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Tensor Entropy for Uniform Hypergraphs [PDF]

open access: yesIEEE 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.
Indika Rajapakse, Can Chen
exaly   +4 more sources
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The Uniformity Lemma for hypergraphs

Graphs and Combinatorics, 1992
This is an extension of Szemerédi's theorem called the Uniformity Lemma for Graphs (see \textit{E. Szemerédi} [Problèmes combinatoires et théorie des graphes, Orsay 1976, Colloq. int. CNRS No. 260, 399-401 (1978; Zbl 0413.05055)]) to \(r\)-uniform hypergraphs. Two applications of the result are announced: proof of a conjecture of Erdős concerning Turán-
Peter Frankl, Vojtech Rödl
openaire   +3 more sources

Non-uniform hypergraphs

2020
Summary: Non-uniform hypergraphs are a generalization of hypergraphs in which not all edges need to have the same cardinality. It allows them to support a more complex data structure. In this paper, we extend some results for non-uniform hypergraphs and generalize the spectral results for uniform hypergraphs to non-uniform hypergraphs.
SHIRDEL, G.H.   +2 more
openaire   +2 more sources

The Laplacian of a uniform hypergraph

Journal of Combinatorial Optimization, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sheng-Long Hu, Liqun Qi 0001
openaire   +2 more sources

Transversal numbers of uniform hypergraphs

open access: yesGraphs and Combinatorics, 1990
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
exaly   +4 more sources

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