Mining Periodic k-Clique from Real-World Sparse Temporal Networks

In temporal networks, nodes and edges are associated with time series. To seeking the periodic pattern in temporal networks, an intuitive method is to searching periodic communities in them. However, most existing studies do not exploit the periodic pattern of communities. The only few works left do not take the sparse propriety of real-world temporal networks into consideration, such that (i) the answers searched for are few, (ii) the computation suffers from poor performance. In this paper, we propose a novel periodic community model in temporal networks, σ -periodic k-clique, and an efficient algorithm for enumerating all σ -periodic k-cliques in real-world sparse temporal networks. We first design a new data structure to store temporal networks in main memory, which can reduce the maintaining cost and support dynamic deletion of nodes and edges. Then, we propose several efficient pruning rules to eliminate unpromising nodes and edges that do not belong to any σ -period k-clique to reduce graph size. Next, we propose an algorithm that directly enumerates σ -periodic k-cliques on temporal graph to avoid redundant computation. Finally, extensive and comprehensive experiments show that our algorithm runs one to three orders of magnitudes faster and requires significantly less memory than the baseline algorithms.