Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/hierarchy.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """ |
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2 Flow Hierarchy. |
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3 """ |
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4 import networkx as nx |
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5 |
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6 __all__ = ["flow_hierarchy"] |
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7 |
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8 |
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9 def flow_hierarchy(G, weight=None): |
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10 """Returns the flow hierarchy of a directed network. |
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11 |
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12 Flow hierarchy is defined as the fraction of edges not participating |
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13 in cycles in a directed graph [1]_. |
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14 |
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15 Parameters |
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17 G : DiGraph or MultiDiGraph |
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18 A directed graph |
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19 |
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20 weight : key,optional (default=None) |
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21 Attribute to use for node weights. If None the weight defaults to 1. |
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22 |
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23 Returns |
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24 ------- |
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25 h : float |
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26 Flow hierarchy value |
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27 |
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28 Notes |
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29 ----- |
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30 The algorithm described in [1]_ computes the flow hierarchy through |
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31 exponentiation of the adjacency matrix. This function implements an |
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32 alternative approach that finds strongly connected components. |
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33 An edge is in a cycle if and only if it is in a strongly connected |
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34 component, which can be found in $O(m)$ time using Tarjan's algorithm. |
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35 |
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36 References |
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37 ---------- |
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38 .. [1] Luo, J.; Magee, C.L. (2011), |
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39 Detecting evolving patterns of self-organizing networks by flow |
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40 hierarchy measurement, Complexity, Volume 16 Issue 6 53-61. |
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41 DOI: 10.1002/cplx.20368 |
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42 http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf |
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43 """ |
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44 if not G.is_directed(): |
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45 raise nx.NetworkXError("G must be a digraph in flow_hierarchy") |
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46 scc = nx.strongly_connected_components(G) |
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47 return 1.0 - sum(G.subgraph(c).size(weight) for c in scc) / float(G.size(weight)) |