_weakly_connected_components(G)
+            c = nx.number_connected_components(U)
+            assert w == c
+
+    def test_is_weakly_connected(self):
+        for G, C in self.gc:
+            U = G.to_undirected()
+            assert nx.is_weakly_connected(G) == nx.is_connected(U)
+
+    def test_null_graph(self):
+        G = nx.DiGraph()
+        assert list(nx.weakly_connected_components(G)) == []
+        assert nx.number_weakly_connected_components(G) == 0
+        with pytest.raises(nx.NetworkXPointlessConcept):
+            next(nx.is_weakly_connected(G))
+
+    def test_connected_raise(self):
+        G = nx.Graph()
+        with pytest.raises(NetworkXNotImplemented):
+            next(nx.weakly_connected_components(G))
+        pytest.raises(NetworkXNotImplemented, nx.number_weakly_connected_components, G)
+        pytest.raises(NetworkXNotImplemented, nx.is_weakly_connected, G)
+
+    def test_connected_mutability(self):
+        DG = nx.path_graph(5, create_using=nx.DiGraph)
+        G = nx.disjoint_union(DG, DG)
+        seen = set()
+        for component in nx.weakly_connected_components(G):
+            assert len(seen & component) == 0
+            seen.update(component)
+            component.clear()
+
+
+def test_is_weakly_connected_empty_graph_raises():
+    G = nx.DiGraph()
+    with pytest.raises(nx.NetworkXPointlessConcept, match="Connectivity is undefined"):
+        nx.is_weakly_connected(G)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/__init__.py

@@ -0,0 +1,4 @@
+from networkx.algorithms.operators.all import *
+from networkx.algorithms.operators.binary import *
+from networkx.algorithms.operators.product import *
+from networkx.algorithms.operators.unary import *

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/all.py

@@ -0,0 +1,321 @@
+"""Operations on many graphs."""
+
+from itertools import chain, repeat
+
+import networkx as nx
+
+__all__ = ["union_all", "compose_all", "disjoint_union_all", "intersection_all"]
+
+
+@nx._dispatchable(graphs="[graphs]", preserve_all_attrs=True, returns_graph=True)
+def union_all(graphs, rename=()):
+    """Returns the union of all graphs.
+
+    The graphs must be disjoint, otherwise an exception is raised.
+
+    Parameters
+    ----------
+    graphs : iterable
+       Iterable of NetworkX graphs
+
+    rename : iterable , optional
+       Node names of graphs can be changed by specifying the tuple
+       rename=('G-','H-') (for example).  Node "u" in G is then renamed
+       "G-u" and "v" in H is renamed "H-v". Infinite generators (like itertools.count)
+       are also supported.
+
+    Returns
+    -------
+    U : a graph with the same type as the first graph in list
+
+    Raises
+    ------
+    ValueError
+       If `graphs` is an empty list.
+
+    NetworkXError
+        In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.
+
+    Notes
+    -----
+    For operating on mixed type graphs, they should be converted to the same type.
+    >>> G = nx.Graph()
+    >>> H = nx.DiGraph()
+    >>> GH = union_all([nx.DiGraph(G), H])
+
+    To force a disjoint union with node relabeling, use
+    disjoint_union_all(G,H) or convert_node_labels_to integers().
+
+    Graph, edge, and node attributes are propagated to the union graph.
+    If a graph attribute is present in multiple graphs, then the value
+    from the last graph in the list with that attribute is used.
+
+    Examples
+    --------
+    >>> G1 = nx.Graph([(1, 2), (2, 3)])
+    >>> G2 = nx.Graph([(4, 5), (5, 6)])
+    >>> result_graph = nx.union_all([G1, G2])
+    >>> result_graph.nodes()
+    NodeView((1, 2, 3, 4, 5, 6))
+    >>> result_graph.edges()
+    EdgeView([(1, 2), (2, 3), (4, 5), (5, 6)])
+
+    See Also
+    --------
+    union
+    disjoint_union_all
+    """
+    R = None
+    seen_nodes = set()
+
+    # rename graph to obtain disjoint node labels
+    def add_prefix(graph, prefix):
+        if prefix is None:
+            return graph
+
+        def label(x):
+            return f"{prefix}{x}"
+
+        return nx.relabel_nodes(graph, label)
+
+    rename = chain(rename, repeat(None))
+    graphs = (add_prefix(G, name) for G, name in zip(graphs, rename))
+
+    for i, G in enumerate(graphs):
+        G_nodes_set = set(G.nodes)
+        if i == 0:
+            # Union is the same type as first graph
+            R = G.__class__()
+        elif G.is_directed() != R.is_directed():
+            raise nx.NetworkXError("All graphs must be directed or undirected.")
+        elif G.is_multigraph() != R.is_multigraph():
+            raise nx.NetworkXError("All graphs must be graphs or multigraphs.")
+        elif not seen_nodes.isdisjoint(G_nodes_set):
+            raise nx.NetworkXError(
+                "The node sets of the graphs are not disjoint.\n"
+                "Use `rename` to specify prefixes for the graphs or use\n"
+                "disjoint_union(G1, G2, ..., GN)."
+            )
+
+        seen_nodes |= G_nodes_set
+        R.graph.update(G.graph)
+        R.add_nodes_from(G.nodes(data=True))
+        R.add_edges_from(
+            G.edges(keys=True, data=True) if G.is_multigraph() else G.edges(data=True)
+        )
+
+    if R is None:
+        raise ValueError("cannot apply union_all to an empty list")
+
+    return R
+
+
+@nx._dispatchable(graphs="[graphs]", preserve_all_attrs=True, returns_graph=True)
+def disjoint_union_all(graphs):
+    """Returns the disjoint union of all graphs.
+
+    This operation forces distinct integer node labels starting with 0
+    for the first graph in the list and numbering consecutively.
+
+    Parameters
+    ----------
+    graphs : iterable
+       Iterable of NetworkX graphs
+
+    Returns
+    -------
+    U : A graph with the same type as the first graph in list
+
+    Raises
+    ------
+    ValueError
+       If `graphs` is an empty list.
+
+    NetworkXError
+        In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.
+
+    Examples
+    --------
+    >>> G1 = nx.Graph([(1, 2), (2, 3)])
+    >>> G2 = nx.Graph([(4, 5), (5, 6)])
+    >>> U = nx.disjoint_union_all([G1, G2])
+    >>> list(U.nodes())
+    [0, 1, 2, 3, 4, 5]
+    >>> list(U.edges())
+    [(0, 1), (1, 2), (3, 4), (4, 5)]
+
+    Notes
+    -----
+    For operating on mixed type graphs, they should be converted to the same type.
+
+    Graph, edge, and node attributes are propagated to the union graph.
+    If a graph attribute is present in multiple graphs, then the value
+    from the last graph in the list with that attribute is used.
+    """
+
+    def yield_relabeled(graphs):
+        first_label = 0
+        for G in graphs:
+            yield nx.convert_node_labels_to_integers(G, first_label=first_label)
+            first_label += len(G)
+
+    R = union_all(yield_relabeled(graphs))
+
+    return R
+
+
+@nx._dispatchable(graphs="[graphs]", preserve_all_attrs=True, returns_graph=True)
+def compose_all(graphs):
+    """Returns the composition of all graphs.
+
+    Composition is the simple union of the node sets and edge sets.
+    The node sets of the supplied graphs need not be disjoint.
+
+    Parameters
+    ----------
+    graphs : iterable
+       Iterable of NetworkX graphs
+
+    Returns
+    -------
+    C : A graph with the same type as the first graph in list
+
+    Raises
+    ------
+    ValueError
+       If `graphs` is an empty list.
+
+    NetworkXError
+        In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.
+
+    Examples
+    --------
+    >>> G1 = nx.Graph([(1, 2), (2, 3)])
+    >>> G2 = nx.Graph([(3, 4), (5, 6)])
+    >>> C = nx.compose_all([G1, G2])
+    >>> list(C.nodes())
+    [1, 2, 3, 4, 5, 6]
+    >>> list(C.edges())
+    [(1, 2), (2, 3), (3, 4), (5, 6)]
+
+    Notes
+    -----
+    For operating on mixed type graphs, they should be converted to the same type.
+
+    Graph, edge, and node attributes are propagated to the union graph.
+    If a graph attribute is present in multiple graphs, then the value
+    from the last graph in the list with that attribute is used.
+    """
+    R = None
+
+    # add graph attributes, H attributes take precedent over G attributes
+    for i, G in enumerate(graphs):
+        if i == 0:
+            # create new graph
+            R = G.__class__()
+        elif G.is_directed() != R.is_directed():
+            raise nx.NetworkXError("All graphs must be directed or undirected.")
+        elif G.is_multigraph() != R.is_multigraph():
+            raise nx.NetworkXError("All graphs must be graphs or multigraphs.")
+
+        R.graph.update(G.graph)
+        R.add_nodes_from(G.nodes(data=True))
+        R.add_edges_from(
+            G.edges(keys=True, data=True) if G.is_multigraph() else G.edges(data=True)
+        )
+
+    if R is None:
+        raise ValueError("cannot apply compose_all to an empty list")
+
+    return R
+
+
+@nx._dispatchable(graphs="[graphs]", returns_graph=True)
+def intersection_all(graphs):
+    """Returns a new graph that contains only the nodes and the edges that exist in
+    all graphs.
+
+    Parameters
+    ----------
+    graphs : iterable
+       Iterable of NetworkX graphs
+
+    Returns
+    -------
+    R : A new graph with the same type as the first graph in list
+
+    Raises
+    ------
+    ValueError
+       If `graphs` is an empty list.
+
+    NetworkXError
+        In case of mixed type graphs, like MultiGraph and Graph, or directed and undirected graphs.
+
+    Notes
+    -----
+    For operating on mixed type graphs, they should be converted to the same type.
+
+    Attributes from the graph, nodes, and edges are not copied to the new
+    graph.
+
+    The resulting graph can be updated with attributes if desired. For example, code which adds the minimum attribute for each node across all graphs could work.
+    >>> g = nx.Graph()
+    >>> g.add_node(0, capacity=4)
+    >>> g.add_node(1, capacity=3)
+    >>> g.add_edge(0, 1)
+
+    >>> h = g.copy()
+    >>> h.nodes[0]["capacity"] = 2
+
+    >>> gh = nx.intersection_all([g, h])
+
+    >>> new_node_attr = {
+    ...     n: min(*(anyG.nodes[n].get("capacity", float("inf")) for anyG in [g, h]))
+    ...     for n in gh
+    ... }
+    >>> nx.set_node_attributes(gh, new_node_attr, "new_capacity")
+    >>> gh.nodes(data=True)
+    NodeDataView({0: {'new_capacity': 2}, 1: {'new_capacity': 3}})
+
+    Examples
+    --------
+    >>> G1 = nx.Graph([(1, 2), (2, 3)])
+    >>> G2 = nx.Graph([(2, 3), (3, 4)])
+    >>> R = nx.intersection_all([G1, G2])
+    >>> list(R.nodes())
+    [2, 3]
+    >>> list(R.edges())
+    [(2, 3)]
+
+    """
+    R = None
+
+    for i, G in enumerate(graphs):
+        G_nodes_set = set(G.nodes)
+        G_edges_set = set(G.edges)
+        if not G.is_directed():
+            if G.is_multigraph():
+                G_edges_set.update((v, u, k) for u, v, k in list(G_edges_set))
+            else:
+                G_edges_set.update((v, u) for u, v in list(G_edges_set))
+        if i == 0:
+            # create new graph
+            R = G.__class__()
+            node_intersection = G_nodes_set
+            edge_intersection = G_edges_set
+        elif G.is_directed() != R.is_directed():
+            raise nx.NetworkXError("All graphs must be directed or undirected.")
+        elif G.is_multigraph() != R.is_multigraph():
+            raise nx.NetworkXError("All graphs must be graphs or multigraphs.")
+        else:
+            node_intersection &= G_nodes_set
+            edge_intersection &= G_edges_set
+
+    if R is None:
+        raise ValueError("cannot apply intersection_all to an empty list")
+
+    R.add_nodes_from(node_intersection)
+    R.add_edges_from(edge_intersection)
+
+    return R

