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Source code for networkx.algorithms.hierarchy
# -*- coding: utf-8 -*- """ Flow Hierarchy. """ # Copyright (C) 2004-2015 by # Aric Hagberg <firstname.lastname@example.org> # Dan Schult <email@example.com> # Pieter Swart <firstname.lastname@example.org> # All rights reserved. # BSD license. import networkx as nx __authors__ = "\n".join(['Ben Edwards (email@example.com)']) __all__ = ['flow_hierarchy'][docs]def flow_hierarchy(G, weight=None): """Returns the flow hierarchy of a directed network. Flow hierarchy is defined as the fraction of edges not participating in cycles in a directed graph _. Parameters ---------- G : DiGraph or MultiDiGraph A directed graph weight : key,optional (default=None) Attribute to use for node weights. If None the weight defaults to 1. Returns ------- h : float Flow heirarchy value Notes ----- The algorithm described in _ computes the flow hierarchy through exponentiation of the adjacency matrix. This function implements an alternative approach that finds strongly connected components. An edge is in a cycle if and only if it is in a strongly connected component, which can be found in `O(m)` time using Tarjan's algorithm. References ---------- ..  Luo, J.; Magee, C.L. (2011), Detecting evolving patterns of self-organizing networks by flow hierarchy measurement, Complexity, Volume 16 Issue 6 53-61. DOI: 10.1002/cplx.20368 http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf """ if not G.is_directed(): raise nx.NetworkXError("G must be a digraph in flow_heirarchy") scc = nx.strongly_connected_components(G) return 1.-sum(G.subgraph(c).size(weight) for c in scc)/float(G.size(weight))