Gd dZddlZdgZddZdS)z Flow Hierarchy. Nflow_hierarchycstjdtj}dt fd|Dz z S)aReturns 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 : float Flow hierarchy value 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 $O(m)$ time using Tarjan's algorithm. References ---------- .. [1] 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 z%G must be a digraph in flow_hierarchyc3hK|],}|V-dSN)subgraphsize).0cGweights =lib/python3.11/site-packages/networkx/algorithms/hierarchy.py z!flow_hierarchy../s;;;!1::a==%%f--;;;;;;) is_directednx NetworkXErrorstrongly_connected_componentssumr )r r sccs`` rrr stF ==??HFGGG *1 - -C s;;;;;s;;;;;affVnnL LLrr)__doc__networkxr__all__rrrrsI  &M&M&M&M&M&Mr