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/binary.py

@@ -0,0 +1,450 @@
+"""
+Operations on graphs including union, intersection, difference.
+"""
+
+import networkx as nx
+
+__all__ = [
+    "union",
+    "compose",
+    "disjoint_union",
+    "intersection",
+    "difference",
+    "symmetric_difference",
+    "full_join",
+]
+_G_H = {"G": 0, "H": 1}
+
+
+@nx._dispatchable(graphs=_G_H, preserve_all_attrs=True, returns_graph=True)
+def union(G, H, rename=()):
+    """Combine graphs G and H. The names of nodes must be unique.
+
+    A name collision between the graphs will raise an exception.
+
+    A renaming facility is provided to avoid name collisions.
+
+
+    Parameters
+    ----------
+    G, H : graph
+       A NetworkX graph
+
+    rename : iterable , optional
+       Node names of G and H can be changed by specifying the tuple
+       rename=('G-','H-') (for example).  Node "u" in G is then renamed
+       "G-u" and "v" in H is renamed "H-v".
+
+    Returns
+    -------
+    U : A union graph with the same type as G.
+
+    See Also
+    --------
+    compose
+    :func:`~networkx.Graph.update`
+    disjoint_union
+
+    Notes
+    -----
+    To combine graphs that have common nodes, consider compose(G, H)
+    or the method, Graph.update().
+
+    disjoint_union() is similar to union() except that it avoids name clashes
+    by relabeling the nodes with sequential integers.
+
+    Edge and node attributes are propagated from G and H to the union graph.
+    Graph attributes are also propagated, but if they are present in both G and H,
+    then the value from H is used.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (1, 2)])
+    >>> H = nx.Graph([(0, 1), (0, 3), (1, 3), (1, 2)])
+    >>> U = nx.union(G, H, rename=("G", "H"))
+    >>> U.nodes
+    NodeView(('G0', 'G1', 'G2', 'H0', 'H1', 'H3', 'H2'))
+    >>> U.edges
+    EdgeView([('G0', 'G1'), ('G0', 'G2'), ('G1', 'G2'), ('H0', 'H1'), ('H0', 'H3'), ('H1', 'H3'), ('H1', 'H2')])
+
+
+    """
+    return nx.union_all([G, H], rename)
+
+
+@nx._dispatchable(graphs=_G_H, preserve_all_attrs=True, returns_graph=True)
+def disjoint_union(G, H):
+    """Combine graphs G and H. The nodes are assumed to be unique (disjoint).
+
+    This algorithm automatically relabels nodes to avoid name collisions.
+
+    Parameters
+    ----------
+    G,H : graph
+       A NetworkX graph
+
+    Returns
+    -------
+    U : A union graph with the same type as G.
+
+    See Also
+    --------
+    union
+    compose
+    :func:`~networkx.Graph.update`
+
+    Notes
+    -----
+    A new graph is created, of the same class as G.  It is recommended
+    that G and H be either both directed or both undirected.
+
+    The nodes of G are relabeled 0 to len(G)-1, and the nodes of H are
+    relabeled len(G) to len(G)+len(H)-1.
+
+    Renumbering forces G and H to be disjoint, so no exception is ever raised for a name collision.
+    To preserve the check for common nodes, use union().
+
+    Edge and node attributes are propagated from G and H to the union graph.
+    Graph attributes are also propagated, but if they are present in both G and H,
+    then the value from H is used.
+
+    To combine graphs that have common nodes, consider compose(G, H)
+    or the method, Graph.update().
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (1, 2)])
+    >>> H = nx.Graph([(0, 3), (1, 2), (2, 3)])
+    >>> G.nodes[0]["key1"] = 5
+    >>> H.nodes[0]["key2"] = 10
+    >>> U = nx.disjoint_union(G, H)
+    >>> U.nodes(data=True)
+    NodeDataView({0: {'key1': 5}, 1: {}, 2: {}, 3: {'key2': 10}, 4: {}, 5: {}, 6: {}})
+    >>> U.edges
+    EdgeView([(0, 1), (0, 2), (1, 2), (3, 4), (4, 6), (5, 6)])
+    """
+    return nx.disjoint_union_all([G, H])
+
+
+@nx._dispatchable(graphs=_G_H, returns_graph=True)
+def intersection(G, H):
+    """Returns a new graph that contains only the nodes and the edges that exist in
+    both G and H.
+
+    Parameters
+    ----------
+    G,H : graph
+       A NetworkX graph. G and H can have different node sets but must be both graphs or both multigraphs.
+
+    Raises
+    ------
+    NetworkXError
+        If one is a MultiGraph and the other one is a graph.
+
+    Returns
+    -------
+    GH : A new graph with the same type as G.
+
+    Notes
+    -----
+    Attributes from the graph, nodes, and edges are not copied to the new
+    graph.  If you want a new graph of the intersection of G and H
+    with the attributes (including edge data) from G use remove_nodes_from()
+    as follows
+
+    >>> G = nx.path_graph(3)
+    >>> H = nx.path_graph(5)
+    >>> R = G.copy()
+    >>> R.remove_nodes_from(n for n in G if n not in H)
+    >>> R.remove_edges_from(e for e in G.edges if e not in H.edges)
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (1, 2)])
+    >>> H = nx.Graph([(0, 3), (1, 2), (2, 3)])
+    >>> R = nx.intersection(G, H)
+    >>> R.nodes
+    NodeView((0, 1, 2))
+    >>> R.edges
+    EdgeView([(1, 2)])
+    """
+    return nx.intersection_all([G, H])
+
+
+@nx._dispatchable(graphs=_G_H, returns_graph=True)
+def difference(G, H):
+    """Returns a new graph that contains the edges that exist in G but not in H.
+
+    The node sets of H and G must be the same.
+
+    Parameters
+    ----------
+    G,H : graph
+       A NetworkX graph. G and H must have the same node sets.
+
+    Returns
+    -------
+    D : A new graph with the same type as G.
+
+    Notes
+    -----
+    Attributes from the graph, nodes, and edges are not copied to the new
+    graph.  If you want a new graph of the difference of G and H with
+    the attributes (including edge data) from G use remove_nodes_from()
+    as follows:
+
+    >>> G = nx.path_graph(3)
+    >>> H = nx.path_graph(5)
+    >>> R = G.copy()
+    >>> R.remove_nodes_from(n for n in G if n in H)
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3)])
+    >>> H = nx.Graph([(0, 1), (1, 2), (0, 3)])
+    >>> R = nx.difference(G, H)
+    >>> R.nodes
+    NodeView((0, 1, 2, 3))
+    >>> R.edges
+    EdgeView([(0, 2), (1, 3)])
+    """
+    # create new graph
+    if not G.is_multigraph() == H.is_multigraph():
+        raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
+    R = nx.create_empty_copy(G, with_data=False)
+
+    if set(G) != set(H):
+        raise nx.NetworkXError("Node sets of graphs not equal")
+
+    if G.is_multigraph():
+        edges = G.edges(keys=True)
+    else:
+        edges = G.edges()
+    for e in edges:
+        if not H.has_edge(*e):
+            R.add_edge(*e)
+    return R
+
+
+@nx._dispatchable(graphs=_G_H, returns_graph=True)
+def symmetric_difference(G, H):
+    """Returns new graph with edges that exist in either G or H but not both.
+
+    The node sets of H and G must be the same.
+
+    Parameters
+    ----------
+    G,H : graph
+       A NetworkX graph.  G and H must have the same node sets.
+
+    Returns
+    -------
+    D : A new graph with the same type as G.
+
+    Notes
+    -----
+    Attributes from the graph, nodes, and edges are not copied to the new
+    graph.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2), (1, 2), (1, 3)])
+    >>> H = nx.Graph([(0, 1), (1, 2), (0, 3)])
+    >>> R = nx.symmetric_difference(G, H)
+    >>> R.nodes
+    NodeView((0, 1, 2, 3))
+    >>> R.edges
+    EdgeView([(0, 2), (0, 3), (1, 3)])
+    """
+    # create new graph
+    if not G.is_multigraph() == H.is_multigraph():
+        raise nx.NetworkXError("G and H must both be graphs or multigraphs.")
+    R = nx.create_empty_copy(G, with_data=False)
+
+    if set(G) != set(H):
+        raise nx.NetworkXError("Node sets of graphs not equal")
+
+    gnodes = set(G)  # set of nodes in G
+    hnodes = set(H)  # set of nodes in H
+    nodes = gnodes.symmetric_difference(hnodes)
+    R.add_nodes_from(nodes)
+
+    if G.is_multigraph():
+        edges = G.edges(keys=True)
+    else:
+        edges = G.edges()
+    # we could copy the data here but then this function doesn't
+    # match intersection and difference
+    for e in edges:
+        if not H.has_edge(*e):
+            R.add_edge(*e)
+
+    if H.is_multigraph():
+        edges = H.edges(keys=True)
+    else:
+        edges = H.edges()
+    for e in edges:
+        if not G.has_edge(*e):
+            R.add_edge(*e)
+    return R
+
+
+@nx._dispatchable(graphs=_G_H, preserve_all_attrs=True, returns_graph=True)
+def compose(G, H):
+    """Compose graph G with H by combining nodes and edges into a single graph.
+
+    The node sets and edges sets do not need to be disjoint.
+
+    Composing preserves the attributes of nodes and edges.
+    Attribute values from H take precedent over attribute values from G.
+
+    Parameters
+    ----------
+    G, H : graph
+       A NetworkX graph
+
+    Returns
+    -------
+    C: A new graph with the same type as G
+
+    See Also
+    --------
+    :func:`~networkx.Graph.update`
+    union
+    disjoint_union
+
+    Notes
+    -----
+    It is recommended that G and H be either both directed or both undirected.
+
+    For MultiGraphs, the edges are identified by incident nodes AND edge-key.
+    This can cause surprises (i.e., edge `(1, 2)` may or may not be the same
+    in two graphs) if you use MultiGraph without keeping track of edge keys.
+
+    If combining the attributes of common nodes is not desired, consider union(),
+    which raises an exception for name collisions.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2)])
+    >>> H = nx.Graph([(0, 1), (1, 2)])
+    >>> R = nx.compose(G, H)
+    >>> R.nodes
+    NodeView((0, 1, 2))
+    >>> R.edges
+    EdgeView([(0, 1), (0, 2), (1, 2)])
+
+    By default, the attributes from `H` take precedent over attributes from `G`.
+    If you prefer another way of combining attributes, you can update them after the compose operation:
+
+    >>> G = nx.Graph([(0, 1, {"weight": 2.0}), (3, 0, {"weight": 100.0})])
+    >>> H = nx.Graph([(0, 1, {"weight": 10.0}), (1, 2, {"weight": -1.0})])
+    >>> nx.set_node_attributes(G, {0: "dark", 1: "light", 3: "black"}, name="color")
+    >>> nx.set_node_attributes(H, {0: "green", 1: "orange", 2: "yellow"}, name="color")
+    >>> GcomposeH = nx.compose(G, H)
+
+    Normally, color attribute values of nodes of GcomposeH come from H. We can workaround this as follows:
+
+    >>> node_data = {
+    ...     n: G.nodes[n]["color"] + " " + H.nodes[n]["color"]
+    ...     for n in G.nodes & H.nodes
+    ... }
+    >>> nx.set_node_attributes(GcomposeH, node_data, "color")
+    >>> print(GcomposeH.nodes[0]["color"])
+    dark green
+
+    >>> print(GcomposeH.nodes[3]["color"])
+    black
+
+    Similarly, we can update edge attributes after the compose operation in a way we prefer:
+
+    >>> edge_data = {
+    ...     e: G.edges[e]["weight"] * H.edges[e]["weight"] for e in G.edges & H.edges
+    ... }
+    >>> nx.set_edge_attributes(GcomposeH, edge_data, "weight")
+    >>> print(GcomposeH.edges[(0, 1)]["weight"])
+    20.0
+
+    >>> print(GcomposeH.edges[(3, 0)]["weight"])
+    100.0
+    """
+    return nx.compose_all([G, H])
+
+
+@nx._dispatchable(graphs=_G_H, preserve_all_attrs=True, returns_graph=True)
+def full_join(G, H, rename=(None, None)):
+    """Returns the full join of graphs G and H.
+
+    Full join is the union of G and H in which all edges between
+    G and H are added.
+    The node sets of G and H must be disjoint,
+    otherwise an exception is raised.
+
+    Parameters
+    ----------
+    G, H : graph
+       A NetworkX graph
+
+    rename : tuple , default=(None, None)
+       Node names of G and H can be changed by specifying the tuple
+       rename=('G-','H-') (for example).  Node "u" in G is then renamed
+       "G-u" and "v" in H is renamed "H-v".
+
+    Returns
+    -------
+    U : The full join graph with the same type as G.
+
+    Notes
+    -----
+    It is recommended that G and H be either both directed or both undirected.
+
+    If G is directed, then edges from G to H are added as well as from H to G.
+
+    Note that full_join() does not produce parallel edges for MultiGraphs.
+
+    The full join operation of graphs G and H is the same as getting
+    their complement, performing a disjoint union, and finally getting
+    the complement of the resulting graph.
+
+    Graph, edge, and node attributes are propagated from G and H
+    to the union graph.  If a graph attribute is present in both
+    G and H the value from H is used.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(0, 1), (0, 2)])
+    >>> H = nx.Graph([(3, 4)])
+    >>> R = nx.full_join(G, H, rename=("G", "H"))
+    >>> R.nodes
+    NodeView(('G0', 'G1', 'G2', 'H3', 'H4'))
+    >>> R.edges
+    EdgeView([('G0', 'G1'), ('G0', 'G2'), ('G0', 'H3'), ('G0', 'H4'), ('G1', 'H3'), ('G1', 'H4'), ('G2', 'H3'), ('G2', 'H4'), ('H3', 'H4')])
+
+    See Also
+    --------
+    union
+    disjoint_union
+    """
+    R = union(G, H, rename)
+
+    def add_prefix(graph, prefix):
+        if prefix is None:
+            return graph
+
+        def label(x):
+            return f"{prefix}{x}"
+
+        return nx.relabel_nodes(graph, label)
+
+    G = add_prefix(G, rename[0])
+    H = add_prefix(H, rename[1])
+
+    for i in G:
+        for j in H:
+            R.add_edge(i, j)
+    if R.is_directed():
+        for i in H:
+            for j in G:
+                R.add_edge(i, j)
+
+    return R

