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Time-topology analysis on temporal graphs

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Abstract

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 \(\mathbb {T}\)-cohesiveness is proposed to evaluate the cohesiveness of a temporal subgraph from the time and topology dimensions jointly. Specifically, given a temporal graph \(\mathcal {G}_s = (V_s, \mathcal {E}_s)\), cohesiveness in the time dimension reflects whether the connections in \(\mathcal {G}_s\) 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 \(\mathcal {G}_s\). Then, \(\mathbb {T}\)-cohesiveness is utilized to perform time-topology analysis on temporal graphs, and two time-topology analysis methods are proposed. In detail, \(\mathbb {T}\)-cohesiveness evolution tracking traces the evolution of the \(\mathbb {T}\)-cohesiveness of a subgraph, and combo searching finds out cohesive subgraphs containing the query vertex, which have \(\mathbb {T}\)-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 \(\mathbb {T}\)-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 \(\mathbb {T}\)-cohesiveness are compared with our method. The experimental results confirm the superiority of our definition.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 61872207) and Baidu Inc.

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Authors and Affiliations

  1. School of Software, Tsinghua University, Beijing, 100084, China

    Yunkai Lou, Chaokun Wang, Tiankai Gu & Hao Feng

  2. Baidu Inc., Beijing, China

    Jun Chen

  3. The Chinese University of Hong Kong, Hong Kong, China

    Jeffrey Xu Yu

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  1. Yunkai Lou
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Correspondence to Chaokun Wang.

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Lou, Y., Wang, C., Gu, T. et al. Time-topology analysis on temporal graphs. The VLDB Journal 32, 815–843 (2023). https://doi.org/10.1007/s00778-022-00772-y

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