Application of Group Testing in Identifying High Betweenness Centrality Vertices in Complex Networks

Group testing is a mathematical technique that uses superimposed code theory to find a specified number of distinct units among a large population, using the fewest number of tests. In this paper, we investigate the applicability of group testing in finding vertices with high betweenness centrality. Betweenness centrality (BC) is a widely applied network analysis objective, for identifying important vertices in complex networks. Most algorithms for computing BC compute the values for all the vertices in the network. However, in practice, only the vertices with the highest BC values are used in analyzing the network, and even then we only need the identities of the vertices–not the exact values. We demonstrate that Latin square based group testing is effective in finding the top two highest BC nodes of most networks. We also show that the instances where group testing fails to obtain the top BC nodes are networks where slight perturbation of the edges can change the ranking of the vertices. An additional benefit of group testing is that it allows us to decompose the betweenness centrality computation into a trivially parallelizable algorithm with high scalability.