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/product.py

@@ -0,0 +1,633 @@
+"""
+Graph products.
+"""
+
+from itertools import product
+
+import networkx as nx
+from networkx.utils import not_implemented_for
+
+__all__ = [
+    "tensor_product",
+    "cartesian_product",
+    "lexicographic_product",
+    "strong_product",
+    "power",
+    "rooted_product",
+    "corona_product",
+    "modular_product",
+]
+_G_H = {"G": 0, "H": 1}
+
+
+def _dict_product(d1, d2):
+    return {k: (d1.get(k), d2.get(k)) for k in set(d1) | set(d2)}
+
+
+# Generators for producing graph products
+def _node_product(G, H):
+    for u, v in product(G, H):
+        yield ((u, v), _dict_product(G.nodes[u], H.nodes[v]))
+
+
+def _directed_edges_cross_edges(G, H):
+    if not G.is_multigraph() and not H.is_multigraph():
+        for u, v, c in G.edges(data=True):
+            for x, y, d in H.edges(data=True):
+                yield (u, x), (v, y), _dict_product(c, d)
+    if not G.is_multigraph() and H.is_multigraph():
+        for u, v, c in G.edges(data=True):
+            for x, y, k, d in H.edges(data=True, keys=True):
+                yield (u, x), (v, y), k, _dict_product(c, d)
+    if G.is_multigraph() and not H.is_multigraph():
+        for u, v, k, c in G.edges(data=True, keys=True):
+            for x, y, d in H.edges(data=True):
+                yield (u, x), (v, y), k, _dict_product(c, d)
+    if G.is_multigraph() and H.is_multigraph():
+        for u, v, j, c in G.edges(data=True, keys=True):
+            for x, y, k, d in H.edges(data=True, keys=True):
+                yield (u, x), (v, y), (j, k), _dict_product(c, d)
+
+
+def _undirected_edges_cross_edges(G, H):
+    if not G.is_multigraph() and not H.is_multigraph():
+        for u, v, c in G.edges(data=True):
+            for x, y, d in H.edges(data=True):
+                yield (v, x), (u, y), _dict_product(c, d)
+    if not G.is_multigraph() and H.is_multigraph():
+        for u, v, c in G.edges(data=True):
+            for x, y, k, d in H.edges(data=True, keys=True):
+                yield (v, x), (u, y), k, _dict_product(c, d)
+    if G.is_multigraph() and not H.is_multigraph():
+        for u, v, k, c in G.edges(data=True, keys=True):
+            for x, y, d in H.edges(data=True):
+                yield (v, x), (u, y), k, _dict_product(c, d)
+    if G.is_multigraph() and H.is_multigraph():
+        for u, v, j, c in G.edges(data=True, keys=True):
+            for x, y, k, d in H.edges(data=True, keys=True):
+                yield (v, x), (u, y), (j, k), _dict_product(c, d)
+
+
+def _edges_cross_nodes(G, H):
+    if G.is_multigraph():
+        for u, v, k, d in G.edges(data=True, keys=True):
+            for x in H:
+                yield (u, x), (v, x), k, d
+    else:
+        for u, v, d in G.edges(data=True):
+            for x in H:
+                if H.is_multigraph():
+                    yield (u, x), (v, x), None, d
+                else:
+                    yield (u, x), (v, x), d
+
+
+def _nodes_cross_edges(G, H):
+    if H.is_multigraph():
+        for x in G:
+            for u, v, k, d in H.edges(data=True, keys=True):
+                yield (x, u), (x, v), k, d
+    else:
+        for x in G:
+            for u, v, d in H.edges(data=True):
+                if G.is_multigraph():
+                    yield (x, u), (x, v), None, d
+                else:
+                    yield (x, u), (x, v), d
+
+
+def _edges_cross_nodes_and_nodes(G, H):
+    if G.is_multigraph():
+        for u, v, k, d in G.edges(data=True, keys=True):
+            for x in H:
+                for y in H:
+                    yield (u, x), (v, y), k, d
+    else:
+        for u, v, d in G.edges(data=True):
+            for x in H:
+                for y in H:
+                    if H.is_multigraph():
+                        yield (u, x), (v, y), None, d
+                    else:
+                        yield (u, x), (v, y), d
+
+
+def _init_product_graph(G, H):
+    if G.is_directed() != H.is_directed():
+        msg = "G and H must be both directed or both undirected"
+        raise nx.NetworkXError(msg)
+    if G.is_multigraph() or H.is_multigraph():
+        GH = nx.MultiGraph()
+    else:
+        GH = nx.Graph()
+    if G.is_directed():
+        GH = GH.to_directed()
+    return GH
+
+
+@nx._dispatchable(graphs=_G_H, preserve_node_attrs=True, returns_graph=True)
+def tensor_product(G, H):
+    r"""Returns the tensor product of G and H.
+
+    The tensor product $P$ of the graphs $G$ and $H$ has a node set that
+    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
+    $P$ has an edge $((u,v), (x,y))$ if and only if $(u,x)$ is an edge in $G$
+    and $(v,y)$ is an edge in $H$.
+
+    Tensor product is sometimes also referred to as the categorical product,
+    direct product, cardinal product or conjunction.
+
+
+    Parameters
+    ----------
+    G, H: graphs
+     Networkx graphs.
+
+    Returns
+    -------
+    P: NetworkX graph
+     The tensor product of G and H. P will be a multi-graph if either G
+     or H is a multi-graph, will be a directed if G and H are directed,
+     and undirected if G and H are undirected.
+
+    Raises
+    ------
+    NetworkXError
+     If G and H are not both directed or both undirected.
+
+    Notes
+    -----
+    Node attributes in P are two-tuple of the G and H node attributes.
+    Missing attributes are assigned None.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> H = nx.Graph()
+    >>> G.add_node(0, a1=True)
+    >>> H.add_node("a", a2="Spam")
+    >>> P = nx.tensor_product(G, H)
+    >>> list(P)
+    [(0, 'a')]
+
+    Edge attributes and edge keys (for multigraphs) are also copied to the
+    new product graph
+    """
+    GH = _init_product_graph(G, H)
+    GH.add_nodes_from(_node_product(G, H))
+    GH.add_edges_from(_directed_edges_cross_edges(G, H))
+    if not GH.is_directed():
+        GH.add_edges_from(_undirected_edges_cross_edges(G, H))
+    return GH
+
+
+@nx._dispatchable(graphs=_G_H, preserve_node_attrs=True, returns_graph=True)
+def cartesian_product(G, H):
+    r"""Returns the Cartesian product of G and H.
+
+    The Cartesian product $P$ of the graphs $G$ and $H$ has a node set that
+    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
+    $P$ has an edge $((u,v),(x,y))$ if and only if either $u$ is equal to $x$
+    and both $v$ and $y$ are adjacent in $H$ or if $v$ is equal to $y$ and
+    both $u$ and $x$ are adjacent in $G$.
+
+    Parameters
+    ----------
+    G, H: graphs
+     Networkx graphs.
+
+    Returns
+    -------
+    P: NetworkX graph
+     The Cartesian product of G and H. P will be a multi-graph if either G
+     or H is a multi-graph. Will be a directed if G and H are directed,
+     and undirected if G and H are undirected.
+
+    Raises
+    ------
+    NetworkXError
+     If G and H are not both directed or both undirected.
+
+    Notes
+    -----
+    Node attributes in P are two-tuple of the G and H node attributes.
+    Missing attributes are assigned None.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> H = nx.Graph()
+    >>> G.add_node(0, a1=True)
+    >>> H.add_node("a", a2="Spam")
+    >>> P = nx.cartesian_product(G, H)
+    >>> list(P)
+    [(0, 'a')]
+
+    Edge attributes and edge keys (for multigraphs) are also copied to the
+    new product graph
+    """
+    GH = _init_product_graph(G, H)
+    GH.add_nodes_from(_node_product(G, H))
+    GH.add_edges_from(_edges_cross_nodes(G, H))
+    GH.add_edges_from(_nodes_cross_edges(G, H))
+    return GH
+
+
+@nx._dispatchable(graphs=_G_H, preserve_node_attrs=True, returns_graph=True)
+def lexicographic_product(G, H):
+    r"""Returns the lexicographic product of G and H.
+
+    The lexicographical product $P$ of the graphs $G$ and $H$ has a node set
+    that is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
+    $P$ has an edge $((u,v), (x,y))$ if and only if $(u,v)$ is an edge in $G$
+    or $u==v$ and $(x,y)$ is an edge in $H$.
+
+    Parameters
+    ----------
+    G, H: graphs
+     Networkx graphs.
+
+    Returns
+    -------
+    P: NetworkX graph
+     The Cartesian product of G and H. P will be a multi-graph if either G
+     or H is a multi-graph. Will be a directed if G and H are directed,
+     and undirected if G and H are undirected.
+
+    Raises
+    ------
+    NetworkXError
+     If G and H are not both directed or both undirected.
+
+    Notes
+    -----
+    Node attributes in P are two-tuple of the G and H node attributes.
+    Missing attributes are assigned None.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> H = nx.Graph()
+    >>> G.add_node(0, a1=True)
+    >>> H.add_node("a", a2="Spam")
+    >>> P = nx.lexicographic_product(G, H)
+    >>> list(P)
+    [(0, 'a')]
+
+    Edge attributes and edge keys (for multigraphs) are also copied to the
+    new product graph
+    """
+    GH = _init_product_graph(G, H)
+    GH.add_nodes_from(_node_product(G, H))
+    # Edges in G regardless of H designation
+    GH.add_edges_from(_edges_cross_nodes_and_nodes(G, H))
+    # For each x in G, only if there is an edge in H
+    GH.add_edges_from(_nodes_cross_edges(G, H))
+    return GH
+
+
+@nx._dispatchable(graphs=_G_H, preserve_node_attrs=True, returns_graph=True)
+def strong_product(G, H):
+    r"""Returns the strong product of G and H.
+
+    The strong product $P$ of the graphs $G$ and $H$ has a node set that
+    is the Cartesian product of the node sets, $V(P)=V(G) \times V(H)$.
+    $P$ has an edge $((u,x), (v,y))$ if any of the following conditions
+    are met:
+
+    - $u=v$ and $(x,y)$ is an edge in $H$
+    - $x=y$ and $(u,v)$ is an edge in $G$
+    - $(u,v)$ is an edge in $G$ and $(x,y)$ is an edge in $H$
+
+    Parameters
+    ----------
+    G, H: graphs
+     Networkx graphs.
+
+    Returns
+    -------
+    P: NetworkX graph
+     The Cartesian product of G and H. P will be a multi-graph if either G
+     or H is a multi-graph. Will be a directed if G and H are directed,
+     and undirected if G and H are undirected.
+
+    Raises
+    ------
+    NetworkXError
+     If G and H are not both directed or both undirected.
+
+    Notes
+    -----
+    Node attributes in P are two-tuple of the G and H node attributes.
+    Missing attributes are assigned None.
+
+    Examples
+    --------
+    >>> G = nx.Graph()
+    >>> H = nx.Graph()
+    >>> G.add_node(0, a1=True)
+    >>> H.add_node("a", a2="Spam")
+    >>> P = nx.strong_product(G, H)
+    >>> list(P)
+    [(0, 'a')]
+
+    Edge attributes and edge keys (for multigraphs) are also copied to the
+    new product graph
+    """
+    GH = _init_product_graph(G, H)
+    GH.add_nodes_from(_node_product(G, H))
+    GH.add_edges_from(_nodes_cross_edges(G, H))
+    GH.add_edges_from(_edges_cross_nodes(G, H))
+    GH.add_edges_from(_directed_edges_cross_edges(G, H))
+    if not GH.is_directed():
+        GH.add_edges_from(_undirected_edges_cross_edges(G, H))
+    return GH
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(returns_graph=True)
+def power(G, k):
+    """Returns the specified power of a graph.
+
+    The $k$th power of a simple graph $G$, denoted $G^k$, is a
+    graph on the same set of nodes in which two distinct nodes $u$ and
+    $v$ are adjacent in $G^k$ if and only if the shortest path
+    distance between $u$ and $v$ in $G$ is at most $k$.
+
+    Parameters
+    ----------
+    G : graph
+        A NetworkX simple graph object.
+
+    k : positive integer
+        The power to which to raise the graph `G`.
+
+    Returns
+    -------
+    NetworkX simple graph
+        `G` to the power `k`.
+
+    Raises
+    ------
+    ValueError
+        If the exponent `k` is not positive.
+
+    NetworkXNotImplemented
+        If `G` is not a simple graph.
+
+    Examples
+    --------
+    The number of edges will never decrease when taking successive
+    powers:
+
+    >>> G = nx.path_graph(4)
+    >>> list(nx.power(G, 2).edges)
+    [(0, 1), (0, 2), (1, 2), (1, 3), (2, 3)]
+    >>> list(nx.power(G, 3).edges)
+    [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]
+
+    The `k` th power of a cycle graph on *n* nodes is the complete graph
+    on *n* nodes, if `k` is at least ``n // 2``:
+
+    >>> G = nx.cycle_graph(5)
+    >>> H = nx.complete_graph(5)
+    >>> nx.is_isomorphic(nx.power(G, 2), H)
+    True
+    >>> G = nx.cycle_graph(8)
+    >>> H = nx.complete_graph(8)
+    >>> nx.is_isomorphic(nx.power(G, 4), H)
+    True
+
+    References
+    ----------
+    .. [1] J. A. Bondy, U. S. R. Murty, *Graph Theory*. Springer, 2008.
+
+    Notes
+    -----
+    This definition of "power graph" comes from Exercise 3.1.6 of
+    *Graph Theory* by Bondy and Murty [1]_.
+
+    """
+    if k <= 0:
+        raise ValueError("k must be a positive integer")
+    H = nx.Graph()
+    H.add_nodes_from(G)
+    # update BFS code to ignore self loops.
+    for n in G:
+        seen = {}  # level (number of hops) when seen in BFS
+        level = 1  # the current level
+        nextlevel = G[n]
+        while nextlevel:
+            thislevel = nextlevel  # advance to next level
+            nextlevel = {}  # and start a new list (fringe)
+            for v in thislevel:
+                if v == n:  # avoid self loop
+                    continue
+                if v not in seen:
+                    seen[v] = level  # set the level of vertex v
+                    nextlevel.update(G[v])  # add neighbors of v
+            if k <= level:
+                break
+            level += 1
+        H.add_edges_from((n, nbr) for nbr in seen)
+    return H
+
+
+@not_implemented_for("multigraph")
+@nx._dispatchable(graphs=_G_H, returns_graph=True)
+def rooted_product(G, H, root):
+    """Return the rooted product of graphs G and H rooted at root in H.
+
+    A new graph is constructed representing the rooted product of
+    the inputted graphs, G and H, with a root in H.
+    A rooted product duplicates H for each nodes in G with the root
+    of H corresponding to the node in G. Nodes are renamed as the direct
+    product of G and H. The result is a subgraph of the cartesian product.
+
+    Parameters
+    ----------
+    G,H : graph
+       A NetworkX graph
+    root : node
+       A node in H
+
+    Returns
+    -------
+    R : The rooted product of G and H with a specified root in H
+
+    Notes
+    -----
+    The nodes of R are the Cartesian Product of the nodes of G and H.
+    The nodes of G and H are not relabeled.
+    """
+    if root not in H:
+        raise nx.NodeNotFound("root must be a vertex in H")
+
+    R = nx.Graph()
+    R.add_nodes_from(product(G, H))
+
+    R.add_edges_from(((e[0], root), (e[1], root)) for e in G.edges())
+    R.add_edges_from(((g, e[0]), (g, e[1])) for g in G for e in H.edges())
+
+    return R
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+@nx._dispatchable(graphs=_G_H, returns_graph=True)
+def corona_product(G, H):
+    r"""Returns the Corona product of G and H.
+
+    The corona product of $G$ and $H$ is the graph $C = G \circ H$ obtained by
+    taking one copy of $G$, called the center graph, $|V(G)|$ copies of $H$,
+    called the outer graph, and making the $i$-th vertex of $G$ adjacent to
+    every vertex of the $i$-th copy of $H$, where $1 ≤ i ≤ |V(G)|$.
+
+    Parameters
+    ----------
+    G, H: NetworkX graphs
+        The graphs to take the carona product of.
+        `G` is the center graph and `H` is the outer graph
+
+    Returns
+    -------
+    C: NetworkX graph
+        The Corona product of G and H.
+
+    Raises
+    ------
+    NetworkXError
+        If G and H are not both directed or both undirected.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(4)
+    >>> H = nx.path_graph(2)
+    >>> C = nx.corona_product(G, H)
+    >>> list(C)
+    [0, 1, 2, 3, (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)]
+    >>> print(C)
+    Graph with 12 nodes and 16 edges
+
+    References
+    ----------
+    [1] M. Tavakoli, F. Rahbarnia, and A. R. Ashrafi,
+        "Studying the corona product of graphs under some graph invariants,"
+        Transactions on Combinatorics, vol. 3, no. 3, pp. 43–49, Sep. 2014,
+        doi: 10.22108/toc.2014.5542.
+    [2] A. Faraji, "Corona Product in Graph Theory," Ali Faraji, May 11, 2021.
+        https://blog.alifaraji.ir/math/graph-theory/corona-product.html (accessed Dec. 07, 2021).
+    """
+    GH = _init_product_graph(G, H)
+    GH.add_nodes_from(G)
+    GH.add_edges_from(G.edges)
+
+    for G_node in G:
+        # copy nodes of H in GH, call it H_i
+        GH.add_nodes_from((G_node, v) for v in H)
+
+        # copy edges of H_i based on H
+        GH.add_edges_from(
+            ((G_node, e0), (G_node, e1), d) for e0, e1, d in H.edges.data()
+        )
+
+        # creating new edges between H_i and a G's node
+        GH.add_edges_from((G_node, (G_node, H_node)) for H_node in H)
+
+    return GH
+
+
+@nx._dispatchable(
+    graphs=_G_H, preserve_edge_attrs=True, preserve_node_attrs=True, returns_graph=True
+)
+def modular_product(G, H):
+    r"""Returns the Modular product of G and H.
+
+    The modular product of `G` and `H` is the graph $M = G \nabla H$,
+    consisting of the node set $V(M) = V(G) \times V(H)$ that is the Cartesian
+    product of the node sets of `G` and `H`. Further, M contains an edge ((u, v), (x, y)):
+
+    - if u is adjacent to x in `G` and v is adjacent to y in `H`, or
+    - if u is not adjacent to x in `G` and v is not adjacent to y in `H`.
+
+    More formally::
+
+        E(M) = {((u, v), (x, y)) | ((u, x) in E(G) and (v, y) in E(H)) or
+                                   ((u, x) not in E(G) and (v, y) not in E(H))}
+
+    Parameters
+    ----------
+    G, H: NetworkX graphs
+        The graphs to take the modular product of.
+
+    Returns
+    -------
+    M: NetworkX graph
+        The Modular product of `G` and `H`.
+
+    Raises
+    ------
+    NetworkXNotImplemented
+        If `G` is not a simple graph.
+
+    Examples
+    --------
+    >>> G = nx.cycle_graph(4)
+    >>> H = nx.path_graph(2)
+    >>> M = nx.modular_product(G, H)
+    >>> list(M)
+    [(0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)]
+    >>> print(M)
+    Graph with 8 nodes and 8 edges
+
+    Notes
+    -----
+    The *modular product* is defined in [1]_ and was first
+    introduced as the *weak modular product*.
+
+    The modular product reduces the problem of counting isomorphic subgraphs
+    in `G` and `H` to the problem of counting cliques in M. The subgraphs of
+    `G` and `H` that are induced by the nodes of a clique in M are
+    isomorphic [2]_ [3]_.
+
+    References
+    ----------
+    .. [1] R. Hammack, W. Imrich, and S. Klavžar,
+        "Handbook of Product Graphs", CRC Press, 2011.
+
+    .. [2] H. G. Barrow and R. M. Burstall,
+        "Subgraph isomorphism, matching relational structures and maximal
+        cliques", Information Processing Letters, vol. 4, issue 4, pp. 83-84,
+        1976, https://doi.org/10.1016/0020-0190(76)90049-1.
+
+    .. [3] V. G. Vizing, "Reduction of the problem of isomorphism and isomorphic
+        entrance to the task of finding the nondensity of a graph." Proc. Third
+        All-Union Conference on Problems of Theoretical Cybernetics. 1974.
+    """
+    if G.is_directed() or H.is_directed():
+        raise nx.NetworkXNotImplemented(
+            "Modular product not implemented for directed graphs"
+        )
+    if G.is_multigraph() or H.is_multigraph():
+        raise nx.NetworkXNotImplemented(
+            "Modular product not implemented for multigraphs"
+        )
+
+    GH = _init_product_graph(G, H)
+    GH.add_nodes_from(_node_product(G, H))
+
+    for u, v, c in G.edges(data=True):
+        for x, y, d in H.edges(data=True):
+            GH.add_edge((u, x), (v, y), **_dict_product(c, d))
+            GH.add_edge((v, x), (u, y), **_dict_product(c, d))
+
+    G = nx.complement(G)
+    H = nx.complement(H)
+
+    for u, v, c in G.edges(data=True):
+        for x, y, d in H.edges(data=True):
+            GH.add_edge((u, x), (v, y), **_dict_product(c, d))
+            GH.add_edge((v, x), (u, y), **_dict_product(c, d))
+
+    return GH

