networkx.algorithms.centrality.group_closeness_centrality¶

group_closeness_centrality(G, S, weight=None)[source]¶

Compute the group closeness centrality for a group of nodes.

Group closeness centrality of a group of nodes \(S\) is a measure of how close the group is to the other nodes in the graph.

\[ \begin{align}\begin{aligned}c_{close}(S) = \frac{|V-S|}{\sum_{v \in V-S} d_{S, v}}\\d_{S, v} = min_{u \in S} (d_{u, v})\end{aligned}\end{align} \]

where \(V\) is the set of nodes, \(d_{S, v}\) is the distance of the group \(S\) from \(v\) defined as above. (\(V-S\) is the set of nodes in \(V\) that are not in \(S\)).

Parameters

G (graph) – A NetworkX graph.
S (list or set) – S is a group of nodes which belong to G, for which group closeness centrality is to be calculated.
weight (None or string, optional (default=None)) – If None, all edge weights are considered equal. Otherwise holds the name of the edge attribute used as weight.

Raises

NodeNotFound – If node(s) in S are not present in G.

Returns

closeness – Group closeness centrality of the group S.

Return type

float