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:
- GNetworkX graph
A strongly-connected graph.
- weightstring
The name of the edge attribute used as weight. This is passed directly to the
wiener_index()
function.- nodeobject
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.
- Returns:
- dictionary or float
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.
- Other Parameters:
- wiener_indexnumber
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.
See also
closeness_centrality
References
[1]Ulrik Brandes, Thomas Erlebach (eds.). Network Analysis: Methodological Foundations. Springer, 2005. <http://books.google.com/books?id=TTNhSm7HYrIC>
Examples
>>> G = nx.cycle_graph(3) >>> nx.closeness_vitality(G) {0: 2.0, 1: 2.0, 2: 2.0}