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 stronglyconnected 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 specifiednode
.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>