The most active community search in large temporal graphs

Community search enables users to find a dense subgraph containing a given query vertex from a large graph modeled network, which has recently received increasing attention. However, few works address the problem in a temporal graph although the vertices and the edges in many real networks often dynamically change over time. This paper introduces the problem known as the most active community search in large temporal graphs. Given a query vertex q and a cohesiveness constraint k, our objective is to find a set of vertices including q that can induce a maximally expanded community subject to some specified connectivity. Meanwhile, for each vertex in the community, the property that there are at least k other vertices co-occurring as its neighbors should be maintained on the most number of time points. To this end, we first propose a novel temporal active core model, i.e. (k,t)-active core, which requires every vertex has at least k neighbors co-occurring in no less than t snapshots. Given a fundamental solution to finding the active core containing q, we present a more efficient algorithm by proposing two upper-bound-based pruning rules. Based on this, we search the most active community containing q by three carefully designed search strategies, i.e., bottom-up search, top-down search, and binary search. Additionally, an effective index structure is devised to reduce the computational cost by limiting the search space to a much smaller range of the complete temporal graph. Finally, we demonstrate the efficiency and the effectiveness of our proposed algorithms and index by conducting extensive experiments on five real-world datasets.