Neighborhood-based Hypergraph Core Decomposition

TL;DR

This paper introduces a neighborhood-based hypergraph core decomposition method that effectively identifies hierarchical subhypergraphs, outperforming existing degree and clique-based methods in applications like disease intervention and diffusion modeling.

Contribution

The paper presents a novel neighborhood-based hypergraph decomposition approach, along with three algorithms, including a scalable parallel method, and a new (neighborhood, degree)-core model with superior performance.

Findings

More effective than degree and clique-based decompositions in case studies

Efficient parallel algorithm decomposes large hypergraphs in under 2 minutes

New (neighborhood, degree)-core model improves diffusion analysis

Abstract

We propose neighborhood-based core decomposition: a novel way of decomposing hypergraphs into hierarchical neighborhood-cohesive subhypergraphs. Alternative approaches to decomposing hypergraphs, e.g., reduction to clique or bipartite graphs, are not meaningful in certain applications, the later also results in inefficient decomposition; while existing degree-based hypergraph decomposition does not distinguish nodes with different neighborhood sizes. Our case studies show that the proposed decomposition is more effective than degree and clique graph-based decompositions in disease intervention and in extracting provably approximate and application-wise meaningful densest subhypergraphs. We propose three algorithms: Peel, its efficient variant E-Peel, and a novel local algorithm: Local-core with parallel implementation. Our most efficient parallel algorithm Local-core(P) decomposes hypergraph with 27M nodes and 17M hyperedges in-memory within 91 seconds by adopting various optimizations. Finally, we develop a new hypergraph-core model, the (neighborhood, degree)-core by considering both neighborhood and degree constraints, design its decomposition algorithm Local-core+Peel, and demonstrate its superiority in spreading diffusion.