Mining Periodic Cliques in Temporal Networks

Seasonal-Periodic Subgraph Mining in Temporal Networks

“…We assume that each t ∈ T is an integer, because the timestamp is an integer in practice. As defined in [6], the de-temporal graph of G T denoted by G = (V , E) is a graph that ignores all the timestamps associated with the temporal edges, where…”

“…Note that, our definition of σ -periodic time support set is different from the one in [6] from two aspects: (1) we consider a continuous subset in T (S) rather than an arbitrary subset; and (2) we claim that an inter-arrival time of the subgraph S is periodic if it is no more than a user-defined period threshold rather than a fixed value (i.e., t k +1 − t k = p). For example, consider a temporal graph in Figure 1.…”

“…By Definition 2.2, the set {7, 8, 10} is a 3-periodic time support set of S if we set p = 2. However, if we use the definition in [6], we will miss above periodic time support set. According to Definition 2.2, we can discover more interesting behaviors pertaining to those rare patterns that have exhibited sufficient number of periodicity in a portion of the temporal graph.…”

“…Radinsky et al [7] developed a temporal model to predict the periodic actions. Qin et al [6] proposed a σ -periodic k-clique model to find the cliques with size larger than k that appears at least σ times periodically in the temporal graph. Since the algorithms and models of these studies are designed for mining periodic behaviors in one period, they cannot discover the seasonal-periodic subgraphs.…”

“…The studies of behavior mining in temporal networks are related to our work. Besides the aforementioned relevant research [3,6,7], Ma et al [5] devised a dense subgraph mining algorithm to identify cohesive subgraphs in a temporal network. Li et al [4] addressed the problem of mining periodic behaviors for moving objects.…”