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