Abstract With the development of deep learning on high-order correlations, hypergraph neural networks have received much attention in recent years. Generally, can be divided into two categories, including spectral-based methods and spatial-based methods. For methods, convolution operation is formulated spectral domain graph, we introduce typical (HGNN), with (Hyper-Atten), hyperbolic network (H...

Abstract In this chapter, we introduce the mathematical foundations of hypergraph and present notations that are used to facilitate deep understanding analysis structure. A is composed a set vertices hyperedges, it generalization graph, where weighted quantifies relative importance hyperedges or vertices. Hypergraph can also be divided into two main categories, i.e., undirected representation d...

In this article we give a polynomial algorithm to recognize if any partial sub hypergraph of a hypergraph has the Helly property

We determine the strong total chromatic number of the complete h-uniform hypergraph Kh, and the complete h-partite hypergraph K,

We introduce the notion of Hypergraph Weighted Model (HWM) that generically associates a tensor network to a hypergraph and then computes a value by tensor contractions directed by its hyperedges. A series r defined on a hypergraph family is said to be recognizable if there exists a HWM that computes it. This model generalizes the notion of rational series on strings and trees. We prove some pr...