Neighborhood-based Hypergraph Core Decomposition

We propose \emph{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: \textbf{Peel}, its efficient variant \textbf{E-Peel}, and a novel local algorithm: \textbf{Local-core} with parallel implementation. Our most efficient parallel algorithm \textbf{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 \textbf{Local-core+Peel}, and demonstrate its superiority in spreading diffusion.