networkx.local_reaching_centrality¶

networkx.local_reaching_centrality(G, v, paths=None, weight=None, normalized=True)[source]¶

Returns the local reaching centrality of a node in a directed graph.

The local reaching centrality of a node in a directed graph is the proportion of other nodes reachable from that node [R1189].

Parameters:

G : DiGraph A NetworkX graph. v : node A node in the directed graph G. paths : dictionary If this is not None it must be a dictionary representation of single-source shortest paths, as computed by, for example, networkx.shortest_path() with source node v. Use this keyword argument if you intend to invoke this function many times but don’t want the paths to be recomputed each time. weight : object Attribute to use for edge weights. If None, each edge weight is assumed to be one. A higher weight implies a stronger connection between nodes and a shorter path length. normalized : bool Whether to normalize the edge weights by the total sum of edge weights.

Returns:

h : float The local reaching centrality of the node v in the graph G.

See also

global_reaching_centrality

References

[R1189]

(1, 2) Mones, Enys, Lilla Vicsek, and Tamás Vicsek. “Hierarchy Measure for Complex Networks.” PLoS ONE 7.3 (2012): e33799. https://dx.doi.org/10.1371/journal.pone.0033799

Examples

>>> import networkx as nx
>>> G = nx.DiGraph()
>>> G.add_edge(1, 2)
>>> G.add_edge(1, 3)
>>> nx.local_reaching_centrality(G, 3)
0.0
>>> G.add_edge(3, 2)
>>> nx.local_reaching_centrality(G, 3)
0.5