Local Approximation of Centrality Measures

Centrality measures provide a means to differentiate the importance of vertices in a network. These measures are mathematically clear, but the algorithms to compute them often have quadratic time complexity or worse. This may lead to significant computational challenges when applied to large networks. In this paper, we propose a local strategy for three frequently used centrality measures: (i) closeness, (ii) betweenness and (iii) PageRank. This local approach uses only the vertices directly adjacent to a target vertex to derive an approximation of the true centrality measure. The approximations are accompanied with an analysis of the approximation error bounds. Our analysis and experiments show that local approximations are quite successful on undirected graphs, and on directed graphs depending on the reciprocity of edges.