Discovering Cohesive Temporal Subgraphs with Temporal Density Aware Exploration

Real-world networks, such as social networks, cryptocurrency networks, and e-commerce networks, always have occurrence time of interactions between nodes. Such networks are typically modeled as temporal graphs. Mining cohesive subgraphs from temporal graphs is practical and essential in numerous data mining applications, since mining cohesive subgraphs gets insights into the time-varying nature of temporal graphs. However, existing studies on mining cohesive subgraphs, such as Densest-Exact and k-truss, are mainly tailored for static graphs (whose edges have no temporal information). Therefore, those cohesive subgraph models cannot indicate both the temporal and the structural characteristics of subgraphs. To this end, we explore the model of cohesive temporal subgraphs by incorporating both the evolving and the structural characteristics of temporal subgraphs. Unfortunately, the volume of time intervals in a temporal network is quadratic. As a result, the time complexity of mining temporal cohesive subgraphs is high. To efficiently address the problem, we first mine the temporal density distribution of temporal graphs. Guided by the distribution, we can safely prune many unqualified time intervals with the linear time cost. Then, the remaining time intervals where cohesive temporal subgraphs fall in are examined using the greedy search. The results of the experiments on nine real-world temporal graphs indicate that our model outperforms state-of-the-art solutions in efficiency and quality. Specifically, our model only takes less than two minutes on a million-vertex DBLP and has the highest overall average ranking in EDB and TC metrics.