networkx.algorithms.distance_measures.barycenter

barycenter(G, weight=None, attr=None, sp=None)

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

Returns:

Nodes of G that induce the barycenter of G.

Return type:

list

Raises:

• 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.

See also

center(), periphery()