Path Centrality: A New Centrality Measure in Social Networks

Processing large graphs is an emerging and increasingly important computation in a variety of application domains, from social networking to genomics and marketing. One of the important and computationally challenging structural graph metrics is node betweenness centrality, a measure of influence of a node in the graph. The best known algorithm for computing exact betweenness centrality runs in time O(nm + n log n), which makes it infeasible on graphs with millions of nodes and edges. The existing randomized algorithms for estimating betweenness centrality significantly reduce the execution time, but their accuracy decreases considerably with the size of the graph. This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, κ-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high κ-path centrality have high node betweenness centrality. The randomized algorithm runs in time O(κ3n2−2α log n) and outputs, for each vertex v, an estimate of its κ-path centrality up to additive error of ±n with probability 1 − 1/n. Experimental evaluations on diverse real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared to known randomized algorithms.