Efficient Densest Subgraphs Discovery in Large Dynamic Graphs by Greedy Approximation

Abstract

Densest subgraph detection has become an important primitive in graph mining tasks when analyzing communities and detecting events in a wide range of application domains. Currently, it is a challenging and practically crucial research issue to develop efficient densest subgraphs mining approaches that can handle both very large and continuously evolving graphs. Although large-scale or dynamic methods have been proposed to find the densest subgraphs, there is still a lack of a promising method to deal with largescale and dynamically evolving graphs. In this paper, the problem is formulated and proved to be NP-Hard, an incremental greedy approximation approach is proposed, and its running time is O(m+n). In order to find the densest subgraph effectively by heuristically merging the local densest subgraphs, firstly, the edge flow of a dynamic graph is divided into several subgraphs in a given period of T . Secondly, a local candidate set is generated by local denser subgraph discovery. Third, the global densest subgraph candidates are collected by heuristically merging. Last, the densest subgraphs are induced from the global densest subgraph candidates with constraints by static densest subgraph discovery algorithm. This incremental approach enables us to scale up the existing densest subgraph discovery algorithms, which focus mainly on small and static graphs and thus can handle very large dynamic graphs. Experiments on real-world networks with billions of nodes for comprehensive evaluations present excellent improvement in efficiency and accuracy: it reduces about 25% running time on average and presents a more accurate estimation of the structure of a graph with more compact subgraphs than the static method.It also performs well when dealing with graphs of varying densities. INDEX TERMSDensest subgraphs, incremental greedy approximation, heuristically merging, local candidate, global densest subgraph candidates.