MiDaS: Representative Sampling from Real-world Hypergraphs

TL;DR

This paper introduces MiDaS, a fast and effective hypergraph sampling method that selects representative sub-hypergraphs by biasing towards high-degree nodes, outperforming existing approaches in speed and representativeness.

Contribution

The paper proposes MiDaS, a novel hypergraph sampling algorithm that efficiently finds representative sub-hypergraphs by leveraging node degree bias, validated through extensive experiments.

Findings

MiDaS outperforms 12 other approaches in representativeness.

MiDaS is several orders of magnitude faster than competitors.

MiDaS automatically adjusts the degree of bias for optimal sampling.

Abstract

Graphs are widely used for representing pairwise interactions in complex systems. Since such real-world graphs are large and often evergrowing, sampling a small representative subgraph is indispensable for various purposes: simulation, visualization, stream processing, representation learning, crawling, to name a few. However, many complex systems consist of group interactions (e.g., collaborations of researchers and discussions on online Q&A platforms), and thus they can be represented more naturally and accurately by hypergraphs (i.e., sets of sets) than by ordinary graphs. Motivated by the prevalence of large-scale hypergraphs, we study the problem of representative sampling from real-world hypergraphs, aiming to answer (Q1) what a representative sub-hypergraph is and (Q2) how we can find a representative one rapidly without an extensive search. Regarding Q1, we propose to measure the goodness of a sub-hypergraph by comparing it with the entire hypergraph in terms of ten graph-level, hyperedge-level, and node-level statistics. Regarding Q2, we first analyze the characteristics of six intuitive approaches in 11 real-world hypergraphs. Then, based on the analysis, we propose MiDaS, which draws hyperedges with a bias towards those with high-degree nodes. Through extensive experiments, we demonstrate that MiDaS is (a) Representative: finding overall the most representative samples among 13 considered approaches, (b) Fast: several orders of magnitude faster than the strongest competitors, which performs an extensive search, and (c) Automatic: rapidly searching a proper degree of bias.