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_all.py

@@ -0,0 +1,328 @@
+import pytest
+
+import networkx as nx
+from networkx.utils import edges_equal
+
+
+def test_union_all_attributes():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+
+    j = g.copy()
+    j.graph["name"] = "j"
+    j.graph["attr"] = "attr"
+    j.nodes[0]["x"] = 7
+
+    ghj = nx.union_all([g, h, j], rename=("g", "h", "j"))
+    assert set(ghj.nodes()) == {"h0", "h1", "g0", "g1", "j0", "j1"}
+    for n in ghj:
+        graph, node = n
+        assert ghj.nodes[n] == eval(graph).nodes[int(node)]
+
+    assert ghj.graph["attr"] == "attr"
+    assert ghj.graph["name"] == "j"  # j graph attributes take precedent
+
+
+def test_intersection_all():
+    G = nx.Graph()
+    H = nx.Graph()
+    R = nx.Graph(awesome=True)
+    G.add_nodes_from([1, 2, 3, 4])
+    G.add_edge(1, 2)
+    G.add_edge(2, 3)
+    H.add_nodes_from([1, 2, 3, 4])
+    H.add_edge(2, 3)
+    H.add_edge(3, 4)
+    R.add_nodes_from([1, 2, 3, 4])
+    R.add_edge(2, 3)
+    R.add_edge(4, 1)
+    I = nx.intersection_all([G, H, R])
+    assert set(I.nodes()) == {1, 2, 3, 4}
+    assert sorted(I.edges()) == [(2, 3)]
+    assert I.graph == {}
+
+
+def test_intersection_all_different_node_sets():
+    G = nx.Graph()
+    H = nx.Graph()
+    R = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4, 6, 7])
+    G.add_edge(1, 2)
+    G.add_edge(2, 3)
+    G.add_edge(6, 7)
+    H.add_nodes_from([1, 2, 3, 4])
+    H.add_edge(2, 3)
+    H.add_edge(3, 4)
+    R.add_nodes_from([1, 2, 3, 4, 8, 9])
+    R.add_edge(2, 3)
+    R.add_edge(4, 1)
+    R.add_edge(8, 9)
+    I = nx.intersection_all([G, H, R])
+    assert set(I.nodes()) == {1, 2, 3, 4}
+    assert sorted(I.edges()) == [(2, 3)]
+
+
+def test_intersection_all_attributes():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+
+    gh = nx.intersection_all([g, h])
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == sorted(g.edges())
+
+
+def test_intersection_all_attributes_different_node_sets():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    g.add_node(2)
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+
+    gh = nx.intersection_all([g, h])
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == sorted(g.edges())
+
+
+def test_intersection_all_multigraph_attributes():
+    g = nx.MultiGraph()
+    g.add_edge(0, 1, key=0)
+    g.add_edge(0, 1, key=1)
+    g.add_edge(0, 1, key=2)
+    h = nx.MultiGraph()
+    h.add_edge(0, 1, key=0)
+    h.add_edge(0, 1, key=3)
+    gh = nx.intersection_all([g, h])
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == [(0, 1)]
+    assert sorted(gh.edges(keys=True)) == [(0, 1, 0)]
+
+
+def test_intersection_all_multigraph_attributes_different_node_sets():
+    g = nx.MultiGraph()
+    g.add_edge(0, 1, key=0)
+    g.add_edge(0, 1, key=1)
+    g.add_edge(0, 1, key=2)
+    g.add_edge(1, 2, key=1)
+    g.add_edge(1, 2, key=2)
+    h = nx.MultiGraph()
+    h.add_edge(0, 1, key=0)
+    h.add_edge(0, 1, key=2)
+    h.add_edge(0, 1, key=3)
+    gh = nx.intersection_all([g, h])
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == [(0, 1), (0, 1)]
+    assert sorted(gh.edges(keys=True)) == [(0, 1, 0), (0, 1, 2)]
+
+
+def test_intersection_all_digraph():
+    g = nx.DiGraph()
+    g.add_edges_from([(1, 2), (2, 3)])
+    h = nx.DiGraph()
+    h.add_edges_from([(2, 1), (2, 3)])
+    gh = nx.intersection_all([g, h])
+    assert sorted(gh.edges()) == [(2, 3)]
+
+
+def test_union_all_and_compose_all():
+    K3 = nx.complete_graph(3)
+    P3 = nx.path_graph(3)
+
+    G1 = nx.DiGraph()
+    G1.add_edge("A", "B")
+    G1.add_edge("A", "C")
+    G1.add_edge("A", "D")
+    G2 = nx.DiGraph()
+    G2.add_edge("1", "2")
+    G2.add_edge("1", "3")
+    G2.add_edge("1", "4")
+
+    G = nx.union_all([G1, G2])
+    H = nx.compose_all([G1, G2])
+    assert edges_equal(G.edges(), H.edges())
+    assert not G.has_edge("A", "1")
+    pytest.raises(nx.NetworkXError, nx.union, K3, P3)
+    H1 = nx.union_all([H, G1], rename=("H", "G1"))
+    assert sorted(H1.nodes()) == [
+        "G1A",
+        "G1B",
+        "G1C",
+        "G1D",
+        "H1",
+        "H2",
+        "H3",
+        "H4",
+        "HA",
+        "HB",
+        "HC",
+        "HD",
+    ]
+
+    H2 = nx.union_all([H, G2], rename=("H", ""))
+    assert sorted(H2.nodes()) == [
+        "1",
+        "2",
+        "3",
+        "4",
+        "H1",
+        "H2",
+        "H3",
+        "H4",
+        "HA",
+        "HB",
+        "HC",
+        "HD",
+    ]
+
+    assert not H1.has_edge("NB", "NA")
+
+    G = nx.compose_all([G, G])
+    assert edges_equal(G.edges(), H.edges())
+
+    G2 = nx.union_all([G2, G2], rename=("", "copy"))
+    assert sorted(G2.nodes()) == [
+        "1",
+        "2",
+        "3",
+        "4",
+        "copy1",
+        "copy2",
+        "copy3",
+        "copy4",
+    ]
+
+    assert sorted(G2.neighbors("copy4")) == []
+    assert sorted(G2.neighbors("copy1")) == ["copy2", "copy3", "copy4"]
+    assert len(G) == 8
+    assert nx.number_of_edges(G) == 6
+
+    E = nx.disjoint_union_all([G, G])
+    assert len(E) == 16
+    assert nx.number_of_edges(E) == 12
+
+    E = nx.disjoint_union_all([G1, G2])
+    assert sorted(E.nodes()) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
+
+    G1 = nx.DiGraph()
+    G1.add_edge("A", "B")
+    G2 = nx.DiGraph()
+    G2.add_edge(1, 2)
+    G3 = nx.DiGraph()
+    G3.add_edge(11, 22)
+    G4 = nx.union_all([G1, G2, G3], rename=("G1", "G2", "G3"))
+    assert sorted(G4.nodes()) == ["G1A", "G1B", "G21", "G22", "G311", "G322"]
+
+
+def test_union_all_multigraph():
+    G = nx.MultiGraph()
+    G.add_edge(1, 2, key=0)
+    G.add_edge(1, 2, key=1)
+    H = nx.MultiGraph()
+    H.add_edge(3, 4, key=0)
+    H.add_edge(3, 4, key=1)
+    GH = nx.union_all([G, H])
+    assert set(GH) == set(G) | set(H)
+    assert set(GH.edges(keys=True)) == set(G.edges(keys=True)) | set(H.edges(keys=True))
+
+
+def test_input_output():
+    l = [nx.Graph([(1, 2)]), nx.Graph([(3, 4)], awesome=True)]
+    U = nx.disjoint_union_all(l)
+    assert len(l) == 2
+    assert U.graph["awesome"]
+    C = nx.compose_all(l)
+    assert len(l) == 2
+    l = [nx.Graph([(1, 2)]), nx.Graph([(1, 2)])]
+    R = nx.intersection_all(l)
+    assert len(l) == 2
+
+
+def test_mixed_type_union():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.Graph()
+        H = nx.MultiGraph()
+        I = nx.Graph()
+        U = nx.union_all([G, H, I])
+    with pytest.raises(nx.NetworkXError):
+        X = nx.Graph()
+        Y = nx.DiGraph()
+        XY = nx.union_all([X, Y])
+
+
+def test_mixed_type_disjoint_union():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.Graph()
+        H = nx.MultiGraph()
+        I = nx.Graph()
+        U = nx.disjoint_union_all([G, H, I])
+    with pytest.raises(nx.NetworkXError):
+        X = nx.Graph()
+        Y = nx.DiGraph()
+        XY = nx.disjoint_union_all([X, Y])
+
+
+def test_mixed_type_intersection():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.Graph()
+        H = nx.MultiGraph()
+        I = nx.Graph()
+        U = nx.intersection_all([G, H, I])
+    with pytest.raises(nx.NetworkXError):
+        X = nx.Graph()
+        Y = nx.DiGraph()
+        XY = nx.intersection_all([X, Y])
+
+
+def test_mixed_type_compose():
+    with pytest.raises(nx.NetworkXError):
+        G = nx.Graph()
+        H = nx.MultiGraph()
+        I = nx.Graph()
+        U = nx.compose_all([G, H, I])
+    with pytest.raises(nx.NetworkXError):
+        X = nx.Graph()
+        Y = nx.DiGraph()
+        XY = nx.compose_all([X, Y])
+
+
+def test_empty_union():
+    with pytest.raises(ValueError):
+        nx.union_all([])
+
+
+def test_empty_disjoint_union():
+    with pytest.raises(ValueError):
+        nx.disjoint_union_all([])
+
+
+def test_empty_compose_all():
+    with pytest.raises(ValueError):
+        nx.compose_all([])
+
+
+def test_empty_intersection_all():
+    with pytest.raises(ValueError):
+        nx.intersection_all([])

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_binary.py

@@ -0,0 +1,453 @@
+import os
+
+import pytest
+
+import networkx as nx
+from networkx.utils import edges_equal
+
+
+def test_union_attributes():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+
+    gh = nx.union(g, h, rename=("g", "h"))
+    assert set(gh.nodes()) == {"h0", "h1", "g0", "g1"}
+    for n in gh:
+        graph, node = n
+        assert gh.nodes[n] == eval(graph).nodes[int(node)]
+
+    assert gh.graph["attr"] == "attr"
+    assert gh.graph["name"] == "h"  # h graph attributes take precedent
+
+
+def test_intersection():
+    G = nx.Graph()
+    H = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4])
+    G.add_edge(1, 2)
+    G.add_edge(2, 3)
+    H.add_nodes_from([1, 2, 3, 4])
+    H.add_edge(2, 3)
+    H.add_edge(3, 4)
+    I = nx.intersection(G, H)
+    assert set(I.nodes()) == {1, 2, 3, 4}
+    assert sorted(I.edges()) == [(2, 3)]
+
+
+def test_intersection_node_sets_different():
+    G = nx.Graph()
+    H = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4, 7])
+    G.add_edge(1, 2)
+    G.add_edge(2, 3)
+    H.add_nodes_from([1, 2, 3, 4, 5, 6])
+    H.add_edge(2, 3)
+    H.add_edge(3, 4)
+    H.add_edge(5, 6)
+    I = nx.intersection(G, H)
+    assert set(I.nodes()) == {1, 2, 3, 4}
+    assert sorted(I.edges()) == [(2, 3)]
+
+
+def test_intersection_attributes():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+    gh = nx.intersection(g, h)
+
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == sorted(g.edges())
+
+
+def test_intersection_attributes_node_sets_different():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_node(2, x=3)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+    h.remove_node(2)
+
+    gh = nx.intersection(g, h)
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == sorted(g.edges())
+
+
+def test_intersection_multigraph_attributes():
+    g = nx.MultiGraph()
+    g.add_edge(0, 1, key=0)
+    g.add_edge(0, 1, key=1)
+    g.add_edge(0, 1, key=2)
+    h = nx.MultiGraph()
+    h.add_edge(0, 1, key=0)
+    h.add_edge(0, 1, key=3)
+    gh = nx.intersection(g, h)
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == [(0, 1)]
+    assert sorted(gh.edges(keys=True)) == [(0, 1, 0)]
+
+
+def test_intersection_multigraph_attributes_node_set_different():
+    g = nx.MultiGraph()
+    g.add_edge(0, 1, key=0)
+    g.add_edge(0, 1, key=1)
+    g.add_edge(0, 1, key=2)
+    g.add_edge(0, 2, key=2)
+    g.add_edge(0, 2, key=1)
+    h = nx.MultiGraph()
+    h.add_edge(0, 1, key=0)
+    h.add_edge(0, 1, key=3)
+    gh = nx.intersection(g, h)
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == [(0, 1)]
+    assert sorted(gh.edges(keys=True)) == [(0, 1, 0)]
+
+
+def test_difference():
+    G = nx.Graph()
+    H = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4])
+    G.add_edge(1, 2)
+    G.add_edge(2, 3)
+    H.add_nodes_from([1, 2, 3, 4])
+    H.add_edge(2, 3)
+    H.add_edge(3, 4)
+    D = nx.difference(G, H)
+    assert set(D.nodes()) == {1, 2, 3, 4}
+    assert sorted(D.edges()) == [(1, 2)]
+    D = nx.difference(H, G)
+    assert set(D.nodes()) == {1, 2, 3, 4}
+    assert sorted(D.edges()) == [(3, 4)]
+    D = nx.symmetric_difference(G, H)
+    assert set(D.nodes()) == {1, 2, 3, 4}
+    assert sorted(D.edges()) == [(1, 2), (3, 4)]
+
+
+def test_difference2():
+    G = nx.Graph()
+    H = nx.Graph()
+    G.add_nodes_from([1, 2, 3, 4])
+    H.add_nodes_from([1, 2, 3, 4])
+    G.add_edge(1, 2)
+    H.add_edge(1, 2)
+    G.add_edge(2, 3)
+    D = nx.difference(G, H)
+    assert set(D.nodes()) == {1, 2, 3, 4}
+    assert sorted(D.edges()) == [(2, 3)]
+    D = nx.difference(H, G)
+    assert set(D.nodes()) == {1, 2, 3, 4}
+    assert sorted(D.edges()) == []
+    H.add_edge(3, 4)
+    D = nx.difference(H, G)
+    assert set(D.nodes()) == {1, 2, 3, 4}
+    assert sorted(D.edges()) == [(3, 4)]
+
+
+def test_difference_attributes():
+    g = nx.Graph()
+    g.add_node(0, x=4)
+    g.add_node(1, x=5)
+    g.add_edge(0, 1, size=5)
+    g.graph["name"] = "g"
+
+    h = g.copy()
+    h.graph["name"] = "h"
+    h.graph["attr"] = "attr"
+    h.nodes[0]["x"] = 7
+
+    gh = nx.difference(g, h)
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == []
+    # node and graph data should not be copied over
+    assert gh.nodes.data() != g.nodes.data()
+    assert gh.graph != g.graph
+
+
+def test_difference_multigraph_attributes():
+    g = nx.MultiGraph()
+    g.add_edge(0, 1, key=0)
+    g.add_edge(0, 1, key=1)
+    g.add_edge(0, 1, key=2)
+    h = nx.MultiGraph()
+    h.add_edge(0, 1, key=0)
+    h.add_edge(0, 1, key=3)
+    gh = nx.difference(g, h)
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == [(0, 1), (0, 1)]
+    assert sorted(gh.edges(keys=True)) == [(0, 1, 1), (0, 1, 2)]
+
+
+def test_difference_raise():
+    G = nx.path_graph(4)
+    H = nx.path_graph(3)
+    pytest.raises(nx.NetworkXError, nx.difference, G, H)
+    pytest.raises(nx.NetworkXError, nx.symmetric_difference, G, H)
+
+
+def test_symmetric_difference_multigraph():
+    g = nx.MultiGraph()
+    g.add_edge(0, 1, key=0)
+    g.add_edge(0, 1, key=1)
+    g.add_edge(0, 1, key=2)
+    h = nx.MultiGraph()
+    h.add_edge(0, 1, key=0)
+    h.add_edge(0, 1, key=3)
+    gh = nx.symmetric_difference(g, h)
+    assert set(gh.nodes()) == set(g.nodes())
+    assert set(gh.nodes()) == set(h.nodes())
+    assert sorted(gh.edges()) == 3 * [(0, 1)]
+    assert sorted(sorted(e) for e in gh.edges(keys=True)) == [
+        [0, 1, 1],
+        [0, 1, 2],
+        [0, 1, 3],
+    ]
+
+
+def test_union_and_compose():
+    K3 = nx.complete_graph(3)
+    P3 = nx.path_graph(3)
+
+    G1 = nx.DiGraph()
+    G1.add_edge("A", "B")
+    G1.add_edge("A", "C")
+    G1.add_edge("A", "D")
+    G2 = nx.DiGraph()
+    G2.add_edge("1", "2")
+    G2.add_edge("1", "3")
+    G2.add_edge("1", "4")
+
+    G = nx.union(G1, G2)
+    H = nx.compose(G1, G2)
+    assert edges_equal(G.edges(), H.edges())
+    assert not G.has_edge("A", 1)
+    pytest.raises(nx.NetworkXError, nx.union, K3, P3)
+    H1 = nx.union(H, G1, rename=("H", "G1"))
+    assert sorted(H1.nodes()) == [
+        "G1A",
+        "G1B",
+        "G1C",
+        "G1D",
+        "H1",
+        "H2",
+        "H3",
+        "H4",
+        "HA",
+        "HB",
+        "HC",
+        "HD",
+    ]
+
+    H2 = nx.union(H, G2, rename=("H", ""))
+    assert sorted(H2.nodes()) == [
+        "1",
+        "2",
+        "3",
+        "4",
+        "H1",
+        "H2",
+        "H3",
+        "H4",
+        "HA",
+        "HB",
+        "HC",
+        "HD",
+    ]
+
+    assert not H1.has_edge("NB", "NA")
+
+    G = nx.compose(G, G)
+    assert edges_equal(G.edges(), H.edges())
+
+    G2 = nx.union(G2, G2, rename=("", "copy"))
+    assert sorted(G2.nodes()) == [
+        "1",
+        "2",
+        "3",
+        "4",
+        "copy1",
+        "copy2",
+        "copy3",
+        "copy4",
+    ]
+
+    assert sorted(G2.neighbors("copy4")) == []
+    assert sorted(G2.neighbors("copy1")) == ["copy2", "copy3", "copy4"]
+    assert len(G) == 8
+    assert nx.number_of_edges(G) == 6
+
+    E = nx.disjoint_union(G, G)
+    assert len(E) == 16
+    assert nx.number_of_edges(E) == 12
+
+    E = nx.disjoint_union(G1, G2)
+    assert sorted(E.nodes()) == [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
+
+    G = nx.Graph()
+    H = nx.Graph()
+    G.add_nodes_from([(1, {"a1": 1})])
+    H.add_nodes_from([(1, {"b1": 1})])
+    R = nx.compose(G, H)
+    assert R.nodes == {1: {"a1": 1, "b1": 1}}
+
+
+def test_union_multigraph():
+    G = nx.MultiGraph()
+    G.add_edge(1, 2, key=0)
+    G.add_edge(1, 2, key=1)
+    H = nx.MultiGraph()
+    H.add_edge(3, 4, key=0)
+    H.add_edge(3, 4, key=1)
+    GH = nx.union(G, H)
+    assert set(GH) == set(G) | set(H)
+    assert set(GH.edges(keys=True)) == set(G.edges(keys=True)) | set(H.edges(keys=True))
+
+
+def test_disjoint_union_multigraph():
+    G = nx.MultiGraph()
+    G.add_edge(0, 1, key=0)
+    G.add_edge(0, 1, key=1)
+    H = nx.MultiGraph()
+    H.add_edge(2, 3, key=0)
+    H.add_edge(2, 3, key=1)
+    GH = nx.disjoint_union(G, H)
+    assert set(GH) == set(G) | set(H)
+    assert set(GH.edges(keys=True)) == set(G.edges(keys=True)) | set(H.edges(keys=True))
+
+
+def test_compose_multigraph():
+    G = nx.MultiGraph()
+    G.add_edge(1, 2, key=0)
+    G.add_edge(1, 2, key=1)
+    H = nx.MultiGraph()
+    H.add_edge(3, 4, key=0)
+    H.add_edge(3, 4, key=1)
+    GH = nx.compose(G, H)
+    assert set(GH) == set(G) | set(H)
+    assert set(GH.edges(keys=True)) == set(G.edges(keys=True)) | set(H.edges(keys=True))
+    H.add_edge(1, 2, key=2)
+    GH = nx.compose(G, H)
+    assert set(GH) == set(G) | set(H)
+    assert set(GH.edges(keys=True)) == set(G.edges(keys=True)) | set(H.edges(keys=True))
+
+
+def test_full_join_graph():
+    # Simple Graphs
+    G = nx.Graph()
+    G.add_node(0)
+    G.add_edge(1, 2)
+    H = nx.Graph()
+    H.add_edge(3, 4)
+
+    U = nx.full_join(G, H)
+    assert set(U) == set(G) | set(H)
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
+
+    # Rename
+    U = nx.full_join(G, H, rename=("g", "h"))
+    assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
+
+    # Rename graphs with string-like nodes
+    G = nx.Graph()
+    G.add_node("a")
+    G.add_edge("b", "c")
+    H = nx.Graph()
+    H.add_edge("d", "e")
+
+    U = nx.full_join(G, H, rename=("g", "h"))
+    assert set(U) == {"ga", "gb", "gc", "hd", "he"}
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
+
+    # DiGraphs
+    G = nx.DiGraph()
+    G.add_node(0)
+    G.add_edge(1, 2)
+    H = nx.DiGraph()
+    H.add_edge(3, 4)
+
+    U = nx.full_join(G, H)
+    assert set(U) == set(G) | set(H)
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
+
+    # DiGraphs Rename
+    U = nx.full_join(G, H, rename=("g", "h"))
+    assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
+
+
+def test_full_join_multigraph():
+    # MultiGraphs
+    G = nx.MultiGraph()
+    G.add_node(0)
+    G.add_edge(1, 2)
+    H = nx.MultiGraph()
+    H.add_edge(3, 4)
+
+    U = nx.full_join(G, H)
+    assert set(U) == set(G) | set(H)
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
+
+    # MultiGraphs rename
+    U = nx.full_join(G, H, rename=("g", "h"))
+    assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H)
+
+    # MultiDiGraphs
+    G = nx.MultiDiGraph()
+    G.add_node(0)
+    G.add_edge(1, 2)
+    H = nx.MultiDiGraph()
+    H.add_edge(3, 4)
+
+    U = nx.full_join(G, H)
+    assert set(U) == set(G) | set(H)
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
+
+    # MultiDiGraphs rename
+    U = nx.full_join(G, H, rename=("g", "h"))
+    assert set(U) == {"g0", "g1", "g2", "h3", "h4"}
+    assert len(U) == len(G) + len(H)
+    assert len(U.edges()) == len(G.edges()) + len(H.edges()) + len(G) * len(H) * 2
+
+
+def test_mixed_type_union():
+    G = nx.Graph()
+    H = nx.MultiGraph()
+    pytest.raises(nx.NetworkXError, nx.union, G, H)
+    pytest.raises(nx.NetworkXError, nx.disjoint_union, G, H)
+    pytest.raises(nx.NetworkXError, nx.intersection, G, H)
+    pytest.raises(nx.NetworkXError, nx.difference, G, H)
+    pytest.raises(nx.NetworkXError, nx.symmetric_difference, G, H)
+    pytest.raises(nx.NetworkXError, nx.compose, G, H)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_product.py

