/usr/lib/python2.7/dist-packages/networkx/algorithms/hierarchy.py is in python-networkx 1.8.1-0ubuntu3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 | # -*- coding: utf-8 -*-
"""
Flow Hierarchy.
"""
# Copyright (C) 2004-2011 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
import networkx as nx
__authors__ = "\n".join(['Ben Edwards (bedwards@cs.unm.edu)'])
__all__ = ['flow_hierarchy']
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 [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 heirarchy 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
"""
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))
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