Proximity tracking on dynamic bipartite graphs: Problem definitions and fast solutions

Large bipartite graphs which evolve and grow over time (e.g., new links arrive, old links die out, or link weights change) arise in many settings, such as social networks, co-citations, market-basket analysis, and collaborative filtering. Our goal is to monitor (i) the centrality of an individual node (e.g., who are the most important authors?) and (ii) the proximity of two nodes or sets of nodes (e.g., who are the most important authors with respect to a particular conference?). Moreover, we want to do this efficiently and incrementally and to provide any-time answers. In this chapter we propose pTrack, which is based on random walks with restart, together with some important modifications to adapt these measures to a dynamic, evolving setting. Additionally, we develop techniques for fast, incremental updates of these measures that allow us to track them continuously, as link updates arrive. In addition, we discuss variants of our method that can handle batch updates, as well as place more emphasis on recent links. Based on proximity tracking, we further proposed cTrack, which enables us to track the centrality of the nodes over time. We demonstrate the effectiveness and efficiency of our methods on several real data sets.