Time-topology analysis on temporal graphs

Many real-world networks have been evolving and are finely modeled as temporal graphs from the viewpoint of the graph theory. A temporal graph is informative and always contains two types of features, i.e., the temporal feature and topological feature, where the temporal feature is related to the establishing time of the relationships in the temporal graph, and the topological feature is influenced by the structure of the graph. In this paper, considering both these two types of features, we perform time-topology analysis on temporal graphs to analyze the cohesiveness of temporal graphs and extract cohesive subgraphs. Firstly, a new metric named 𝕋 -cohesiveness is proposed to evaluate the cohesiveness of a temporal subgraph from the time and topology dimensions jointly. Specifically, given a temporal graph 𝒢_s = (V_s, ℰ_s) , cohesiveness in the time dimension reflects whether the connections in 𝒢_s happen in a short period of time, while cohesiveness in the topology dimension indicates whether the vertices in V_s are densely connected and have few connections with vertices out of 𝒢_s . Then, 𝕋 -cohesiveness is utilized to perform time-topology analysis on temporal graphs, and two time-topology analysis methods are proposed. In detail, 𝕋 -cohesiveness evolution tracking traces the evolution of the 𝕋 -cohesiveness of a subgraph, and combo searching finds out cohesive subgraphs containing the query vertex, which have 𝕋 -cohesiveness values larger than a given threshold. Moreover, since combo searching is NP-hard, a pruning strategy is proposed to estimate the upper bound of the 𝕋 -cohesiveness value, and then improve the efficiency of combo searching. Experimental results demonstrate the efficiency of the proposed time-topology analysis methods and the pruning strategy. Besides, four more definitions of 𝕋 -cohesiveness are compared with our method. The experimental results confirm the superiority of our definition.