@@ -0,0 +1,491 @@
+import pytest
+
+import networkx as nx
+from networkx.utils import edges_equal
+
+
+def test_tensor_product_raises():
+    with pytest.raises(nx.NetworkXError):
+        P = nx.tensor_product(nx.DiGraph(), nx.Graph())
+
+
+def test_tensor_product_null():
+    null = nx.null_graph()
+    empty10 = nx.empty_graph(10)
+    K3 = nx.complete_graph(3)
+    K10 = nx.complete_graph(10)
+    P3 = nx.path_graph(3)
+    P10 = nx.path_graph(10)
+    # null graph
+    G = nx.tensor_product(null, null)
+    assert nx.is_isomorphic(G, null)
+    # null_graph X anything = null_graph and v.v.
+    G = nx.tensor_product(null, empty10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(null, K3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(null, K10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(null, P3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(null, P10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(empty10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(K3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(K10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(P3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.tensor_product(P10, null)
+    assert nx.is_isomorphic(G, null)
+
+
+def test_tensor_product_size():
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    K5 = nx.complete_graph(5)
+
+    G = nx.tensor_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.tensor_product(K3, K5)
+    assert nx.number_of_nodes(G) == 3 * 5
+
+
+def test_tensor_product_combinations():
+    # basic smoke test, more realistic tests would be useful
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    G = nx.tensor_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.tensor_product(P5, nx.MultiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.tensor_product(nx.MultiGraph(P5), K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.tensor_product(nx.MultiGraph(P5), nx.MultiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+
+    G = nx.tensor_product(nx.DiGraph(P5), nx.DiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+
+
+def test_tensor_product_classic_result():
+    K2 = nx.complete_graph(2)
+    G = nx.petersen_graph()
+    G = nx.tensor_product(G, K2)
+    assert nx.is_isomorphic(G, nx.desargues_graph())
+
+    G = nx.cycle_graph(5)
+    G = nx.tensor_product(G, K2)
+    assert nx.is_isomorphic(G, nx.cycle_graph(10))
+
+    G = nx.tetrahedral_graph()
+    G = nx.tensor_product(G, K2)
+    assert nx.is_isomorphic(G, nx.cubical_graph())
+
+
+def test_tensor_product_random():
+    G = nx.erdos_renyi_graph(10, 2 / 10.0)
+    H = nx.erdos_renyi_graph(10, 2 / 10.0)
+    GH = nx.tensor_product(G, H)
+
+    for u_G, u_H in GH.nodes():
+        for v_G, v_H in GH.nodes():
+            if H.has_edge(u_H, v_H) and G.has_edge(u_G, v_G):
+                assert GH.has_edge((u_G, u_H), (v_G, v_H))
+            else:
+                assert not GH.has_edge((u_G, u_H), (v_G, v_H))
+
+
+def test_cartesian_product_multigraph():
+    G = nx.MultiGraph()
+    G.add_edge(1, 2, key=0)
+    G.add_edge(1, 2, key=1)
+    H = nx.MultiGraph()
+    H.add_edge(3, 4, key=0)
+    H.add_edge(3, 4, key=1)
+    GH = nx.cartesian_product(G, H)
+    assert set(GH) == {(1, 3), (2, 3), (2, 4), (1, 4)}
+    assert {(frozenset([u, v]), k) for u, v, k in GH.edges(keys=True)} == {
+        (frozenset([u, v]), k)
+        for u, v, k in [
+            ((1, 3), (2, 3), 0),
+            ((1, 3), (2, 3), 1),
+            ((1, 3), (1, 4), 0),
+            ((1, 3), (1, 4), 1),
+            ((2, 3), (2, 4), 0),
+            ((2, 3), (2, 4), 1),
+            ((2, 4), (1, 4), 0),
+            ((2, 4), (1, 4), 1),
+        ]
+    }
+
+
+def test_cartesian_product_raises():
+    with pytest.raises(nx.NetworkXError):
+        P = nx.cartesian_product(nx.DiGraph(), nx.Graph())
+
+
+def test_cartesian_product_null():
+    null = nx.null_graph()
+    empty10 = nx.empty_graph(10)
+    K3 = nx.complete_graph(3)
+    K10 = nx.complete_graph(10)
+    P3 = nx.path_graph(3)
+    P10 = nx.path_graph(10)
+    # null graph
+    G = nx.cartesian_product(null, null)
+    assert nx.is_isomorphic(G, null)
+    # null_graph X anything = null_graph and v.v.
+    G = nx.cartesian_product(null, empty10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(null, K3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(null, K10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(null, P3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(null, P10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(empty10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(K3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(K10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(P3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.cartesian_product(P10, null)
+    assert nx.is_isomorphic(G, null)
+
+
+def test_cartesian_product_size():
+    # order(GXH)=order(G)*order(H)
+    K5 = nx.complete_graph(5)
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    G = nx.cartesian_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    assert nx.number_of_edges(G) == nx.number_of_edges(P5) * nx.number_of_nodes(
+        K3
+    ) + nx.number_of_edges(K3) * nx.number_of_nodes(P5)
+    G = nx.cartesian_product(K3, K5)
+    assert nx.number_of_nodes(G) == 3 * 5
+    assert nx.number_of_edges(G) == nx.number_of_edges(K5) * nx.number_of_nodes(
+        K3
+    ) + nx.number_of_edges(K3) * nx.number_of_nodes(K5)
+
+
+def test_cartesian_product_classic():
+    # test some classic product graphs
+    P2 = nx.path_graph(2)
+    P3 = nx.path_graph(3)
+    # cube = 2-path X 2-path
+    G = nx.cartesian_product(P2, P2)
+    G = nx.cartesian_product(P2, G)
+    assert nx.is_isomorphic(G, nx.cubical_graph())
+
+    # 3x3 grid
+    G = nx.cartesian_product(P3, P3)
+    assert nx.is_isomorphic(G, nx.grid_2d_graph(3, 3))
+
+
+def test_cartesian_product_random():
+    G = nx.erdos_renyi_graph(10, 2 / 10.0)
+    H = nx.erdos_renyi_graph(10, 2 / 10.0)
+    GH = nx.cartesian_product(G, H)
+
+    for u_G, u_H in GH.nodes():
+        for v_G, v_H in GH.nodes():
+            if (u_G == v_G and H.has_edge(u_H, v_H)) or (
+                u_H == v_H and G.has_edge(u_G, v_G)
+            ):
+                assert GH.has_edge((u_G, u_H), (v_G, v_H))
+            else:
+                assert not GH.has_edge((u_G, u_H), (v_G, v_H))
+
+
+def test_lexicographic_product_raises():
+    with pytest.raises(nx.NetworkXError):
+        P = nx.lexicographic_product(nx.DiGraph(), nx.Graph())
+
+
+def test_lexicographic_product_null():
+    null = nx.null_graph()
+    empty10 = nx.empty_graph(10)
+    K3 = nx.complete_graph(3)
+    K10 = nx.complete_graph(10)
+    P3 = nx.path_graph(3)
+    P10 = nx.path_graph(10)
+    # null graph
+    G = nx.lexicographic_product(null, null)
+    assert nx.is_isomorphic(G, null)
+    # null_graph X anything = null_graph and v.v.
+    G = nx.lexicographic_product(null, empty10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(null, K3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(null, K10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(null, P3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(null, P10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(empty10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(K3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(K10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(P3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.lexicographic_product(P10, null)
+    assert nx.is_isomorphic(G, null)
+
+
+def test_lexicographic_product_size():
+    K5 = nx.complete_graph(5)
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    G = nx.lexicographic_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.lexicographic_product(K3, K5)
+    assert nx.number_of_nodes(G) == 3 * 5
+
+
+def test_lexicographic_product_combinations():
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    G = nx.lexicographic_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.lexicographic_product(nx.MultiGraph(P5), K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.lexicographic_product(P5, nx.MultiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.lexicographic_product(nx.MultiGraph(P5), nx.MultiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+
+    # No classic easily found classic results for lexicographic product
+
+
+def test_lexicographic_product_random():
+    G = nx.erdos_renyi_graph(10, 2 / 10.0)
+    H = nx.erdos_renyi_graph(10, 2 / 10.0)
+    GH = nx.lexicographic_product(G, H)
+
+    for u_G, u_H in GH.nodes():
+        for v_G, v_H in GH.nodes():
+            if G.has_edge(u_G, v_G) or (u_G == v_G and H.has_edge(u_H, v_H)):
+                assert GH.has_edge((u_G, u_H), (v_G, v_H))
+            else:
+                assert not GH.has_edge((u_G, u_H), (v_G, v_H))
+
+
+def test_strong_product_raises():
+    with pytest.raises(nx.NetworkXError):
+        P = nx.strong_product(nx.DiGraph(), nx.Graph())
+
+
+def test_strong_product_null():
+    null = nx.null_graph()
+    empty10 = nx.empty_graph(10)
+    K3 = nx.complete_graph(3)
+    K10 = nx.complete_graph(10)
+    P3 = nx.path_graph(3)
+    P10 = nx.path_graph(10)
+    # null graph
+    G = nx.strong_product(null, null)
+    assert nx.is_isomorphic(G, null)
+    # null_graph X anything = null_graph and v.v.
+    G = nx.strong_product(null, empty10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(null, K3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(null, K10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(null, P3)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(null, P10)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(empty10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(K3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(K10, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(P3, null)
+    assert nx.is_isomorphic(G, null)
+    G = nx.strong_product(P10, null)
+    assert nx.is_isomorphic(G, null)
+
+
+def test_strong_product_size():
+    K5 = nx.complete_graph(5)
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    G = nx.strong_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.strong_product(K3, K5)
+    assert nx.number_of_nodes(G) == 3 * 5
+
+
+def test_strong_product_combinations():
+    P5 = nx.path_graph(5)
+    K3 = nx.complete_graph(3)
+    G = nx.strong_product(P5, K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.strong_product(nx.MultiGraph(P5), K3)
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.strong_product(P5, nx.MultiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+    G = nx.strong_product(nx.MultiGraph(P5), nx.MultiGraph(K3))
+    assert nx.number_of_nodes(G) == 5 * 3
+
+    # No classic easily found classic results for strong product
+
+
+def test_strong_product_random():
+    G = nx.erdos_renyi_graph(10, 2 / 10.0)
+    H = nx.erdos_renyi_graph(10, 2 / 10.0)
+    GH = nx.strong_product(G, H)
+
+    for u_G, u_H in GH.nodes():
+        for v_G, v_H in GH.nodes():
+            if (
+                (u_G == v_G and H.has_edge(u_H, v_H))
+                or (u_H == v_H and G.has_edge(u_G, v_G))
+                or (G.has_edge(u_G, v_G) and H.has_edge(u_H, v_H))
+            ):
+                assert GH.has_edge((u_G, u_H), (v_G, v_H))
+            else:
+                assert not GH.has_edge((u_G, u_H), (v_G, v_H))
+
+
+def test_graph_power_raises():
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.power(nx.MultiDiGraph(), 2)
+
+
+def test_graph_power():
+    # wikipedia example for graph power
+    G = nx.cycle_graph(7)
+    G.add_edge(6, 7)
+    G.add_edge(7, 8)
+    G.add_edge(8, 9)
+    G.add_edge(9, 2)
+    H = nx.power(G, 2)
+
+    assert edges_equal(
+        list(H.edges()),
+        [
+            (0, 1),
+            (0, 2),
+            (0, 5),
+            (0, 6),
+            (0, 7),
+            (1, 9),
+            (1, 2),
+            (1, 3),
+            (1, 6),
+            (2, 3),
+            (2, 4),
+            (2, 8),
+            (2, 9),
+            (3, 4),
+            (3, 5),
+            (3, 9),
+            (4, 5),
+            (4, 6),
+            (5, 6),
+            (5, 7),
+            (6, 7),
+            (6, 8),
+            (7, 8),
+            (7, 9),
+            (8, 9),
+        ],
+    )
+
+
+def test_graph_power_negative():
+    with pytest.raises(ValueError):
+        nx.power(nx.Graph(), -1)
+
+
+def test_rooted_product_raises():
+    with pytest.raises(nx.NodeNotFound):
+        nx.rooted_product(nx.Graph(), nx.path_graph(2), 10)
+
+
+def test_rooted_product():
+    G = nx.cycle_graph(5)
+    H = nx.Graph()
+    H.add_edges_from([("a", "b"), ("b", "c"), ("b", "d")])
+    R = nx.rooted_product(G, H, "a")
+    assert len(R) == len(G) * len(H)
+    assert R.size() == G.size() + len(G) * H.size()
+
+
+def test_corona_product():
+    G = nx.cycle_graph(3)
+    H = nx.path_graph(2)
+    C = nx.corona_product(G, H)
+    assert len(C) == (len(G) * len(H)) + len(G)
+    assert C.size() == G.size() + len(G) * H.size() + len(G) * len(H)
+
+
+def test_modular_product():
+    G = nx.path_graph(3)
+    H = nx.path_graph(4)
+    M = nx.modular_product(G, H)
+    assert len(M) == len(G) * len(H)
+
+    assert edges_equal(
+        list(M.edges()),
+        [
+            ((0, 0), (1, 1)),
+            ((0, 0), (2, 2)),
+            ((0, 0), (2, 3)),
+            ((0, 1), (1, 0)),
+            ((0, 1), (1, 2)),
+            ((0, 1), (2, 3)),
+            ((0, 2), (1, 1)),
+            ((0, 2), (1, 3)),
+            ((0, 2), (2, 0)),
+            ((0, 3), (1, 2)),
+            ((0, 3), (2, 0)),
+            ((0, 3), (2, 1)),
+            ((1, 0), (2, 1)),
+            ((1, 1), (2, 0)),
+            ((1, 1), (2, 2)),
+            ((1, 2), (2, 1)),
+            ((1, 2), (2, 3)),
+            ((1, 3), (2, 2)),
+        ],
+    )
+
+
+def test_modular_product_raises():
+    G = nx.Graph([(0, 1), (1, 2), (2, 0)])
+    H = nx.Graph([(0, 1), (1, 2), (2, 0)])
+    DG = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
+    DH = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.modular_product(G, DH)
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.modular_product(DG, H)
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.modular_product(DG, DH)
+
+    MG = nx.MultiGraph([(0, 1), (1, 2), (2, 0), (0, 1)])
+    MH = nx.MultiGraph([(0, 1), (1, 2), (2, 0), (0, 1)])
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.modular_product(G, MH)
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.modular_product(MG, H)
+    with pytest.raises(nx.NetworkXNotImplemented):
+        nx.modular_product(MG, MH)
+    with pytest.raises(nx.NetworkXNotImplemented):
+        # check multigraph with no multiedges
+        nx.modular_product(nx.MultiGraph(G), H)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/tests/test_unary.py

