Spaces:
Running
Running
| """ | |
| Flow Hierarchy. | |
| """ | |
| import networkx as nx | |
| __all__ = ["flow_hierarchy"] | |
| 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 | |
| http://web.mit.edu/~cmagee/www/documents/28-DetectingEvolvingPatterns_FlowHierarchy.pdf | |
| """ | |
| 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) | |