Approximating Personalized Katz Centrality in Dynamic Graphs

Abstract

Dynamic graphs can capture changing relationships in many real datasets that evolve over time. One of the most basic questions about networks is the identification of the “most important” vertices in a network. Measures of vertex importance called centrality measures are used to rank vertices in a graph. In this work, we focus on Katz Centrality. Typically, scores are calculated through linear algebra but in this paper we present an new alternative, agglomerative method of calculating Katz scores and extend it for dynamic graphs. We show that our static algorithm is several orders of magnitude faster than the typical linear algebra approach while maintaining good quality of the scores. Furthermore, our dynamic graph algorithm is faster than pure static recomputation every time the graph changes and maintains high recall of the highly ranked vertices on both synthetic and real graphs.