@@ -0,0 +1,55 @@
+import pytest
+
+import networkx as nx
+
+
+def test_complement():
+    null = nx.null_graph()
+    empty1 = nx.empty_graph(1)
+    empty10 = nx.empty_graph(10)
+    K3 = nx.complete_graph(3)
+    K5 = nx.complete_graph(5)
+    K10 = nx.complete_graph(10)
+    P2 = nx.path_graph(2)
+    P3 = nx.path_graph(3)
+    P5 = nx.path_graph(5)
+    P10 = nx.path_graph(10)
+    # complement of the complete graph is empty
+
+    G = nx.complement(K3)
+    assert nx.is_isomorphic(G, nx.empty_graph(3))
+    G = nx.complement(K5)
+    assert nx.is_isomorphic(G, nx.empty_graph(5))
+    # for any G, G=complement(complement(G))
+    P3cc = nx.complement(nx.complement(P3))
+    assert nx.is_isomorphic(P3, P3cc)
+    nullcc = nx.complement(nx.complement(null))
+    assert nx.is_isomorphic(null, nullcc)
+    b = nx.bull_graph()
+    bcc = nx.complement(nx.complement(b))
+    assert nx.is_isomorphic(b, bcc)
+
+
+def test_complement_2():
+    G1 = nx.DiGraph()
+    G1.add_edge("A", "B")
+    G1.add_edge("A", "C")
+    G1.add_edge("A", "D")
+    G1C = nx.complement(G1)
+    assert sorted(G1C.edges()) == [
+        ("B", "A"),
+        ("B", "C"),
+        ("B", "D"),
+        ("C", "A"),
+        ("C", "B"),
+        ("C", "D"),
+        ("D", "A"),
+        ("D", "B"),
+        ("D", "C"),
+    ]
+
+
+def test_reverse1():
+    # Other tests for reverse are done by the DiGraph and MultiDigraph.
+    G1 = nx.Graph()
+    pytest.raises(nx.NetworkXError, nx.reverse, G1)

minigpt2/lib/python3.10/site-packages/networkx/algorithms/operators/unary.py

@@ -0,0 +1,77 @@
+"""Unary operations on graphs"""
+
+import networkx as nx
+
+__all__ = ["complement", "reverse"]
+
+
+@nx._dispatchable(returns_graph=True)
+def complement(G):
+    """Returns the graph complement of G.
+
+    Parameters
+    ----------
+    G : graph
+       A NetworkX graph
+
+    Returns
+    -------
+    GC : A new graph.
+
+    Notes
+    -----
+    Note that `complement` does not create self-loops and also
+    does not produce parallel edges for MultiGraphs.
+
+    Graph, node, and edge data are not propagated to the new graph.
+
+    Examples
+    --------
+    >>> G = nx.Graph([(1, 2), (1, 3), (2, 3), (3, 4), (3, 5)])
+    >>> G_complement = nx.complement(G)
+    >>> G_complement.edges()  # This shows the edges of the complemented graph
+    EdgeView([(1, 4), (1, 5), (2, 4), (2, 5), (4, 5)])
+
+    """
+    R = G.__class__()
+    R.add_nodes_from(G)
+    R.add_edges_from(
+        ((n, n2) for n, nbrs in G.adjacency() for n2 in G if n2 not in nbrs if n != n2)
+    )
+    return R
+
+
+@nx._dispatchable(returns_graph=True)
+def reverse(G, copy=True):
+    """Returns the reverse directed graph of G.
+
+    Parameters
+    ----------
+    G : directed graph
+        A NetworkX directed graph
+    copy : bool
+        If True, then a new graph is returned. If False, then the graph is
+        reversed in place.
+
+    Returns
+    -------
+    H : directed graph
+        The reversed G.
+
+    Raises
+    ------
+    NetworkXError
+        If graph is undirected.
+
+    Examples
+    --------
+    >>> G = nx.DiGraph([(1, 2), (1, 3), (2, 3), (3, 4), (3, 5)])
+    >>> G_reversed = nx.reverse(G)
+    >>> G_reversed.edges()
+    OutEdgeView([(2, 1), (3, 1), (3, 2), (4, 3), (5, 3)])
+
+    """
+    if not G.is_directed():
+        raise nx.NetworkXError("Cannot reverse an undirected graph.")
+    else:
+        return G.reverse(copy=copy)

minigpt2/lib/python3.10/site-packages/networkx/drawing/__init__.py

@@ -0,0 +1,7 @@
+# graph drawing and interface to graphviz
+
+from .layout import *
+from .nx_latex import *
+from .nx_pylab import *
+from . import nx_agraph
+from . import nx_pydot

