Fast computing betweenness centrality with virtual nodes on large sparse networks

Abstract

Betweenness centrality is an essential index for analysis of complex networks. However, the calculation of betweenness centrality is quite time-consuming and the fastest known algorithm uses O(N(M + N log N)) time and O(N + M) space for weighted networks, where N and M are the number of nodes and edges in the network, respectively. By inserting virtual nodes into the weighted edges and transforming the shortest path problem into a breadth-first search (BFS) problem, we propose an algorithm that can compute the betweenness centrality in O(w̄D̄N 2) time for integer-weighted networks, where w̄ is the average weight of edges and D̄ is the average degree in the network. Considerable time can be saved with the proposed algorithm when w̄