Results 41 to 50 of about 1,354,678 (274)
Exact Recovery in the General Hypergraph Stochastic Block Model [PDF]
IEEE Transactions on Information Theory, 2021 This paper investigates fundamental limits of exact recovery in the general $d$ -uniform hypergraph stochastic block model ( $d$ -HSBM), wherein $n$ nodes are partitioned into $k$ disjoint communities with relative sizes $(p_{1},\ldots , p_{k ...
Q. Zhang, V. Tan
semanticscholar +1 more source
Domination game on uniform hypergraphs [PDF]
Discrete Applied Mathematics, 2019 In this paper we introduce and study the domination game on hypergraphs. This is played on a hypergraph $\mathcal{H}$ by two players, namely Dominator and Staller, who alternately select vertices such that each selected vertex enlarges the set of vertices dominated so far. The game is over if all vertices of $\mathcal{H}$ are dominated.
Máté Vizer +4 more
openaire +4 more sources
The Turán Density of Tight Cycles in Three-Uniform Hypergraphs [PDF]
International mathematics research notices, 2022 The Turán density of an $r$-uniform hypergraph ${\mathcal {H}}$, denoted $\pi ({\mathcal {H}})$, is the limit of the maximum density of an $n$-vertex $r$-uniform hypergraph not containing a copy of ${\mathcal {H}}$, as $n \to \infty $.
Nina Kamvcev +2 more
semanticscholar +1 more source
The spectrum of a class of uniform hypergraphs [PDF]
Linear Algebra and its Applications, 2020 A generalized power hypergraph $\mathcal{H}^k_s$ is obtained from a base hypergraph $\mathcal{H}$ by means of some simple edge-expansion operations. Kang, Liu, Qi and Yuan [8] proved that the nonzero eigenvalues of $\mathcal{H}$ give rise to nonzero eigenvalues of $\mathcal{H}^k_s$. In this paper we show that all nonzero eigenvalues of $\mathcal{H}^k_s$
Kauê Cardoso +2 more
openaire +3 more sources
Hypergraph assortativity: A dynamical systems perspective. [PDF]
Chaos, 2021 The largest eigenvalue of the matrix describing a network's contact structure is often important in predicting the behavior of dynamical processes. We extend this notion to hypergraphs and motivate the importance of an analogous eigenvalue, the expansion
Nicholas W. Landry, J. Restrepo
semanticscholar +1 more source
Spectra of uniform hypergraphs
Linear Algebra and its Applications, 2012 We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a. multidimensional arrays.
Aaron Dutle, Joshua Cooper
openaire +3 more sources
-partite self-complementary and almost self-complementary -uniform hypergraphs
AKCE International Journal of Graphs and Combinatorics, 2020 A hypergraph is said to be -partite -uniform if its vertex set can be partitioned into non-empty sets so that every edge in the edge set , consists of precisely one vertex from each set , . It is denoted as or if for .
L.N. Kamble +2 more
doaj +1 more source
On the Sizes of (k, l)-Edge-Maximal r-Uniform Hypergraphs
Discussiones Mathematicae Graph Theory, 2023 Let H = (V, E) be a hypergraph, where V is a set of vertices and E is a set of non-empty subsets of V called edges. If all edges of H have the same cardinality r, then H is an r-uniform hypergraph; if E consists of all r-subsets of V, then H is a ...
Tian Yingzhi +3 more
doaj +1 more source
An Irrational Lagrangian Density of a Single Hypergraph [PDF]
SIAM Journal on Discrete Mathematics, 2021 The Turán number of an r-uniform graph F , denoted by ex(n, F ), is the maximum number of edges in an F -free r-uniform graph on n vertices. The Turán density of F is defined as π(F ) = lim n→∞ ex(n,F ) (nr) .
Zilong Yan, Yuejian Peng
semanticscholar +1 more source
Tensor Entropy for Uniform Hypergraphs [PDF]
IEEE Transactions on Network Science and Engineering, 2020 In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the Laplacian tensors, to fit into the Shannon entropy formula.
Can Chen, Indika Rajapakse
openaire +3 more sources