Source code for networkx.algorithms.hierarchy

Flow Hierarchy.
import networkx as nx

__all__ = ["flow_hierarchy"]

[docs] @nx._dispatchable(edge_attrs="weight") def flow_hierarchy(G, weight=None): """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 : string, optional (default=None) Attribute to use for edge 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 """ if not G.is_directed(): raise nx.NetworkXError("G must be a digraph in flow_hierarchy") scc = nx.strongly_connected_components(G) return 1 - sum(G.subgraph(c).size(weight) for c in scc) / G.size(weight)