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"""
Vitality measures.
"""
# Copyright (C) 2010 by
# Aric Hagberg <hagberg@lanl.gov>
# Dan Schult <dschult@colgate.edu>
# Pieter Swart <swart@lanl.gov>
# All rights reserved.
# BSD license.
__author__ = "\n".join(['Aric Hagberg (hagberg@lanl.gov)',
'Renato Fabbri'])
__all__ = ['closeness_vitality']
import networkx as nx
def weiner_index(G, weight=None):
# compute sum of distances between all node pairs
# (with optional weights)
weiner=0.0
if weight is None:
for n in G:
path_length=nx.single_source_shortest_path_length(G,n)
weiner+=sum(path_length.values())
else:
for n in G:
path_length=nx.single_source_dijkstra_path_length(G,
n,weight=weight)
weiner+=sum(path_length.values())
return weiner
def closeness_vitality(G, v=None, weight=None):
"""Compute closeness vitality for nodes.
Closeness vitality at a node is the change in the sum of distances
between all node pairs when excluding a that node.
Parameters
----------
G : graph
A networkx graph
v : node, optional
Return only the value for node v.
weight : None or string, optional
If None, edge weights are ignored.
Otherwise holds the name of the edge attribute used as weight.
Returns
-------
nodes : dictionary
Dictionary with nodes as keys and closeness vitality as the value.
Examples
--------
>>> G=nx.cycle_graph(3)
>>> nx.closeness_vitality(G)
{0: 4.0, 1: 4.0, 2: 4.0}
See Also
--------
closeness_centrality()
Notes
-----
"""
wig=weiner_index(G,weight)
closeness_vitality={}
for n in G:
# remove edges connected to node n and keep list of edges with data
# could remove node n but it doesn't count anyway
edges=G.edges(n,data=True)
if G.is_directed():
edges+=G.in_edges(n,data=True)
G.remove_edges_from(edges)
closeness_vitality[n]=wig-weiner_index(G,weight)
# add edges and data back to graph
G.add_edges_from(edges)
if v is not None:
return closeness_vitality[v]
else:
return closeness_vitality
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