Betweenness Centrality

A graph-theoretic measure of a node's importance defined as the sum (or normalized sum) over all ordered pairs of the fraction of shortest paths between the pair that pass through the node; quantifies the node's role as a connector or bridge in shortest-path routing.

A node-level network metric equal to the sum, over all ordered pairs of distinct nodes s and t (s ≠ t ≠ v), of the fraction of shortest paths between s and t that pass through node v: BC(v) = ∑_{s≠v≠t} σ_st(v) / σ_st, where σ_st is the number of shortest paths between s and t and σ_st(v) is the number of those paths that include v.