55 lines
1.9 KiB
Python
55 lines
1.9 KiB
Python
"""Functions for generating stochastic graphs from a given weighted directed
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graph.
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"""
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import networkx as nx
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from networkx.classes import DiGraph, MultiDiGraph
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from networkx.utils import not_implemented_for
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__all__ = ["stochastic_graph"]
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@not_implemented_for("undirected")
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@nx._dispatchable(
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edge_attrs="weight", mutates_input={"not copy": 1}, returns_graph=True
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)
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def stochastic_graph(G, copy=True, weight="weight"):
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"""Returns a right-stochastic representation of directed graph `G`.
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A right-stochastic graph is a weighted digraph in which for each
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node, the sum of the weights of all the out-edges of that node is
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1. If the graph is already weighted (for example, via a 'weight'
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edge attribute), the reweighting takes that into account.
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Parameters
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----------
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G : directed graph
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A :class:`~networkx.DiGraph` or :class:`~networkx.MultiDiGraph`.
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copy : boolean, optional
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If this is True, then this function returns a new graph with
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the stochastic reweighting. Otherwise, the original graph is
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modified in-place (and also returned, for convenience).
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weight : edge attribute key (optional, default='weight')
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Edge attribute key used for reading the existing weight and
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setting the new weight. If no attribute with this key is found
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for an edge, then the edge weight is assumed to be 1. If an edge
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has a weight, it must be a positive number.
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"""
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if copy:
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G = MultiDiGraph(G) if G.is_multigraph() else DiGraph(G)
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# There is a tradeoff here: the dictionary of node degrees may
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# require a lot of memory, whereas making a call to `G.out_degree`
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# inside the loop may be costly in computation time.
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degree = dict(G.out_degree(weight=weight))
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for u, v, d in G.edges(data=True):
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if degree[u] == 0:
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d[weight] = 0
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else:
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d[weight] = d.get(weight, 1) / degree[u]
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nx._clear_cache(G)
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return G
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