Abstract: Betweenness centrality (BC) is a widely used indicator to measure the importance of network vertices. Currently the fastest time complexity of the algorithm is O(V×E). When computing the BC of vertices in networks, we need to do n times searches of single source shortest path. In big data era, networks have more nodes and edges, and the amount of calculation of BC algorithm is large. The huge amount of calculation makes the algorithm need a long time to compute each vertices’ BC value, and the algorithm cannot be applied in practice. The related work focuses on approximation to reduce the running time of BC algorithm, but they also can not reduce the amount of calculation of BC algorithm significantly. In order to further reduce the amount of the calculation of BC algorithm, we propose a vertex weighted approximation algorithm to reduce the amount of calculation of BC algorithm, and the algorithm can make the calculation process be repeated many times to accumulate on a calculation by vertex weighted and select high-impact vertex as source to compute BC. We can reduce the amount of calculation significantly in this way, and meet the requirement of lower error rate and high performance. The approximation algorithm of BC based on vertex weighted can achieve 25 times speedup, and the error rate is lower than percentage of 0.01.

Key words: betweenness centrality (BC) algorithm, calculation, influence, vertex weighted, approximation