Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

networkx.algorithms.centrality.local_reaching_centrality

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 1.

Parameters
  • G (DiGraph) – A NetworkX DiGraph.

  • v (node) – A node in the directed graph G.

  • paths (dictionary (default=None)) – 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 (None or string, optional (default=None)) – 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, optional (default=True)) – Whether to normalize the edge weights by the total sum of edge weights.

Returns

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

Return type

float

Examples

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

References

1

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