flow_hierarchy¶

flow_hierarchy
(G, weight=None)[source]¶ 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 – Flow heirarchy value
Return type: 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 time using Tarjan’s algorithm.
References
[1] (1, 2) Luo, J.; Magee, C.L. (2011), Detecting evolving patterns of selforganizing networks by flow hierarchy measurement, Complexity, Volume 16 Issue 6 5361. DOI: 10.1002/cplx.20368 http://web.mit.edu/~cmagee/www/documents/28DetectingEvolvingPatterns_FlowHierarchy.pdf