On the second eigenvalue of hypergraphs
Web1 de jul. de 2024 · Let G be a connected hypergraph with even uniformity, which contains cut vertices. Then G is the coalescence of two nontrivial connected sub-hypergraphs (called branches) at a cut vertex. Let $$\\mathscr{A}(G)$$ A ( G ) be the adjacency tensor of G. The least H-eigenvalue of $$\\mathscr{A}(G)$$ A ( G ) refers to the least real … Web15 de nov. de 2013 · Second, can we calculate all Laplacian H-eigenvalues for some special k-uniform hypergraphs, such as sunflowers and loose cycles? This is useful if …
On the second eigenvalue of hypergraphs
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Webthreshold bound for the second eigenvalue of regular hypergraphs. Indeed, it is shown in Section 3 that there is an exact analogy to the graph case. We use it first to set a lower … Web1 de mar. de 1995 · On the second eigenvalue of hypergraphs. where n = V . Let G = (V,E) be a 3-uniform hypergraph; i.e. E is a subset of subsets of V of size 3. We consider …
Web1 de set. de 1996 · Abstract. To a regular hypergraph we attach an operator, called its adjacency matrix, and study the second largest eigenvalue as well as the overall distribution of the spectrum of this operator. Our definition and results extend naturally what is known for graphs, including the analogous threshold bound [formula]for k -regular … WebSecond, 2HR-DR used the directed hypergraph convolution network, which needs the eigenvalue decomposition of Laplacion matrices when calculating the spectrum convolution of hypergraphs, and that requires that the Laplacian matrices are real symmetric matrices (we are not able to ensure that non-symmetric matrices can certainly perform …
Web1 de out. de 2013 · PDF The adjacency matrices for graphs are generalized to the adjacency tensors for uniform hypergraphs, ... On the second eigenvalue of … Webrelate the eigenvector corresponding to the second largest eigenvalue of the canonical tensor to hypergraph quasi-randomness. Chung [Chu93] defines a notion of Laplacians for hypergraphs and studies the relationship between its eigenvalues and a very di erent notion of hypergraph cuts and homologies. [PRT12, SKM12,
Web6 de jul. de 2024 · We generalize the classical sharp bounds for the largest eigenvalue of the normalized Laplace operator, N/ (N-1)\leq \lambda_N\leq 2, to the case of chemical hypergraphs. 1. Introduction. In [ 1 ], the author together with Jürgen Jost introduced the notion of chemical hypergraph, that is, a hypergraph with the additional structure that …
WebIo the largest eigenvalue; 2° the second largest eigenvalue; 3° the smallest positive eigenvalue; 4° the largest negative eigenvalue; 5° the second smallest eigenvalue; 6° the smallest eigenvalue. For a survey on the largest eigenvalue of a graph see the paper [27] by D. Cvetkovic and P. Rowiinson (see also [26], the third edition, pp. 381 ... how did jesus use apologeticsWebLenz and Mubayi [LM12, LM15, LM13] related the eigenvector corresponding to the second largest eigenvalue of the canonical tensor to hypergraph quasi-randomness. Chung [Chu93] defined a notion of Laplacian for hypergraphs and studied the relationship between its eigenvalues and a very different notion of hypergraph cuts and homologies. how many sheds can i have in my gardenWeb17 de nov. de 2024 · We derive Cheeger inequalities for directed graphs and hypergraphs using the reweighted eigenvalue approach that was recently developed for vertex expansion in undirected graphs [OZ22,KLT22,JPV22]. The goal is to develop a new spectral theory for directed graphs and an alternative spectral theory for hypergraphs. The first … how did jethro tull\u0027s seed drill workWeb8 de dez. de 2015 · Lower bounds for the first and the second eigenvalue of uniform hypergraphs which are regular and linear are obtained. One of these bounds is a … how many shaves should a razor lastWeb@MISC{Friedman89onthe, author = {Joel Friedman and Avi Wigderson}, title = {On the second eigenvalue of hypergraphs}, year = {1989}} Share. OpenURL . ... absolute … how did jesus treat scribesWebA model of regular infinite hypertrees is developed to mimic for hypergraphs what infinite trees do for graphs. Two notions of spectra, or “first eigenvalue,” are then examined for … how did jethro cave dieWeb18 de jun. de 2024 · In this paper, we use the conjugate gradient method with a simple line search, which can reduce the number of computations of objective functions and gradients, to compute the largest H-eigenvalue of the large-scale tensors generated from uniform directed hypergraphs. For this kind of tensor, we provide a fast tensor-vector product … how did jesus turn water into wine