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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._dispatchable |
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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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power = np.linalg.matrix_power(A.toarray(), walk_length) |
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result = { |
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u: {v: power.item(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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