# rustworkx.graph_betweenness_centrality#

graph_betweenness_centrality(graph, /, normalized=True, endpoints=False, parallel_threshold=50)#

Compute the betweenness centrality of all nodes in a PyGraph.

Betweenness centrality of a node $$v$$ is the sum of the fraction of all-pairs shortest paths that pass through :mathv

$c_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}$

where $$V$$ is the set of nodes, $$\sigma(s, t)$$ is the number of shortest $$(s, t)$$ paths, and $$\sigma(s, t|v)$$ is the number of those paths passing through some node $$v$$ other than $$s, t$$. If $$s = t$$, $$\sigma(s, t) = 1$$, and if $$v \in {s, t}$$, $$\sigma(s, t|v) = 0$$

The algorithm used in this function is based on:

Ulrik Brandes, A Faster Algorithm for Betweenness Centrality. Journal of Mathematical Sociology 25(2):163-177, 2001.

This function is multithreaded and will run in parallel if the number of nodes in the graph is above the value of parallel_threshold (it defaults to 50). If the function will be running in parallel the env var RAYON_NUM_THREADS can be used to adjust how many threads will be used.

## See Also#

graph_edge_betweenness_centrality

param PyGraph graph:

The input graph

param bool normalized:

Whether to normalize the betweenness scores by the number of distinct paths between all pairs of nodes.

param bool endpoints:

Whether to include the endpoints of paths in pathlengths used to compute the betweenness.

param int parallel_threshold:

The number of nodes to calculate the the betweenness centrality in parallel at if the number of nodes in the graph is less than this value it will run in a single thread. The default value is 50

returns:

a read-only dict-like object whose keys are the node indices and values are the betweenness score for each node.

rtype:

CentralityMapping