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.

翻译：我们提出基于邻域的核分解：一种将超图分解为层次化邻域凝聚子超图的新方法。其他超图分解方法（例如转化为团图或二分图）在某些应用中缺乏意义，后者还会导致分解效率低下；而现有基于度的超图分解无法区分具有不同邻域大小的节点。我们的案例研究表明，所提出的分解方法在疾病干预以及提取可证明近似且应用上有意义的最密子超图方面，比基于度和团图的分解更有效。我们提出了三种算法：Peel、其高效变体E-Peel，以及一种新颖的局部算法：具有并行实现的Local-core。我们最高效的并行算法Local-core(P)通过采用多种优化，在91秒内内存中分解了包含2700万节点和1700万超边的超图。最后，我们开发了一种新的超图核模型——（邻域，度）核，同时考虑邻域和度约束，设计了其分解算法Local-core+Peel，并证明了其在传播扩散中的优越性。