49 lines
1.5 KiB
Python
49 lines
1.5 KiB
Python
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"""
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Flow Hierarchy.
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"""
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import networkx as nx
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__all__ = ["flow_hierarchy"]
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@nx._dispatchable(edge_attrs="weight")
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def flow_hierarchy(G, weight=None):
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"""Returns the flow hierarchy of a directed network.
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Flow hierarchy is defined as the fraction of edges not participating
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in cycles in a directed graph [1]_.
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Parameters
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----------
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G : DiGraph or MultiDiGraph
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A directed graph
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weight : string, optional (default=None)
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Attribute to use for edge weights. If None the weight defaults to 1.
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Returns
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-------
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h : float
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Flow hierarchy value
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Notes
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-----
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The algorithm described in [1]_ computes the flow hierarchy through
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exponentiation of the adjacency matrix. This function implements an
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alternative approach that finds strongly connected components.
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An edge is in a cycle if and only if it is in a strongly connected
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component, which can be found in $O(m)$ time using Tarjan's algorithm.
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References
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----------
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.. [1] Luo, J.; Magee, C.L. (2011),
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Detecting evolving patterns of self-organizing networks by flow
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hierarchy measurement, Complexity, Volume 16 Issue 6 53-61.
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DOI: 10.1002/cplx.20368
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http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf
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"""
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if not G.is_directed():
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raise nx.NetworkXError("G must be a digraph in flow_hierarchy")
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scc = nx.strongly_connected_components(G)
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return 1 - sum(G.subgraph(c).size(weight) for c in scc) / G.size(weight)
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