A temporal graph is an undirected graph where each edge is associated with a timestamp indicating when it occurs. As a fundamental topic in graph analysis, community search (CS) in temporal graphs has received much attention. Existing CS works on temporal graphs typically identify sets of vertices that form a k -core within a specific time window (temporal k -core). However, they overlook the duration of a temporal community, which is the continues time period that its members remain unchanged. Intuitively, the longer the duration of a temporal community, the higher its stability. Long-duration communities are useful in many areas, such as event detection and network analysis. In this paper, we introduce a novel community model, called temporal durable community (TDC), which is the temporal k -core with the longest duration in the temporal graph, and aim to efficiently find the TDC containing a query vertex. To solve this problem, we first propose a novel online algorithm based on binary search. We further develop two index structures that can quickly determine the duration of a given temporal k -core, followed by query algorithms. Experiments on ten real large temporal graphs show that our TDC model is effective for finding stable communities, and our index-based query algorithms are up to five orders of magnitude faster than the online algorithm.
Zhou et al. (Wed,) studied this question.