Global Betweenness Identities in the Networks

Betweenness centrality plays a crucial role in the identification of the critical nodes and links. Last year, we obtain the betweenness identities in connected network and demonstrate that the average shortest distance is determined by the betweenness centrality in connected network. In this paper, we extend the betweenness identities in the undirected networks, whether connected or unconnected networks. The betweenness identities reveal the relationship of the betweenness and the average shortest distances of the connected components in the undirected network.