Core-periphery Models for Hypergraphs

TL;DR

This paper introduces a scalable hypergraph model for core-periphery structure, along with an inference algorithm that learns node reputation and provides theoretical bounds, demonstrating superior performance on large real-world datasets.

Contribution

The paper presents a novel hypergraph core-periphery model, a scalable inference algorithm, and theoretical bounds, advancing analysis of large hypergraph structures.

Findings

Model outperforms baselines in fitting hypergraph data

Algorithm scales linearly with number of nodes after preprocessing

Provides theoretical bounds on core size in hypergraphs

Abstract

We introduce a random hypergraph model for core-periphery structure. By leveraging our model's sufficient statistics, we develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is practically linear wrt. the number of nodes in the graph after a preprocessing step that is almost linear in the number of hyperedges, as well as a scalable sampling algorithm. Our inference algorithm is capable of learning embeddings that correspond to the reputation (rank) of a node within the hypergraph. We also give theoretical bounds on the size of the core of hypergraphs generated by our model. We experiment with hypergraph data that range to $\sim 10^5$ hyperedges mined from the Microsoft Academic Graph, Stack Exchange, and GitHub and show that our model outperforms baselines wrt. producing good fits.