minigpt2/lib/python3.10/site-packages/networkx/drawing/layout.py

@@ -0,0 +1,1630 @@
+"""
+******
+Layout
+******
+
+Node positioning algorithms for graph drawing.
+
+For `random_layout()` the possible resulting shape
+is a square of side [0, scale] (default: [0, 1])
+Changing `center` shifts the layout by that amount.
+
+For the other layout routines, the extent is
+[center - scale, center + scale] (default: [-1, 1]).
+
+Warning: Most layout routines have only been tested in 2-dimensions.
+
+"""
+
+import networkx as nx
+from networkx.utils import np_random_state
+
+__all__ = [
+    "bipartite_layout",
+    "circular_layout",
+    "forceatlas2_layout",
+    "kamada_kawai_layout",
+    "random_layout",
+    "rescale_layout",
+    "rescale_layout_dict",
+    "shell_layout",
+    "spring_layout",
+    "spectral_layout",
+    "planar_layout",
+    "fruchterman_reingold_layout",
+    "spiral_layout",
+    "multipartite_layout",
+    "bfs_layout",
+    "arf_layout",
+]
+
+
+def _process_params(G, center, dim):
+    # Some boilerplate code.
+    import numpy as np
+
+    if not isinstance(G, nx.Graph):
+        empty_graph = nx.Graph()
+        empty_graph.add_nodes_from(G)
+        G = empty_graph
+
+    if center is None:
+        center = np.zeros(dim)
+    else:
+        center = np.asarray(center)
+
+    if len(center) != dim:
+        msg = "length of center coordinates must match dimension of layout"
+        raise ValueError(msg)
+
+    return G, center
+
+
+@np_random_state(3)
+def random_layout(G, center=None, dim=2, seed=None):
+    """Position nodes uniformly at random in the unit square.
+
+    For every node, a position is generated by choosing each of dim
+    coordinates uniformly at random on the interval [0.0, 1.0).
+
+    NumPy (http://scipy.org) is required for this function.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    dim : int
+        Dimension of layout.
+
+    seed : int, RandomState instance or None  optional (default=None)
+        Set the random state for deterministic node layouts.
+        If int, `seed` is the seed used by the random number generator,
+        if numpy.random.RandomState instance, `seed` is the random
+        number generator,
+        if None, the random number generator is the RandomState instance used
+        by numpy.random.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Examples
+    --------
+    >>> G = nx.lollipop_graph(4, 3)
+    >>> pos = nx.random_layout(G)
+
+    """
+    import numpy as np
+
+    G, center = _process_params(G, center, dim)
+    pos = seed.rand(len(G), dim) + center
+    pos = pos.astype(np.float32)
+    pos = dict(zip(G, pos))
+
+    return pos
+
+
+def circular_layout(G, scale=1, center=None, dim=2):
+    # dim=2 only
+    """Position nodes on a circle.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    dim : int
+        Dimension of layout.
+        If dim>2, the remaining dimensions are set to zero
+        in the returned positions.
+        If dim<2, a ValueError is raised.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Raises
+    ------
+    ValueError
+        If dim < 2
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.circular_layout(G)
+
+    Notes
+    -----
+    This algorithm currently only works in two dimensions and does not
+    try to minimize edge crossings.
+
+    """
+    import numpy as np
+
+    if dim < 2:
+        raise ValueError("cannot handle dimensions < 2")
+
+    G, center = _process_params(G, center, dim)
+
+    paddims = max(0, (dim - 2))
+
+    if len(G) == 0:
+        pos = {}
+    elif len(G) == 1:
+        pos = {nx.utils.arbitrary_element(G): center}
+    else:
+        # Discard the extra angle since it matches 0 radians.
+        theta = np.linspace(0, 1, len(G) + 1)[:-1] * 2 * np.pi
+        theta = theta.astype(np.float32)
+        pos = np.column_stack(
+            [np.cos(theta), np.sin(theta), np.zeros((len(G), paddims))]
+        )
+        pos = rescale_layout(pos, scale=scale) + center
+        pos = dict(zip(G, pos))
+
+    return pos
+
+
+def shell_layout(G, nlist=None, rotate=None, scale=1, center=None, dim=2):
+    """Position nodes in concentric circles.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    nlist : list of lists
+       List of node lists for each shell.
+
+    rotate : angle in radians (default=pi/len(nlist))
+       Angle by which to rotate the starting position of each shell
+       relative to the starting position of the previous shell.
+       To recreate behavior before v2.5 use rotate=0.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    dim : int
+        Dimension of layout, currently only dim=2 is supported.
+        Other dimension values result in a ValueError.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Raises
+    ------
+    ValueError
+        If dim != 2
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> shells = [[0], [1, 2, 3]]
+    >>> pos = nx.shell_layout(G, shells)
+
+    Notes
+    -----
+    This algorithm currently only works in two dimensions and does not
+    try to minimize edge crossings.
+
+    """
+    import numpy as np
+
+    if dim != 2:
+        raise ValueError("can only handle 2 dimensions")
+
+    G, center = _process_params(G, center, dim)
+
+    if len(G) == 0:
+        return {}
+    if len(G) == 1:
+        return {nx.utils.arbitrary_element(G): center}
+
+    if nlist is None:
+        # draw the whole graph in one shell
+        nlist = [list(G)]
+
+    radius_bump = scale / len(nlist)
+
+    if len(nlist[0]) == 1:
+        # single node at center
+        radius = 0.0
+    else:
+        # else start at r=1
+        radius = radius_bump
+
+    if rotate is None:
+        rotate = np.pi / len(nlist)
+    first_theta = rotate
+    npos = {}
+    for nodes in nlist:
+        # Discard the last angle (endpoint=False) since 2*pi matches 0 radians
+        theta = (
+            np.linspace(0, 2 * np.pi, len(nodes), endpoint=False, dtype=np.float32)
+            + first_theta
+        )
+        pos = radius * np.column_stack([np.cos(theta), np.sin(theta)]) + center
+        npos.update(zip(nodes, pos))
+        radius += radius_bump
+        first_theta += rotate
+
+    return npos
+
+
+def bipartite_layout(
+    G, nodes, align="vertical", scale=1, center=None, aspect_ratio=4 / 3
+):
+    """Position nodes in two straight lines.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    nodes : list or container
+        Nodes in one node set of the bipartite graph.
+        This set will be placed on left or top.
+
+    align : string (default='vertical')
+        The alignment of nodes. Vertical or horizontal.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    aspect_ratio : number (default=4/3):
+        The ratio of the width to the height of the layout.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node.
+
+    Examples
+    --------
+    >>> G = nx.bipartite.gnmk_random_graph(3, 5, 10, seed=123)
+    >>> top = nx.bipartite.sets(G)[0]
+    >>> pos = nx.bipartite_layout(G, top)
+
+    Notes
+    -----
+    This algorithm currently only works in two dimensions and does not
+    try to minimize edge crossings.
+
+    """
+
+    import numpy as np
+
+    if align not in ("vertical", "horizontal"):
+        msg = "align must be either vertical or horizontal."
+        raise ValueError(msg)
+
+    G, center = _process_params(G, center=center, dim=2)
+    if len(G) == 0:
+        return {}
+
+    height = 1
+    width = aspect_ratio * height
+    offset = (width / 2, height / 2)
+
+    top = dict.fromkeys(nodes)
+    bottom = [v for v in G if v not in top]
+    nodes = list(top) + bottom
+
+    left_xs = np.repeat(0, len(top))
+    right_xs = np.repeat(width, len(bottom))
+    left_ys = np.linspace(0, height, len(top))
+    right_ys = np.linspace(0, height, len(bottom))
+
+    top_pos = np.column_stack([left_xs, left_ys]) - offset
+    bottom_pos = np.column_stack([right_xs, right_ys]) - offset
+
+    pos = np.concatenate([top_pos, bottom_pos])
+    pos = rescale_layout(pos, scale=scale) + center
+    if align == "horizontal":
+        pos = pos[:, ::-1]  # swap x and y coords
+    pos = dict(zip(nodes, pos))
+    return pos
+
+
+@np_random_state(10)
+def spring_layout(
+    G,
+    k=None,
+    pos=None,
+    fixed=None,
+    iterations=50,
+    threshold=1e-4,
+    weight="weight",
+    scale=1,
+    center=None,
+    dim=2,
+    seed=None,
+):
+    """Position nodes using Fruchterman-Reingold force-directed algorithm.
+
+    The algorithm simulates a force-directed representation of the network
+    treating edges as springs holding nodes close, while treating nodes
+    as repelling objects, sometimes called an anti-gravity force.
+    Simulation continues until the positions are close to an equilibrium.
+
+    There are some hard-coded values: minimal distance between
+    nodes (0.01) and "temperature" of 0.1 to ensure nodes don't fly away.
+    During the simulation, `k` helps determine the distance between nodes,
+    though `scale` and `center` determine the size and place after
+    rescaling occurs at the end of the simulation.
+
+    Fixing some nodes doesn't allow them to move in the simulation.
+    It also turns off the rescaling feature at the simulation's end.
+    In addition, setting `scale` to `None` turns off rescaling.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    k : float (default=None)
+        Optimal distance between nodes.  If None the distance is set to
+        1/sqrt(n) where n is the number of nodes.  Increase this value
+        to move nodes farther apart.
+
+    pos : dict or None  optional (default=None)
+        Initial positions for nodes as a dictionary with node as keys
+        and values as a coordinate list or tuple.  If None, then use
+        random initial positions.
+
+    fixed : list or None  optional (default=None)
+        Nodes to keep fixed at initial position.
+        Nodes not in ``G.nodes`` are ignored.
+        ValueError raised if `fixed` specified and `pos` not.
+
+    iterations : int  optional (default=50)
+        Maximum number of iterations taken
+
+    threshold: float optional (default = 1e-4)
+        Threshold for relative error in node position changes.
+        The iteration stops if the error is below this threshold.
+
+    weight : string or None   optional (default='weight')
+        The edge attribute that holds the numerical value used for
+        the edge weight.  Larger means a stronger attractive force.
+        If None, then all edge weights are 1.
+
+    scale : number or None (default: 1)
+        Scale factor for positions. Not used unless `fixed is None`.
+        If scale is None, no rescaling is performed.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+        Not used unless `fixed is None`.
+
+    dim : int
+        Dimension of layout.
+
+    seed : int, RandomState instance or None  optional (default=None)
+        Used only for the initial positions in the algorithm.
+        Set the random state for deterministic node layouts.
+        If int, `seed` is the seed used by the random number generator,
+        if numpy.random.RandomState instance, `seed` is the random
+        number generator,
+        if None, the random number generator is the RandomState instance used
+        by numpy.random.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.spring_layout(G)
+
+    # The same using longer but equivalent function name
+    >>> pos = nx.fruchterman_reingold_layout(G)
+    """
+    import numpy as np
+
+    G, center = _process_params(G, center, dim)
+
+    if fixed is not None:
+        if pos is None:
+            raise ValueError("nodes are fixed without positions given")
+        for node in fixed:
+            if node not in pos:
+                raise ValueError("nodes are fixed without positions given")
+        nfixed = {node: i for i, node in enumerate(G)}
+        fixed = np.asarray([nfixed[node] for node in fixed if node in nfixed])
+
+    if pos is not None:
+        # Determine size of existing domain to adjust initial positions
+        dom_size = max(coord for pos_tup in pos.values() for coord in pos_tup)
+        if dom_size == 0:
+            dom_size = 1
+        pos_arr = seed.rand(len(G), dim) * dom_size + center
+
+        for i, n in enumerate(G):
+            if n in pos:
+                pos_arr[i] = np.asarray(pos[n])
+    else:
+        pos_arr = None
+        dom_size = 1
+
+    if len(G) == 0:
+        return {}
+    if len(G) == 1:
+        return {nx.utils.arbitrary_element(G.nodes()): center}
+
+    try:
+        # Sparse matrix
+        if len(G) < 500:  # sparse solver for large graphs
+            raise ValueError
+        A = nx.to_scipy_sparse_array(G, weight=weight, dtype="f")
+        if k is None and fixed is not None:
+            # We must adjust k by domain size for layouts not near 1x1
+            nnodes, _ = A.shape
+            k = dom_size / np.sqrt(nnodes)
+        pos = _sparse_fruchterman_reingold(
+            A, k, pos_arr, fixed, iterations, threshold, dim, seed
+        )
+    except ValueError:
+        A = nx.to_numpy_array(G, weight=weight)
+        if k is None and fixed is not None:
+            # We must adjust k by domain size for layouts not near 1x1
+            nnodes, _ = A.shape
+            k = dom_size / np.sqrt(nnodes)
+        pos = _fruchterman_reingold(
+            A, k, pos_arr, fixed, iterations, threshold, dim, seed
+        )
+    if fixed is None and scale is not None:
+        pos = rescale_layout(pos, scale=scale) + center
+    pos = dict(zip(G, pos))
+    return pos
+
+
+fruchterman_reingold_layout = spring_layout
+
+
+@np_random_state(7)
+def _fruchterman_reingold(
+    A, k=None, pos=None, fixed=None, iterations=50, threshold=1e-4, dim=2, seed=None
+):
+    # Position nodes in adjacency matrix A using Fruchterman-Reingold
+    # Entry point for NetworkX graph is fruchterman_reingold_layout()
+    import numpy as np
+
+    try:
+        nnodes, _ = A.shape
+    except AttributeError as err:
+        msg = "fruchterman_reingold() takes an adjacency matrix as input"
+        raise nx.NetworkXError(msg) from err
+
+    if pos is None:
+        # random initial positions
+        pos = np.asarray(seed.rand(nnodes, dim), dtype=A.dtype)
+    else:
+        # make sure positions are of same type as matrix
+        pos = pos.astype(A.dtype)
+
+    # optimal distance between nodes
+    if k is None:
+        k = np.sqrt(1.0 / nnodes)
+    # the initial "temperature"  is about .1 of domain area (=1x1)
+    # this is the largest step allowed in the dynamics.
+    # We need to calculate this in case our fixed positions force our domain
+    # to be much bigger than 1x1
+    t = max(max(pos.T[0]) - min(pos.T[0]), max(pos.T[1]) - min(pos.T[1])) * 0.1
+    # simple cooling scheme.
+    # linearly step down by dt on each iteration so last iteration is size dt.
+    dt = t / (iterations + 1)
+    delta = np.zeros((pos.shape[0], pos.shape[0], pos.shape[1]), dtype=A.dtype)
+    # the inscrutable (but fast) version
+    # this is still O(V^2)
+    # could use multilevel methods to speed this up significantly
+    for iteration in range(iterations):
+        # matrix of difference between points
+        delta = pos[:, np.newaxis, :] - pos[np.newaxis, :, :]
+        # distance between points
+        distance = np.linalg.norm(delta, axis=-1)
+        # enforce minimum distance of 0.01
+        np.clip(distance, 0.01, None, out=distance)
+        # displacement "force"
+        displacement = np.einsum(
+            "ijk,ij->ik", delta, (k * k / distance**2 - A * distance / k)
+        )
+        # update positions
+        length = np.linalg.norm(displacement, axis=-1)
+        length = np.where(length < 0.01, 0.1, length)
+        delta_pos = np.einsum("ij,i->ij", displacement, t / length)
+        if fixed is not None:
+            # don't change positions of fixed nodes
+            delta_pos[fixed] = 0.0
+        pos += delta_pos
+        # cool temperature
+        t -= dt
+        if (np.linalg.norm(delta_pos) / nnodes) < threshold:
+            break
+    return pos
+
+
+@np_random_state(7)
+def _sparse_fruchterman_reingold(
+    A, k=None, pos=None, fixed=None, iterations=50, threshold=1e-4, dim=2, seed=None
+):
+    # Position nodes in adjacency matrix A using Fruchterman-Reingold
+    # Entry point for NetworkX graph is fruchterman_reingold_layout()
+    # Sparse version
+    import numpy as np
+    import scipy as sp
+
+    try:
+        nnodes, _ = A.shape
+    except AttributeError as err:
+        msg = "fruchterman_reingold() takes an adjacency matrix as input"
+        raise nx.NetworkXError(msg) from err
+    # make sure we have a LIst of Lists representation
+    try:
+        A = A.tolil()
+    except AttributeError:
+        A = (sp.sparse.coo_array(A)).tolil()
+
+    if pos is None:
+        # random initial positions
+        pos = np.asarray(seed.rand(nnodes, dim), dtype=A.dtype)
+    else:
+        # make sure positions are of same type as matrix
+        pos = pos.astype(A.dtype)
+
+    # no fixed nodes
+    if fixed is None:
+        fixed = []
+
+    # optimal distance between nodes
+    if k is None:
+        k = np.sqrt(1.0 / nnodes)
+    # the initial "temperature"  is about .1 of domain area (=1x1)
+    # this is the largest step allowed in the dynamics.
+    t = max(max(pos.T[0]) - min(pos.T[0]), max(pos.T[1]) - min(pos.T[1])) * 0.1
+    # simple cooling scheme.
+    # linearly step down by dt on each iteration so last iteration is size dt.
+    dt = t / (iterations + 1)
+
+    displacement = np.zeros((dim, nnodes))
+    for iteration in range(iterations):
+        displacement *= 0
+        # loop over rows
+        for i in range(A.shape[0]):
+            if i in fixed:
+                continue
+            # difference between this row's node position and all others
+            delta = (pos[i] - pos).T
+            # distance between points
+            distance = np.sqrt((delta**2).sum(axis=0))
+            # enforce minimum distance of 0.01
+            distance = np.where(distance < 0.01, 0.01, distance)
+            # the adjacency matrix row
+            Ai = A.getrowview(i).toarray()  # TODO: revisit w/ sparse 1D container
+            # displacement "force"
+            displacement[:, i] += (
+                delta * (k * k / distance**2 - Ai * distance / k)
+            ).sum(axis=1)
+        # update positions
+        length = np.sqrt((displacement**2).sum(axis=0))
+        length = np.where(length < 0.01, 0.1, length)
+        delta_pos = (displacement * t / length).T
+        pos += delta_pos
+        # cool temperature
+        t -= dt
+        if (np.linalg.norm(delta_pos) / nnodes) < threshold:
+            break
+    return pos
+
+
+def kamada_kawai_layout(
+    G, dist=None, pos=None, weight="weight", scale=1, center=None, dim=2
+):
+    """Position nodes using Kamada-Kawai path-length cost-function.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    dist : dict (default=None)
+        A two-level dictionary of optimal distances between nodes,
+        indexed by source and destination node.
+        If None, the distance is computed using shortest_path_length().
+
+    pos : dict or None  optional (default=None)
+        Initial positions for nodes as a dictionary with node as keys
+        and values as a coordinate list or tuple.  If None, then use
+        circular_layout() for dim >= 2 and a linear layout for dim == 1.
+
+    weight : string or None   optional (default='weight')
+        The edge attribute that holds the numerical value used for
+        the edge weight.  If None, then all edge weights are 1.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    dim : int
+        Dimension of layout.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.kamada_kawai_layout(G)
+    """
+    import numpy as np
+
+    G, center = _process_params(G, center, dim)
+    nNodes = len(G)
+    if nNodes == 0:
+        return {}
+
+    if dist is None:
+        dist = dict(nx.shortest_path_length(G, weight=weight))
+    dist_mtx = 1e6 * np.ones((nNodes, nNodes))
+    for row, nr in enumerate(G):
+        if nr not in dist:
+            continue
+        rdist = dist[nr]
+        for col, nc in enumerate(G):
+            if nc not in rdist:
+                continue
+            dist_mtx[row][col] = rdist[nc]
+
+    if pos is None:
+        if dim >= 3:
+            pos = random_layout(G, dim=dim)
+        elif dim == 2:
+            pos = circular_layout(G, dim=dim)
+        else:
+            pos = dict(zip(G, np.linspace(0, 1, len(G))))
+    pos_arr = np.array([pos[n] for n in G])
+
+    pos = _kamada_kawai_solve(dist_mtx, pos_arr, dim)
+
+    pos = rescale_layout(pos, scale=scale) + center
+    return dict(zip(G, pos))
+
+
+def _kamada_kawai_solve(dist_mtx, pos_arr, dim):
+    # Anneal node locations based on the Kamada-Kawai cost-function,
+    # using the supplied matrix of preferred inter-node distances,
+    # and starting locations.
+
+    import numpy as np
+    import scipy as sp
+
+    meanwt = 1e-3
+    costargs = (np, 1 / (dist_mtx + np.eye(dist_mtx.shape[0]) * 1e-3), meanwt, dim)
+
+    optresult = sp.optimize.minimize(
+        _kamada_kawai_costfn,
+        pos_arr.ravel(),
+        method="L-BFGS-B",
+        args=costargs,
+        jac=True,
+    )
+
+    return optresult.x.reshape((-1, dim))
+
+
+def _kamada_kawai_costfn(pos_vec, np, invdist, meanweight, dim):
+    # Cost-function and gradient for Kamada-Kawai layout algorithm
+    nNodes = invdist.shape[0]
+    pos_arr = pos_vec.reshape((nNodes, dim))
+
+    delta = pos_arr[:, np.newaxis, :] - pos_arr[np.newaxis, :, :]
+    nodesep = np.linalg.norm(delta, axis=-1)
+    direction = np.einsum("ijk,ij->ijk", delta, 1 / (nodesep + np.eye(nNodes) * 1e-3))
+
+    offset = nodesep * invdist - 1.0
+    offset[np.diag_indices(nNodes)] = 0
+
+    cost = 0.5 * np.sum(offset**2)
+    grad = np.einsum("ij,ij,ijk->ik", invdist, offset, direction) - np.einsum(
+        "ij,ij,ijk->jk", invdist, offset, direction
+    )
+
+    # Additional parabolic term to encourage mean position to be near origin:
+    sumpos = np.sum(pos_arr, axis=0)
+    cost += 0.5 * meanweight * np.sum(sumpos**2)
+    grad += meanweight * sumpos
+
+    return (cost, grad.ravel())
+
+
+def spectral_layout(G, weight="weight", scale=1, center=None, dim=2):
+    """Position nodes using the eigenvectors of the graph Laplacian.
+
+    Using the unnormalized Laplacian, the layout shows possible clusters of
+    nodes which are an approximation of the ratio cut. If dim is the number of
+    dimensions then the positions are the entries of the dim eigenvectors
+    corresponding to the ascending eigenvalues starting from the second one.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    weight : string or None   optional (default='weight')
+        The edge attribute that holds the numerical value used for
+        the edge weight.  If None, then all edge weights are 1.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    dim : int
+        Dimension of layout.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.spectral_layout(G)
+
+    Notes
+    -----
+    Directed graphs will be considered as undirected graphs when
+    positioning the nodes.
+
+    For larger graphs (>500 nodes) this will use the SciPy sparse
+    eigenvalue solver (ARPACK).
+    """
+    # handle some special cases that break the eigensolvers
+    import numpy as np
+
+    G, center = _process_params(G, center, dim)
+
+    if len(G) <= 2:
+        if len(G) == 0:
+            pos = np.array([])
+        elif len(G) == 1:
+            pos = np.array([center])
+        else:
+            pos = np.array([np.zeros(dim), np.array(center) * 2.0])
+        return dict(zip(G, pos))
+    try:
+        # Sparse matrix
+        if len(G) < 500:  # dense solver is faster for small graphs
+            raise ValueError
+        A = nx.to_scipy_sparse_array(G, weight=weight, dtype="d")
+        # Symmetrize directed graphs
+        if G.is_directed():
+            A = A + np.transpose(A)
+        pos = _sparse_spectral(A, dim)
+    except (ImportError, ValueError):
+        # Dense matrix
+        A = nx.to_numpy_array(G, weight=weight)
+        # Symmetrize directed graphs
+        if G.is_directed():
+            A += A.T
+        pos = _spectral(A, dim)
+
+    pos = rescale_layout(pos, scale=scale) + center
+    pos = dict(zip(G, pos))
+    return pos
+
+
+def _spectral(A, dim=2):
+    # Input adjacency matrix A
+    # Uses dense eigenvalue solver from numpy
