Mining of Real-world Hypergraphs: Patterns, Tools, and Generators

Abstract

Group interactions are prevalent in various complex systems (e.g., collaborations of researchers and group discussions on online Q&A sites), and they are commonly modeled as hypergraphs. Hyperedges, which compose a hypergraph, are non-empty subsets of any number of nodes, and thus each hyperedge naturally represents a group interaction among entities. The higher-order nature of hypergraphs brings about unique structural properties that have not been considered in ordinary pairwise graphs. In this tutorial, we offer a comprehensive overview of a new research topic called hypergraph mining. We first present recently revealed structural properties of real-world hypergraphs, including (a) static and dynamic patterns, (b) global and local patterns, and (c) connectivity and overlapping patterns. Together with the patterns, we describe advanced data mining tools used for their discovery. Lastly, we introduce simple yet realistic hypergraph generative models that provide an explanation of the structural properties. Materials and details of this tutorial can also be found at https://sites.google.com/view/hypergraph-tutorial.