~iFSrSSKrS/r\R"SS9SSj5rg)z Flow Hierarchy. Nflow_hierarchyweight) edge_attrsc@^^[R"T5(a[R"S5eTR5(d[R"S5e[R"T5nS[ UU4SjU55TR T5- - $)aqReturns 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 : string, optional (default=None) Attribute to use for edge weights. If None the weight defaults to 1. Returns ------- h : float Flow hierarchy value Raises ------ NetworkXError If `G` is not a directed graph or if `G` has no edges. 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-flow_hierarchy not applicable to empty graphsz%G must be a digraph in flow_hierarchyc3d># UH%nTRU5RT5v M' g7fN)subgraphsize).0cGrs Z/home/mande/repo/quber/.venv/lib/python3.13/site-packages/networkx/algorithms/hierarchy.py !flow_hierarchy..9s';s!1::a=%%f--ss-0)nxis_empty NetworkXError is_directedstrongly_connected_componentssumr )rrsccs`` rrr suT {{1~~NOO ==??FGG * *1 -C s;s;;affVnL LLr )__doc__networkxr__all__ _dispatchablerrrrs8  X&.M'.Mr