The goal of this paper is to present a centrality measurement for the nodes of a hypergraph, by using existing literature which extends eigenvector centrality from a graph to a hypergraph, and literature which give a general centrality measurement for a graph. We’ll use this measurement to say more about the number of communications in a hypergraph, to implement a learning mechanism, and to con...

Let k be a positive integer. A hypergraphH is k-partition-connected if for every partition P of V (H), there are at least k(|P |−1) hyperedges intersecting at least two classes of P . In this paper, we determine the minimum number of hyperedges in a hypergraph whose addition makes the resulting hypergraph k-partition-connected. We also characterize the hyperedges of a k-partition-connected hype...

In 1986, Johnson and Perry proved a class of inequalities for uniform hypergraphs which included the following: for any such hypergraph, the geometric mean over the hyperedges of the geometric means of the degrees of the nodes on the hyperedge is no less than the average degree in the hypergraph, with equality only if the hypergraph is regular. Here, we prove a wider class of inequalities in a ...

We prove a removal lemma for infinitely-many forbidden hypergraphs. It affirmatively settles a question on property testing raised by Alon and Shapira (2005) [2, 3]. All monotone hypergraph properties and all hereditary partite hypergraph properties are testable. Our proof constructs a constant-time probabilistic algorithm to edit a small number of edges. It also gives a quantitative bound in t...

Given a set of propositions, one can consider its inconsistency hypergraph. Then the safisfiability of sets of clauses with respect to that hypergraph (see [2], [4]) turns out to be the usual satisfiability. The problem is which hypergraphs can be obtained from sets of formulas as inconsistency hypergraphs. In the present paper it is shown that this can be done for all hypergraphs with countabl...

Fundamental local symmetry breaking problems such as Maximal Independent Set (MIS) and coloring have been recognized as important by the community, and studied extensively in (standard) graphs. In particular, fast (i.e., logarithmic run time) randomized algorithms are well-established for MIS and ∆ + 1-coloring in both the LOCAL and CONGEST distributed computing models. On the other hand, compa...

Recently, Storm [10] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm’s Theorem. Furthermore, we generalize the...

We prove that the vertex degree threshold for tiling C3 4 (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on n ∈ 4N vertices is (n−1 2 ) − ( 4 n 2 ) + 8n + c, where c = 1 if n ∈ 8N and c = −2 otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling. C © 2014 Wiley Periodicals, Inc. J. Graph...

Recently, Storm [8] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it. We define the Bartholdi zeta function of a hypergraph, and present a determinant expression of it. Furthermore, we give a determinant expression for the Bartholdi zeta function of semiregular bipartite graph. As a corollary, we obtain a decomposition formula for the Bartholdi...

Community extraction plays an important role in network analysis. This paper discusses communities in hypergraphs. Since hypergraphs can represent multi-relational networks, they are important structures in many domains. In this study, the definition of communities based on the number of adjacent links/nodes is extended to a hypergraph. Four extended models are proposed. The adequacy of these m...