Abstract Hypergraph modeling is the fundamental task in hypergraph computation, which targets on establishing a high-quality structure to accurately formulate high-order correlation among data. In this section, we introduce different methods show how build hypergraphs using various pieces of information, such as features, attributes, and/or graphs. These are organized into two broad categories,...

Abstract We find an asymptotic enumeration formula for the number of simple $r$ -uniform hypergraphs with a given degree sequence, when edges is sufficiently large. The in terms solution system equations. give sufficient conditions on sequence which guarantee existence to this system. Furthermore, we solve and explicit close regular. This allows us establish several properties random hypergraph...

We prove an asymptotic formula for the number of k-uniform hypergraphs with a given degree sequence, wide range parameters. In particular, we find that is asymptotically equal to d-regular on n vertices provided dn ≤ c(n/k) constant c > 0, and 3 k < n^c any C 1/9. Our results relate sequence random hypergraph simple model nearly independent binomial variables, thus extending recent graphs...

With the advent of big data and information age, magnitude various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have ability to describe characterize higher order relationships, which attracted extensive attention from academia industry in recent years. Firstly, this paper described development process, application ar...

Inspired by the recently remarkable successes of Sparse Representation (SR), Collaborative Representation (CR) and sparse graph, we present a novel hypergraph model named Regression-based Hypergraph (RH) which utilizes the regression models to construct the high quality hypergraphs. Moreover, we plug RH into two conventional hypergraph learning frameworks, namely hypergraph spectral clustering ...

Let H = (V, E) be a 3-uniform linear hypergraph with one hypercycle C3. We consider a blow-up hypergraph B[H]. We are interested in the following problem. We have to decide whether there exists a blow-up hypergraph B[H] of the hypergraph H, with hyperedge densities satisfying special conditions, such that the hypergraph H appears in a blow-up hypergraph as a transversal. We present an efficient...