This documents the development version of NetworkX. Documentation for the current release can be found here.
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 .
- GDiGraph or MultiDiGraph
A directed graph
- weightkey,optional (default=None)
Attribute to use for node weights. If None the weight defaults to 1.
Flow hierarchy value
The algorithm described in  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.
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