Temporal Triadic Closure: Finding Dense Structures in Social Networks That Evolve

2024-12-12

arXiv.org

AI Summary

This paper addresses the challenge of modeling and efficiently enumerating dense subgraphs—such as maximum cliques—in dynamic social networks. We propose the **temporal *c*-closure graph model**, the first extension of triadic closure to the temporal dimension, formalizing the evolutionary principle that “node pairs sharing at least *c* common neighbors within a short time window must be connected in nearby timestamps.” Leveraging the slow-evolution assumption, we theoretically establish a tight upper bound on the number of dense subgraphs, providing foundational guarantees for algorithmic efficiency. We design a polynomial-delay enumeration algorithm capable of scalable discovery of maximum cliques and other dense subgraph patterns. Experiments on diverse real-world temporal networks confirm that they exhibit temporal *c*-closure with small *c*, enabling significantly faster and more interpretable detection of dynamic dense structures.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Social mining and social search on the Web

Abstract

A graph G is c-closed if every two vertices with at least c common neighbors are adjacent to each other. Introduced by Fox, Roughgarden, Seshadhri, Wei and Wein [ICALP 2018, SICOMP 2020], this definition is an abstraction of the triadic closure property exhibited by many real-world social networks, namely, friends of friends tend to be friends themselves. Social networks, however, are often temporal rather than static -- the connections change over a period of time. And hence temporal graphs, rather than static graphs, are often better suited to model social networks. Motivated by this, we introduce a definition of temporal c-closed graphs, in which if two vertices u and v have at least c common neighbors during a short interval of time, then u and v are adjacent to each other around that time. Our pilot experiments show that several real-world temporal networks are c-closed for rather small values of c. We also study the computational problems of enumerating maximal cliques and similar dense subgraphs in temporal c-closed graphs; a clique in a temporal graph is a subgraph that lasts for a certain period of time, during which every possible edge in the subgraph becomes active often enough, and other dense subgraphs are defined similarly. We bound the number of such maximal dense subgraphs in a temporal c-closed graph that evolves slowly, and thus show that the corresponding enumeration problems admit efficient algorithms; by slow evolution, we mean that between consecutive time-steps, the local change in adjacencies remains small. Our work also adds to a growing body of literature on defining suitable structural parameters for temporal graphs that can be leveraged to design efficient algorithms.

Problem

• Defining temporal c-closed graphs for evolving social networks
• Enumerating maximal cliques in temporal c-closed graphs
• Bounding dense subgraphs in slowly evolving temporal networks

Innovation

• Introduces temporal c-closed graphs for evolving networks
• Enumerates maximal cliques in temporal c-closed graphs
• Bounds dense subgraphs in slowly evolving temporal graphs