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.

Other Parameters:
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.
	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}