| """ |
| Flow Hierarchy. |
| """ |
|
|
| import networkx as nx |
|
|
| __all__ = ["flow_hierarchy"] |
|
|
|
|
| @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 |
| |
| 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 |
| """ |
| |
| if nx.is_empty(G): |
| raise nx.NetworkXError("flow_hierarchy not applicable to empty graphs") |
| 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) |
|
|
