ó ,µ[c@s=dZddlZdjdgƒZdgZdd„ZdS(s Flow Hierarchy. iÿÿÿÿNs s!Ben Edwards (bedwards@cs.unm.edu)tflow_hierarchycsaˆjƒstjdƒ‚ntjˆƒ}dt‡‡fd†|DƒƒtˆjˆƒƒS(s‚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 [1]_. 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 hierarchy value Notes ----- The algorithm described in [1]_ 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 ---------- .. [1] 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 s%G must be a digraph in flow_heirarchygð?c3s'|]}ˆj|ƒjˆƒVqdS(N(tsubgraphtsize(t.0tc(tGtweight(s<lib/python2.7/site-packages/networkx/algorithms/hierarchy.pys 6s(t is_directedtnxt NetworkXErrortstrongly_connected_componentstsumtfloatR(RRtscc((RRs<lib/python2.7/site-packages/networkx/algorithms/hierarchy.pyRs# (t__doc__tnetworkxRtjoint __authors__t__all__tNoneR(((s<lib/python2.7/site-packages/networkx/algorithms/hierarchy.pyts