55 lines
1.7 KiB
Python
55 lines
1.7 KiB
Python
# -*- coding: utf-8 -*-
|
|
"""
|
|
Flow Hierarchy.
|
|
"""
|
|
# Copyright (C) 2004-2019 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 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
|
|
"""
|
|
if not G.is_directed():
|
|
raise nx.NetworkXError("G must be a digraph in flow_hierarchy")
|
|
scc = nx.strongly_connected_components(G)
|
|
return 1. - sum(G.subgraph(c).size(weight) for c in scc) / float(G.size(weight))
|