Results 71 to 80 of about 56,309 (276)
The signless Laplacian matrix of hypergraphs
Special Matrices, 2022 In this article, we define signless Laplacian matrix of a hypergraph and obtain structural properties from its eigenvalues. We generalize several known results for graphs, relating the spectrum of this matrix to structural parameters of the hypergraph ...
Cardoso Kauê, Trevisan Vilmar
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Dimensions of hypergraphs [PDF]
Journal of Combinatorial Theory, Series B, 1992 AbstractThe dimension D(S) of a family S of subsets of n = {1, 2, …, n} is defined as the minimum number of permutations of n such that every A ∈ S is an intersection of initial segments of the permutations. Equivalent characterizations of D(S) are given in terms of suitable arrangements, interval dimension, order dimension, and the chromatic number of
William T. Trotter, Peter C. Fishburn
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MSHC: a multi-stage hypergraph clustering algorithm
Shenzhen Daxue xuebao. Ligong banAs a high-dimensional extension of ordinary graphs, hypergraphs can more flexibly reflect high-order complex relationships between nodes. Hypergraph clustering aims to discover complex high-order correlations in powerful hypergraph structures.
ZHANG Chunying +4 more
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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 Complexity science provides a powerful framework for understanding physical, biological and social systems, and network analysis is one of its principal tools. Since many complex systems exhibit multilateral interactions that change over time, in recent years, network scientists have become increasingly interested in modelling and ...
Corinna Coupette +2 more
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Spectral Properties of Oriented Hypergraphs
, 2014 An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of $+1$ or $-1$. The adjacency and Laplacian eigenvalues of an oriented hypergraph are studied. Eigenvalue bounds for both the adjacency and Laplacian matrices of an
Reff, Nathan
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On partitioning of hypergraphs
Discrete Mathematics, 2007 We study edge-isoperimetric problems (EIP) for hypergraphs and extend some technique in this area from graphs to hypergraphs. In particular, we establish some new results on a relationship between the EIP and some extremal poset problems, and apply them to obtain an exact solution of the EIP for certain hypergraph families.
S. Bezrukov, Battiti, Roberto
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Decompositions of complete 3-uniform hypergraphs into cycles of constant prime length [PDF]
Opuscula Mathematica, 2020 A complete \(3\)-uniform hypergraph of order \(n\) has vertex set \(V\) with \(|V|=n\) and the set of all \(3\)-subsets of \(V\) as its edge set. A \(t\)-cycle in this hypergraph is \(v_1, e_1, v_2, e_2,\dots, v_t, e_t, v_1\) where \(v_1, v_2,\dots, v_t\)
R. Lakshmi, T. Poovaragavan
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Entropic measure and hypergraph states
, 2013 We investigate some properties of the entanglement of hypergraph states in purely hypergraph theoretical terms. We first introduce an approach for computing local entropic measure on qubit t of a hypergraph state by using the Hamming weight of the so ...
Bao, Yan-ru +4 more
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Journal of the London Mathematical Society, 2019 Let $\text{Tr}(n,m,k)$ denote the largest number of distinct projections onto $k$ coordinates guaranteed in any family of $m$ binary vectors of length $n$. The classical Sauer-Perles-Shelah Lemma implies that $\text{Tr}(n, n^r, k) = 2^k$ for $k \le r$. While determining $\text{Tr}(n,n^r,k)$ precisely for general $k$ seems hopeless even for constant $r$,
Noga Alon +5 more
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The Electronic Journal of Linear Algebra, 2020 In this paper, energies associated with hypergraphs are studied. More precisely, results are obtained for the incidence and the singless Laplacian energies of uniform hypergraphs. In particular, bounds for the incidence energy are obtained as functions of well known parameters, such as maximum degree, Zagreb index and spectral radius.
Kauê Cardoso, Vilmar Trevisan
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