Betweenness Centrality of Honeycomb

Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. The betweenness centrality of a vertex is defined as the fraction of shortest paths that pass through that vertex over all pairs of vertices. It measures the control a vertex has over communication in the network, and can be used to identify key vertices in the network. High centrality indices indicate that a vertex can reach other vertices on relatively short paths, or that a vertex lies on a considerable fraction of shortest paths connecting pairs of other vertices. In this paper, we find the betweenness centrality of the honeycomb mesh, which has important applications in mobile networks.