Pairwise Co-betweenness for Several Types of Network

Vertex betweenness centrality is essential in the analysis of social and information networks, and it quantify vertex importance in terms of its quantity of information along geodesic paths in network. Edge betweenness is similar to the vertex betweenness. Co-betweenness centrality is a natural developed notion to extend vertex betweenness centrality to sets of vertices, and pairwise co-betweenness is a special case of co-betweenness. In this paper, we analysis the pairwise co-betweenness of WS network model with the different reconnection probability which including rule, smallworld and random network. The pairwise co-betweenness value is represented by several different ways, and it shows some regularity with changing reconnection probability of each edge in WS network model. Meanwhile, for communitystructure network, we obtain vertex-induced subgraph with the highest betweenness vertices, and the edge-induced subgraph with the highest pairwise co-betweenness edges. We demonstrate that the edge of cross-groups is consistent with the edges with top incidental pairwise co-betweenness. Finally, further illustration to the interaction of pairwise co-betweenness and network structure is provided by a practical social network.