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+"""Function for computing walks in a graph."""
+
+import networkx as nx
+
+__all__ = ["number_of_walks"]
+
+
+@nx._dispatchable
+def number_of_walks(G, walk_length):
+ """Returns the number of walks connecting each pair of nodes in `G`
+
+ A *walk* is a sequence of nodes in which each adjacent pair of nodes
+ in the sequence is adjacent in the graph. A walk can repeat the same
+ edge and go in the opposite direction just as people can walk on a
+ set of paths, but standing still is not counted as part of the walk.
+
+ This function only counts the walks with `walk_length` edges. Note that
+ the number of nodes in the walk sequence is one more than `walk_length`.
+ The number of walks can grow very quickly on a larger graph
+ and with a larger walk length.
+
+ Parameters
+ ----------
+ G : NetworkX graph
+
+ walk_length : int
+ A nonnegative integer representing the length of a walk.
+
+ Returns
+ -------
+ dict
+ A dictionary of dictionaries in which outer keys are source
+ nodes, inner keys are target nodes, and inner values are the
+ number of walks of length `walk_length` connecting those nodes.
+
+ Raises
+ ------
+ ValueError
+ If `walk_length` is negative
+
+ Examples
+ --------
+
+ >>> G = nx.Graph([(0, 1), (1, 2)])
+ >>> walks = nx.number_of_walks(G, 2)
+ >>> walks
+ {0: {0: 1, 1: 0, 2: 1}, 1: {0: 0, 1: 2, 2: 0}, 2: {0: 1, 1: 0, 2: 1}}
+ >>> total_walks = sum(sum(tgts.values()) for _, tgts in walks.items())
+
+ You can also get the number of walks from a specific source node using the
+ returned dictionary. For example, number of walks of length 1 from node 0
+ can be found as follows:
+
+ >>> walks = nx.number_of_walks(G, 1)
+ >>> walks[0]
+ {0: 0, 1: 1, 2: 0}
+ >>> sum(walks[0].values()) # walks from 0 of length 1
+ 1
+
+ Similarly, a target node can also be specified:
+
+ >>> walks[0][1]
+ 1
+
+ """
+ import numpy as np
+
+ if walk_length < 0:
+ raise ValueError(f"`walk_length` cannot be negative: {walk_length}")
+
+ A = nx.adjacency_matrix(G, weight=None)
+ # TODO: Use matrix_power from scipy.sparse when available
+ # power = sp.sparse.linalg.matrix_power(A, walk_length)
+ power = np.linalg.matrix_power(A.toarray(), walk_length)
+ result = {
+ u: {v: power.item(u_idx, v_idx) for v_idx, v in enumerate(G)}
+ for u_idx, u in enumerate(G)
+ }
+ return result