Betweenness Centrality

Betweenness Centrality

  • The higher a node’s centrality is the more “dependent” other nodes are on it
  • Based on shortest paths between nodes and the number of paths that pass through two points and the total number of paths
  • BC(i) = SUMs≠i≠ t∈Vμst(i) / μst where μst is the number of paths from s and t and μst(i) is the number of paths from s and t that pass through node i


Input: V, a vertex and G, a graph

  1. For all pairs of vertices (v1 and v2) in graph G, compute every shortest path between them
  2. Using v1 and v2, compute the fraction of paths between these vertices that pass through V
  3. Sum over all pairs of vertices

More Information and other Algorithms:

  1. Approximating Betweenness Centrality
References to use of this measure in literature:
  1. Collaboration and Integration of Community-Based Health and Human Services in a Nonprofit Managed Care System
  2. The Peer Context of Adolescent Substance Use: Findings from Social Network Analysis
  3. Peer Standing and Substance Use in Early-Adolescent Grade-Level Networks: A Short-Term Longitudinal Study