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annotate planemo/lib/python3.7/site-packages/networkx/algorithms/hierarchy.py @ 1:56ad4e20f292 draft

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"planemo upload commit 6eee67778febed82ddd413c3ca40b3183a3898f1"
author guerler
date Fri, 31 Jul 2020 00:32:28 -0400
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1 # -*- coding: utf-8 -*-
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2 """
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3 Flow Hierarchy.
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4 """
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5 # Copyright (C) 2004-2019 by
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6 # Aric Hagberg <hagberg@lanl.gov>
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7 # Dan Schult <dschult@colgate.edu>
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8 # Pieter Swart <swart@lanl.gov>
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9 # All rights reserved.
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10 # BSD license.
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11 import networkx as nx
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12 __authors__ = "\n".join(['Ben Edwards (bedwards@cs.unm.edu)'])
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13 __all__ = ['flow_hierarchy']
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14
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15
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16 def flow_hierarchy(G, weight=None):
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17 """Returns the flow hierarchy of a directed network.
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18
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19 Flow hierarchy is defined as the fraction of edges not participating
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20 in cycles in a directed graph [1]_.
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21
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22 Parameters
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23 ----------
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24 G : DiGraph or MultiDiGraph
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25 A directed graph
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26
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27 weight : key,optional (default=None)
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28 Attribute to use for node weights. If None the weight defaults to 1.
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29
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30 Returns
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31 -------
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32 h : float
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33 Flow hierarchy value
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34
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35 Notes
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36 -----
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37 The algorithm described in [1]_ computes the flow hierarchy through
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38 exponentiation of the adjacency matrix. This function implements an
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39 alternative approach that finds strongly connected components.
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40 An edge is in a cycle if and only if it is in a strongly connected
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41 component, which can be found in $O(m)$ time using Tarjan's algorithm.
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42
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43 References
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44 ----------
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45 .. [1] Luo, J.; Magee, C.L. (2011),
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46 Detecting evolving patterns of self-organizing networks by flow
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47 hierarchy measurement, Complexity, Volume 16 Issue 6 53-61.
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48 DOI: 10.1002/cplx.20368
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49 http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf
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50 """
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51 if not G.is_directed():
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52 raise nx.NetworkXError("G must be a digraph in flow_hierarchy")
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53 scc = nx.strongly_connected_components(G)
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54 return 1. - sum(G.subgraph(c).size(weight) for c in scc) / float(G.size(weight))