Important nodes mining based on a novel personalized temporal motif pagerank algorithm in temporal networks

In temporal networks, PageRank-based methods are usually used to calculate the importance of nodes. However, almost all the methods focus on the first-order relationships between nodes while ignore higher-order interactions between nodes in the graph. Considering that temporal motifs are recurring, higher-order and significant network connectivity patterns, which can capture both temporal and higher-order structural features in dynamic networks, this paper proposes a novel Personalized Temporal Motif PageRank (PTMP) algorithm to measure the importance of nodes in temporal networks. Specifically, to capture temporal information and higher-order features, we develop a method extracting temporal motif instances from temporal networks, and design an algorithm to compute the weighted motif adjacency matrix and the diagonal motif out-degree matrix, then define a motif transition matrix, which contains the personalized feature and can be used to compute the importance score of nodes. Finally, we make the steady-state analysis for the PTMP algorithm and compare it with other state-of-the-art baselines on multiple real-world datasets. The experimental results demonstrate that the PTMP algorithm is capable of mining much richer important nodes information accurately and effectively.