+    import numpy as np
+
+    try:
+        nnodes, _ = A.shape
+    except AttributeError as err:
+        msg = "spectral() takes an adjacency matrix as input"
+        raise nx.NetworkXError(msg) from err
+
+    # form Laplacian matrix where D is diagonal of degrees
+    D = np.identity(nnodes, dtype=A.dtype) * np.sum(A, axis=1)
+    L = D - A
+
+    eigenvalues, eigenvectors = np.linalg.eig(L)
+    # sort and keep smallest nonzero
+    index = np.argsort(eigenvalues)[1 : dim + 1]  # 0 index is zero eigenvalue
+    return np.real(eigenvectors[:, index])
+
+
+def _sparse_spectral(A, dim=2):
+    # Input adjacency matrix A
+    # Uses sparse eigenvalue solver from scipy
+    # Could use multilevel methods here, see Koren "On spectral graph drawing"
+    import numpy as np
+    import scipy as sp
+
+    try:
+        nnodes, _ = A.shape
+    except AttributeError as err:
+        msg = "sparse_spectral() takes an adjacency matrix as input"
+        raise nx.NetworkXError(msg) from err
+
+    # form Laplacian matrix
+    # TODO: Rm csr_array wrapper in favor of spdiags array constructor when available
+    D = sp.sparse.csr_array(sp.sparse.spdiags(A.sum(axis=1), 0, nnodes, nnodes))
+    L = D - A
+
+    k = dim + 1
+    # number of Lanczos vectors for ARPACK solver.What is the right scaling?
+    ncv = max(2 * k + 1, int(np.sqrt(nnodes)))
+    # return smallest k eigenvalues and eigenvectors
+    eigenvalues, eigenvectors = sp.sparse.linalg.eigsh(L, k, which="SM", ncv=ncv)
+    index = np.argsort(eigenvalues)[1:k]  # 0 index is zero eigenvalue
+    return np.real(eigenvectors[:, index])
+
+
+def planar_layout(G, scale=1, center=None, dim=2):
+    """Position nodes without edge intersections.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G. If G is of type
+        nx.PlanarEmbedding, the positions are selected accordingly.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    dim : int
+        Dimension of layout.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Raises
+    ------
+    NetworkXException
+        If G is not planar
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.planar_layout(G)
+    """
+    import numpy as np
+
+    if dim != 2:
+        raise ValueError("can only handle 2 dimensions")
+
+    G, center = _process_params(G, center, dim)
+
+    if len(G) == 0:
+        return {}
+
+    if isinstance(G, nx.PlanarEmbedding):
+        embedding = G
+    else:
+        is_planar, embedding = nx.check_planarity(G)
+        if not is_planar:
+            raise nx.NetworkXException("G is not planar.")
+    pos = nx.combinatorial_embedding_to_pos(embedding)
+    node_list = list(embedding)
+    pos = np.vstack([pos[x] for x in node_list])
+    pos = pos.astype(np.float64)
+    pos = rescale_layout(pos, scale=scale) + center
+    return dict(zip(node_list, pos))
+
+
+def spiral_layout(G, scale=1, center=None, dim=2, resolution=0.35, equidistant=False):
+    """Position nodes in a spiral layout.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+    scale : number (default: 1)
+        Scale factor for positions.
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+    dim : int, default=2
+        Dimension of layout, currently only dim=2 is supported.
+        Other dimension values result in a ValueError.
+    resolution : float, default=0.35
+        The compactness of the spiral layout returned.
+        Lower values result in more compressed spiral layouts.
+    equidistant : bool, default=False
+        If True, nodes will be positioned equidistant from each other
+        by decreasing angle further from center.
+        If False, nodes will be positioned at equal angles
+        from each other by increasing separation further from center.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node
+
+    Raises
+    ------
+    ValueError
+        If dim != 2
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.spiral_layout(G)
+    >>> nx.draw(G, pos=pos)
+
+    Notes
+    -----
+    This algorithm currently only works in two dimensions.
+
+    """
+    import numpy as np
+
+    if dim != 2:
+        raise ValueError("can only handle 2 dimensions")
+
+    G, center = _process_params(G, center, dim)
+
+    if len(G) == 0:
+        return {}
+    if len(G) == 1:
+        return {nx.utils.arbitrary_element(G): center}
+
+    pos = []
+    if equidistant:
+        chord = 1
+        step = 0.5
+        theta = resolution
+        theta += chord / (step * theta)
+        for _ in range(len(G)):
+            r = step * theta
+            theta += chord / r
+            pos.append([np.cos(theta) * r, np.sin(theta) * r])
+
+    else:
+        dist = np.arange(len(G), dtype=float)
+        angle = resolution * dist
+        pos = np.transpose(dist * np.array([np.cos(angle), np.sin(angle)]))
+
+    pos = rescale_layout(np.array(pos), scale=scale) + center
+
+    pos = dict(zip(G, pos))
+
+    return pos
+
+
+def multipartite_layout(G, subset_key="subset", align="vertical", scale=1, center=None):
+    """Position nodes in layers of straight lines.
+
+    Parameters
+    ----------
+    G : NetworkX graph or list of nodes
+        A position will be assigned to every node in G.
+
+    subset_key : string or dict (default='subset')
+        If a string, the key of node data in G that holds the node subset.
+        If a dict, keyed by layer number to the nodes in that layer/subset.
+
+    align : string (default='vertical')
+        The alignment of nodes. Vertical or horizontal.
+
+    scale : number (default: 1)
+        Scale factor for positions.
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node.
+
+    Examples
+    --------
+    >>> G = nx.complete_multipartite_graph(28, 16, 10)
+    >>> pos = nx.multipartite_layout(G)
+
+    or use a dict to provide the layers of the layout
+
+    >>> G = nx.Graph([(0, 1), (1, 2), (1, 3), (3, 4)])
+    >>> layers = {"a": [0], "b": [1], "c": [2, 3], "d": [4]}
+    >>> pos = nx.multipartite_layout(G, subset_key=layers)
+
+    Notes
+    -----
+    This algorithm currently only works in two dimensions and does not
+    try to minimize edge crossings.
+
+    Network does not need to be a complete multipartite graph. As long as nodes
+    have subset_key data, they will be placed in the corresponding layers.
+
+    """
+    import numpy as np
+
+    if align not in ("vertical", "horizontal"):
+        msg = "align must be either vertical or horizontal."
+        raise ValueError(msg)
+
+    G, center = _process_params(G, center=center, dim=2)
+    if len(G) == 0:
+        return {}
+
+    try:
+        # check if subset_key is dict-like
+        if len(G) != sum(len(nodes) for nodes in subset_key.values()):
+            raise nx.NetworkXError(
+                "all nodes must be in one subset of `subset_key` dict"
+            )
+    except AttributeError:
+        # subset_key is not a dict, hence a string
+        node_to_subset = nx.get_node_attributes(G, subset_key)
+        if len(node_to_subset) != len(G):
+            raise nx.NetworkXError(
+                f"all nodes need a subset_key attribute: {subset_key}"
+            )
+        subset_key = nx.utils.groups(node_to_subset)
+
+    # Sort by layer, if possible
+    try:
+        layers = dict(sorted(subset_key.items()))
+    except TypeError:
+        layers = subset_key
+
+    pos = None
+    nodes = []
+    width = len(layers)
+    for i, layer in enumerate(layers.values()):
+        height = len(layer)
+        xs = np.repeat(i, height)
+        ys = np.arange(0, height, dtype=float)
+        offset = ((width - 1) / 2, (height - 1) / 2)
+        layer_pos = np.column_stack([xs, ys]) - offset
+        if pos is None:
+            pos = layer_pos
+        else:
+            pos = np.concatenate([pos, layer_pos])
+        nodes.extend(layer)
+    pos = rescale_layout(pos, scale=scale) + center
+    if align == "horizontal":
+        pos = pos[:, ::-1]  # swap x and y coords
+    pos = dict(zip(nodes, pos))
+    return pos
+
+
+@np_random_state("seed")
+def arf_layout(
+    G,
+    pos=None,
+    scaling=1,
+    a=1.1,
+    etol=1e-6,
+    dt=1e-3,
+    max_iter=1000,
+    *,
+    seed=None,
+):
+    """Arf layout for networkx
+
+    The attractive and repulsive forces (arf) layout [1]
+    improves the spring layout in three ways. First, it
+    prevents congestion of highly connected nodes due to
+    strong forcing between nodes. Second, it utilizes the
+    layout space more effectively by preventing large gaps
+    that spring layout tends to create. Lastly, the arf
+    layout represents symmetries in the layout better than
+    the default spring layout.
+
+    Parameters
+    ----------
+    G : nx.Graph or nx.DiGraph
+        Networkx graph.
+    pos : dict
+        Initial  position of  the nodes.  If set  to None  a
+        random layout will be used.
+    scaling : float
+        Scales the radius of the circular layout space.
+    a : float
+        Strength of springs between connected nodes. Should be larger than 1. The greater a, the clearer the separation ofunconnected sub clusters.
+    etol : float
+        Gradient sum of spring forces must be larger than `etol` before successful termination.
+    dt : float
+        Time step for force differential equation simulations.
+    max_iter : int
+        Max iterations before termination of the algorithm.
+    seed : int, RandomState instance or None  optional (default=None)
+        Set the random state for deterministic node layouts.
+        If int, `seed` is the seed used by the random number generator,
+        if numpy.random.RandomState instance, `seed` is the random
+        number generator,
+        if None, the random number generator is the RandomState instance used
+        by numpy.random.
+
+    References
+    .. [1] "Self-Organization Applied to Dynamic Network Layout", M. Geipel,
+            International Journal of Modern Physics C, 2007, Vol 18, No 10, pp. 1537-1549.
+            https://doi.org/10.1142/S0129183107011558 https://arxiv.org/abs/0704.1748
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node.
+
+    Examples
+    --------
+    >>> G = nx.grid_graph((5, 5))
+    >>> pos = nx.arf_layout(G)
+
+    """
+    import warnings
+
+    import numpy as np
+
+    if a <= 1:
+        msg = "The parameter a should be larger than 1"
+        raise ValueError(msg)
+
+    pos_tmp = nx.random_layout(G, seed=seed)
+    if pos is None:
+        pos = pos_tmp
+    else:
+        for node in G.nodes():
+            if node not in pos:
+                pos[node] = pos_tmp[node].copy()
+
+    # Initialize spring constant matrix
+    N = len(G)
+    # No nodes no computation
+    if N == 0:
+        return pos
+
+    # init force of springs
+    K = np.ones((N, N)) - np.eye(N)
+    node_order = {node: i for i, node in enumerate(G)}
+    for x, y in G.edges():
+        if x != y:
+            idx, jdx = (node_order[i] for i in (x, y))
+            K[idx, jdx] = a
+
+    # vectorize values
+    p = np.asarray(list(pos.values()))
+
+    # equation 10 in [1]
+    rho = scaling * np.sqrt(N)
+
+    # looping variables
+    error = etol + 1
+    n_iter = 0
+    while error > etol:
+        diff = p[:, np.newaxis] - p[np.newaxis]
+        A = np.linalg.norm(diff, axis=-1)[..., np.newaxis]
+        # attraction_force - repulsions force
+        # suppress nans due to division; caused by diagonal set to zero.
+        # Does not affect the computation due to nansum
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            change = K[..., np.newaxis] * diff - rho / A * diff
+        change = np.nansum(change, axis=0)
+        p += change * dt
+
+        error = np.linalg.norm(change, axis=-1).sum()
+        if n_iter > max_iter:
+            break
+        n_iter += 1
+    return dict(zip(G.nodes(), p))
+
+
+@np_random_state("seed")
+def forceatlas2_layout(
+    G,
+    pos=None,
+    *,
+    max_iter=100,
+    jitter_tolerance=1.0,
+    scaling_ratio=2.0,
+    gravity=1.0,
+    distributed_action=False,
+    strong_gravity=False,
+    node_mass=None,
+    node_size=None,
+    weight=None,
+    dissuade_hubs=False,
+    linlog=False,
+    seed=None,
+    dim=2,
+):
+    """Position nodes using the ForceAtlas2 force-directed layout algorithm.
+
+    This function applies the ForceAtlas2 layout algorithm [1]_ to a NetworkX graph,
+    positioning the nodes in a way that visually represents the structure of the graph.
+    The algorithm uses physical simulation to minimize the energy of the system,
+    resulting in a more readable layout.
+
+    Parameters
+    ----------
+    G : nx.Graph
+        A NetworkX graph to be laid out.
+    pos : dict or None, optional
+        Initial positions of the nodes. If None, random initial positions are used.
+    max_iter : int (default: 100)
+        Number of iterations for the layout optimization.
+    jitter_tolerance : float (default: 1.0)
+        Controls the tolerance for adjusting the speed of layout generation.
+    scaling_ratio : float (default: 2.0)
+        Determines the scaling of attraction and repulsion forces.
+    distributed_attraction : bool (default: False)
+        Distributes the attraction force evenly among nodes.
+    strong_gravity : bool (default: False)
+        Applies a strong gravitational pull towards the center.
+    node_mass : dict or None, optional
+        Maps nodes to their masses, influencing the attraction to other nodes.
+    node_size : dict or None, optional
+        Maps nodes to their sizes, preventing crowding by creating a halo effect.
+    dissuade_hubs : bool (default: False)
+        Prevents the clustering of hub nodes.
+    linlog : bool (default: False)
+        Uses logarithmic attraction instead of linear.
+    seed : int, RandomState instance or None  optional (default=None)
+        Used only for the initial positions in the algorithm.
+        Set the random state for deterministic node layouts.
+        If int, `seed` is the seed used by the random number generator,
+        if numpy.random.RandomState instance, `seed` is the random
+        number generator,
+        if None, the random number generator is the RandomState instance used
+        by numpy.random.
+    dim : int (default: 2)
+        Sets the dimensions for the layout. Ignored if `pos` is provided.
+
+    Examples
+    --------
+    >>> import networkx as nx
+    >>> G = nx.florentine_families_graph()
+    >>> pos = nx.forceatlas2_layout(G)
+    >>> nx.draw(G, pos=pos)
+
+    References
+    ----------
+    .. [1] Jacomy, M., Venturini, T., Heymann, S., & Bastian, M. (2014).
+           ForceAtlas2, a continuous graph layout algorithm for handy network
+           visualization designed for the Gephi software. PloS one, 9(6), e98679.
+           https://doi.org/10.1371/journal.pone.0098679
+    """
+    import numpy as np
+
+    if len(G) == 0:
+        return {}
+    # parse optional pos positions
+    if pos is None:
+        pos = nx.random_layout(G, dim=dim, seed=seed)
+        pos_arr = np.array(list(pos.values()))
+    else:
+        # set default node interval within the initial pos values
+        pos_init = np.array(list(pos.values()))
+        max_pos = pos_init.max(axis=0)
+        min_pos = pos_init.min(axis=0)
+        dim = max_pos.size
+        pos_arr = min_pos + seed.rand(len(G), dim) * (max_pos - min_pos)
+        for idx, node in enumerate(G):
+            if node in pos:
+                pos_arr[idx] = pos[node].copy()
+
+    mass = np.zeros(len(G))
+    size = np.zeros(len(G))
+
+    # Only adjust for size when the users specifies size other than default (1)
+    adjust_sizes = False
+    if node_size is None:
+        node_size = {}
+    else:
+        adjust_sizes = True
+
+    if node_mass is None:
+        node_mass = {}
+
+    for idx, node in enumerate(G):
+        mass[idx] = node_mass.get(node, G.degree(node) + 1)
+        size[idx] = node_size.get(node, 1)
+
+    n = len(G)
+    gravities = np.zeros((n, dim))
+    attraction = np.zeros((n, dim))
+    repulsion = np.zeros((n, dim))
+    A = nx.to_numpy_array(G, weight=weight)
+
+    def estimate_factor(n, swing, traction, speed, speed_efficiency, jitter_tolerance):
+        """Computes the scaling factor for the force in the ForceAtlas2 layout algorithm.
+
+        This   helper  function   adjusts   the  speed   and
+        efficiency  of the  layout generation  based on  the
+        current state of  the system, such as  the number of
+        nodes, current swing, and traction forces.
+
+        Parameters
+        ----------
+        n : int
+            Number of nodes in the graph.
+        swing : float
+            The current swing, representing the oscillation of the nodes.
+        traction : float
+            The current traction force, representing the attraction between nodes.
+        speed : float
+            The current speed of the layout generation.
+        speed_efficiency : float
+            The efficiency of the current speed, influencing how fast the layout converges.
+        jitter_tolerance : float
+            The tolerance for jitter, affecting how much speed adjustment is allowed.
+
+        Returns
+        -------
+        tuple
+            A tuple containing the updated speed and speed efficiency.
+
+        Notes
+        -----
+        This function is a part of the ForceAtlas2 layout algorithm and is used to dynamically adjust the
+        layout parameters to achieve an optimal and stable visualization.
+
+        """
+        import numpy as np
+
+        # estimate jitter
+        opt_jitter = 0.05 * np.sqrt(n)
+        min_jitter = np.sqrt(opt_jitter)
+        max_jitter = 10
+        min_speed_efficiency = 0.05
+
+        other = min(max_jitter, opt_jitter * traction / n**2)
+        jitter = jitter_tolerance * max(min_jitter, other)
+
+        if swing / traction > 2.0:
+            if speed_efficiency > min_speed_efficiency:
+                speed_efficiency *= 0.5
+            jitter = max(jitter, jitter_tolerance)
+        if swing == 0:
+            target_speed = np.inf
+        else:
+            target_speed = jitter * speed_efficiency * traction / swing
+
+        if swing > jitter * traction:
+            if speed_efficiency > min_speed_efficiency:
+                speed_efficiency *= 0.7
+        elif speed < 1000:
+            speed_efficiency *= 1.3
+
+        max_rise = 0.5
+        speed = speed + min(target_speed - speed, max_rise * speed)
+        return speed, speed_efficiency
+
+    speed = 1
+    speed_efficiency = 1
+    swing = 1
+    traction = 1
+    for _ in range(max_iter):
+        # compute pairwise difference
+        diff = pos_arr[:, None] - pos_arr[None]
+        # compute pairwise distance
+        distance = np.linalg.norm(diff, axis=-1)
+
+        # linear attraction
+        if linlog:
+            attraction = -np.log(1 + distance) / distance
+            np.fill_diagonal(attraction, 0)
+            attraction = np.einsum("ij, ij -> ij", attraction, A)
+            attraction = np.einsum("ijk, ij -> ik", diff, attraction)
+
+        else:
+            attraction = -np.einsum("ijk, ij -> ik", diff, A)
+
+        if distributed_action:
+            attraction /= mass[:, None]
+
+        # repulsion
+        tmp = mass[:, None] @ mass[None]
+        if adjust_sizes:
+            distance += -size[:, None] - size[None]
+
+        d2 = distance**2
+        # remove self-interaction
+        np.fill_diagonal(tmp, 0)
+        np.fill_diagonal(d2, 1)
+        factor = (tmp / d2) * scaling_ratio
+        repulsion = np.einsum("ijk, ij -> ik", diff, factor)
+
+        # gravity
+        gravities = (
+            -gravity
+            * mass[:, None]
+            * pos_arr
+            / np.linalg.norm(pos_arr, axis=-1)[:, None]
+        )
+
+        if strong_gravity:
+            gravities *= np.linalg.norm(pos_arr, axis=-1)[:, None]
+        # total forces
+        update = attraction + repulsion + gravities
+
+        # compute total swing and traction
+        swing += (mass * np.linalg.norm(pos_arr - update, axis=-1)).sum()
+        traction += (0.5 * mass * np.linalg.norm(pos_arr + update, axis=-1)).sum()
+
+        speed, speed_efficiency = estimate_factor(
+            n,
+            swing,
+            traction,
+            speed,
+            speed_efficiency,
+            jitter_tolerance,
+        )
+
+        # update pos
+        if adjust_sizes:
+            swinging = mass * np.linalg.norm(update, axis=-1)
+            factor = 0.1 * speed / (1 + np.sqrt(speed * swinging))
+            df = np.linalg.norm(update, axis=-1)
+            factor = np.minimum(factor * df, 10.0 * np.ones(df.shape)) / df
+        else:
+            swinging = mass * np.linalg.norm(update, axis=-1)
+            factor = speed / (1 + np.sqrt(speed * swinging))
+
+        pos_arr += update * factor[:, None]
+        if abs((update * factor[:, None]).sum()) < 1e-10:
+            break
+
+    return dict(zip(G, pos_arr))
+
+
+def rescale_layout(pos, scale=1):
+    """Returns scaled position array to (-scale, scale) in all axes.
+
+    The function acts on NumPy arrays which hold position information.
+    Each position is one row of the array. The dimension of the space
+    equals the number of columns. Each coordinate in one column.
+
+    To rescale, the mean (center) is subtracted from each axis separately.
+    Then all values are scaled so that the largest magnitude value
+    from all axes equals `scale` (thus, the aspect ratio is preserved).
+    The resulting NumPy Array is returned (order of rows unchanged).
+
+    Parameters
+    ----------
+    pos : numpy array
+        positions to be scaled. Each row is a position.
+
+    scale : number (default: 1)
+        The size of the resulting extent in all directions.
+
+    Returns
+    -------
+    pos : numpy array
+        scaled positions. Each row is a position.
+
+    See Also
+    --------
+    rescale_layout_dict
+    """
+    import numpy as np
+
+    # Find max length over all dimensions
+    pos -= pos.mean(axis=0)
+    lim = np.abs(pos).max()  # max coordinate for all axes
+    # rescale to (-scale, scale) in all directions, preserves aspect
+    if lim > 0:
+        pos *= scale / lim
+    return pos
+
+
+def rescale_layout_dict(pos, scale=1):
+    """Return a dictionary of scaled positions keyed by node
+
+    Parameters
+    ----------
+    pos : A dictionary of positions keyed by node
+
+    scale : number (default: 1)
+        The size of the resulting extent in all directions.
+
+    Returns
+    -------
+    pos : A dictionary of positions keyed by node
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> pos = {0: np.array((0, 0)), 1: np.array((1, 1)), 2: np.array((0.5, 0.5))}
+    >>> nx.rescale_layout_dict(pos)
+    {0: array([-1., -1.]), 1: array([1., 1.]), 2: array([0., 0.])}
+
+    >>> pos = {0: np.array((0, 0)), 1: np.array((-1, 1)), 2: np.array((-0.5, 0.5))}
+    >>> nx.rescale_layout_dict(pos, scale=2)
+    {0: array([ 2., -2.]), 1: array([-2.,  2.]), 2: array([0., 0.])}
+
+    See Also
+    --------
+    rescale_layout
+    """
+    import numpy as np
+
+    if not pos:  # empty_graph
+        return {}
+    pos_v = np.array(list(pos.values()))
+    pos_v = rescale_layout(pos_v, scale=scale)
+    return dict(zip(pos, pos_v))
+
+
+def bfs_layout(G, start, *, align="vertical", scale=1, center=None):
+    """Position nodes according to breadth-first search algorithm.
+
+    Parameters
+    ----------
+    G : NetworkX graph
+        A position will be assigned to every node in G.
+
+    start : node in `G`
+        Starting node for bfs
+
+    center : array-like or None
+        Coordinate pair around which to center the layout.
+
+    Returns
+    -------
+    pos : dict
+        A dictionary of positions keyed by node.
+
+    Examples
+    --------
+    >>> G = nx.path_graph(4)
+    >>> pos = nx.bfs_layout(G, 0)
+
+    Notes
+    -----
+    This algorithm currently only works in two dimensions and does not
+    try to minimize edge crossings.
+
+    """
+    G, center = _process_params(G, center, 2)
+
+    # Compute layers with BFS
+    layers = dict(enumerate(nx.bfs_layers(G, start)))
+
+    if len(G) != sum(len(nodes) for nodes in layers.values()):
+        raise nx.NetworkXError(
+            "bfs_layout didn't include all nodes. Perhaps use input graph:\n"
+            "        G.subgraph(nx.node_connected_component(G, start))"
+        )
+
+    # Compute node positions with multipartite_layout
+    return multipartite_layout(
+        G, subset_key=layers, align=align, scale=scale, center=center
+    )