# networkx.algorithms.distance_measures.barycenter¶

barycenter(G, weight=None, attr=None, sp=None)[source]

Calculate barycenter of a connected graph, optionally with edge weights.

The barycenter a connected graph $$G$$ is the subgraph induced by the set of its nodes $$v$$ minimizing the objective function

$\sum_{u \in V(G)} d_G(u, v),$

where $$d_G$$ is the (possibly weighted) path length. The barycenter is also called the median. See [West01], p. 78.

Parameters: G (networkx.Graph) – The connected graph $$G$$. weight (str, optional) – Passed through to shortest_path_length(). attr (str, optional) – If given, write the value of the objective function to each node’s attr attribute. Otherwise do not store the value. sp (dict of dicts, optional) – All pairs shortest path lengths as a dictionary of dictionaries Nodes of G that induce the barycenter of G. list networkx.NetworkXNoPath – If G is disconnected. G may appear disconnected to barycenter() if sp is given but is missing shortest path lengths for any pairs. ValueError – If sp and weight are both given.