TM-Miner: TFS-Based Algorithm for Mining Temporal Motifs in Large Temporal Network

Temporal network is a basic tool for representing complex systems, such as communication networks and social networks; besides the temporal motif (TM) plays an important role in the analysis of temporal networks. Without considering the temporal information, most existing motif mining methods focus on static networks and are not suitable for mining temporal motifs. In this paper, we study the problem of temporal motif mining for the temporal network. To formulate the problem, we define the temporal motif as a frequently connected subgraph that has a similar sequence of information flows. Moreover, an efficient algorithm called TM-Miner is proposed. Based on the time first search (TFS) algorithm, the TM-Miner builds a canonical labeling system that uses a new lexicographic order and maps the temporal graph to the unique minimum TFS code. By utilizing the canonical labeling system, the computational cost of temporal graph isomorphism is reduced and the efficiency of the algorithm is improved. Finally, we evaluate the performance of the TM-Miner algorithm in real datasets and extensive experiments demonstrate that it is faster than the existing algorithms.