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| """Functions for generating stochastic graphs from a given weighted directed | |
| graph. | |
| """ | |
| import networkx as nx | |
| from networkx.classes import DiGraph, MultiDiGraph | |
| from networkx.utils import not_implemented_for | |
| __all__ = ["stochastic_graph"] | |
| def stochastic_graph(G, copy=True, weight="weight"): | |
| """Returns a right-stochastic representation of directed graph `G`. | |
| A right-stochastic graph is a weighted digraph in which for each | |
| node, the sum of the weights of all the out-edges of that node is | |
| 1. If the graph is already weighted (for example, via a 'weight' | |
| edge attribute), the reweighting takes that into account. | |
| Parameters | |
| ---------- | |
| G : directed graph | |
| A :class:`~networkx.DiGraph` or :class:`~networkx.MultiDiGraph`. | |
| copy : boolean, optional | |
| If this is True, then this function returns a new graph with | |
| the stochastic reweighting. Otherwise, the original graph is | |
| modified in-place (and also returned, for convenience). | |
| weight : edge attribute key (optional, default='weight') | |
| Edge attribute key used for reading the existing weight and | |
| setting the new weight. If no attribute with this key is found | |
| for an edge, then the edge weight is assumed to be 1. If an edge | |
| has a weight, it must be a positive number. | |
| """ | |
| if copy: | |
| G = MultiDiGraph(G) if G.is_multigraph() else DiGraph(G) | |
| # There is a tradeoff here: the dictionary of node degrees may | |
| # require a lot of memory, whereas making a call to `G.out_degree` | |
| # inside the loop may be costly in computation time. | |
| degree = dict(G.out_degree(weight=weight)) | |
| for u, v, d in G.edges(data=True): | |
| if degree[u] == 0: | |
| d[weight] = 0 | |
| else: | |
| d[weight] = d.get(weight, 1) / degree[u] | |
| return G | |