Fast incremental computation of harmonic closeness centrality in directed weighted networks

Abstract

This paper proposes a novel approach to efficiently compute the exact closeness centrality values of all nodes in dynamically evolving directed and weighted networks. Closeness centrality is one of the most frequently used centrality measures in the field of social network analysis. It uses the total distance to all other nodes to determine node centrality. Previous work has addressed the problem of dynamically updating closeness centrality values for either undirected networks or only for the top- $k$ nodes in terms of closeness centrality. Here, we propose a fast approach for exactly computing all closeness centrality values at each timestamp of directed and weighted evolving networks. Such networks are prevalent in many real-world situations. The main ingredients of our approach are a combination of work filtering methods and efficient incremental updates that avoid unnecessary recomputation. We tested the approach on several real-world datasets of dynamic small-world networks and found that we have mean speed-ups of about 33 times. In addition, the method is highly parallelizable.