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 toshortest_path_length()
.attr (
str
, optional) – If given, write the value of the objective function to each node’sattr
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 ofG
. Return type
 Raises
NetworkXNoPath – If
G
is disconnected.G
may appear disconnected tobarycenter()
ifsp
is given but is missing shortest path lengths for any pairs.ValueError – If
sp
andweight
are both given.
See also