networkx.algorithms.vitality.closeness_vitality

closeness_vitality(G, node=None, weight=None, wiener_index=None)[source]

Returns the closeness vitality for nodes in the graph.

The closeness vitality of a node, defined in Section 3.6.2 of [1], is the change in the sum of distances between all node pairs when excluding that node.

Parameters:
  • G (NetworkX graph) – A strongly-connected graph.
  • weight (string) – The name of the edge attribute used as weight. This is passed directly to the wiener_index() function.
  • node (object) – If specified, only the closeness vitality for this node will be returned. Otherwise, a dictionary mapping each node to its closeness vitality will be returned.
Other Parameters:
 

wiener_index (number) – If you have already computed the Wiener index of the graph G, you can provide that value here. Otherwise, it will be computed for you.

Returns:

If node is None, this function returns a dictionary with nodes as keys and closeness vitality as the value. Otherwise, it returns only the closeness vitality for the specified node.

The closeness vitality of a node may be negative infinity if removing that node would disconnect the graph.

Return type:

dictionary or float

Examples

>>> G = nx.cycle_graph(3)
>>> nx.closeness_vitality(G)
{0: 2.0, 1: 2.0, 2: 2.0}

See also

closeness_centrality()

References

[1]Ulrik Brandes, Thomas Erlebach (eds.). Network Analysis: Methodological Foundations. Springer, 2005. <http://books.google.com/books?id=TTNhSm7HYrIC>