On the second eigenvalue of hypergraphs

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August undefined, 2024

WebLower bounds for the first and the second eigenvalue of uniform regular hypergraphs are obtained. One of these bounds is a generalization of the Alon–Boppana Theorem to … Web15 de out. de 2013 · We call λ b the smallest Z-eigenvalue of the adjacency tensor T A for r-uniform hypergraph G, denoted as λ b (G). We call λ 1 the largest Z-eigenvalue of the …

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WebLenz 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. 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 ... people\u0027s republic of china embassy in usa

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Web9 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 … 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 … Web2 Hypergraphs Second case: aout q [ain q = maxa 1 Given a hyperarc aq 2AH with aout q [ain q = maxa 1, then the hyperarc consists of n = aout q + ain q = maxa 1 different … tokyo drift 10 hours

Some graphs with small second eigenvalue SpringerLink

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Web2 Hypergraphs Second case: aout q [ain q = maxa 1 Given a hyperarc aq 2AH with aout q [ain q = maxa 1, then the hyperarc consists of n = aout q + ain q = maxa 1 different vertices. This means, that any indices describing hyperarc aq have exactly one redundant vertex, either a duplicate of an output vertex or a duplicate of an input vertex. Web6 de fev. de 2024 · Abstract. Chung, Graham, and Wilson proved that a graph is quasirandom if and only if there is a large gap between its first and second largest eigenvalue. Recently, the authors extended this characterization to coregular -uniform hypergraphs -uniform hypergraph is coregular. In this paper we remove the coregular … people\u0027s republic of china in malayWeb1 de jan. de 2005 · J.Kahn, Szemerédi, J.Friedman,On the second eigenvalue in random regular graphs, Proceedings of the 21st ACM STOC (1989). pp 587–598. Google Scholar L. Lovàsz, Covering and coloring of hypergraphs, Preceding of the 4th Sourtheastern people\u0027s republic of china under mao zedong

"WebA 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 … " - On the second eigenvalue of hypergraphs

On the second eigenvalue of hypergraphs

Hypergraph Markov Operators, Eigenvalues and Approximation …

WebON THE SECOND EIGENVALUE OF HYPERGRAPHS JOEL FRIEDMAN*, and AVI WIGDERSON Received November 7, 1989 Revised February 26, 1992 1. The Second … WebIn this paper we consider spectral extremal problems for hypergraphs. We give two general criteria under which such results may be deduced from “strong stability” forms of the …

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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 … WebIf u;v;wis a triple achieving the above sup, we shall call (u;v;w)oru v wan eigenvector.We can also de ne d-regular for a general trilinear form as above, and therefore extend the notion …

Web8 de mar. de 2024 · Fan Y-Z, Wang Y, Bao Y-H, Wan J-C, Li M, Zhu Z (2024) Eigenvectors of Laplacian or signless Laplacian of hypergraphs associated with zero eigenvalue. Linear Algebra Appl 579:244–261. Article MathSciNet Google Scholar Fan L, Zhu Z, Wang Y (2024) Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices. Web1 de dez. de 2012 · J. Friedman, On the second eigenvalue and random walks in randomd-regular graphs, Combinatorica 11 (1991), 331–362. Google Scholar Cross Ref J. Friedman, A Proof of Alon's second eigenvalue conjectureand related problem, Memoirs of the American Mathematical Society, 2008, p. 100.

Web26 de jun. de 2024 · We determine all connected {K 1,3 , K 5 − e}-free graphs whose second largest eigenvalue does not exceed 1. Our result includes all connected line … 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 jul. de 2016 · br0070 J. Friedman, Some graphs with small second eigenvalue, Combinatorica, 15 (1995) 31-42. Google Scholar Digital Library; br0080 J. Friedman, A. Wigderson, On the second eigenvalue of hypergraphs, Combinatorica, 15 (1995) 43-65. Google Scholar Digital Library

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 … people\u0027s republic of china flag meaningWeb14 de jan. de 2015 · For each of the quasirandom properties that is described, we define the largest and the second largest eigenvalues. We show that a hypergraph satisfies … tokyo drift eurobeat remixWebLeast eigenvalue 4. Second largest eigenvalue 5. Other eigenvalues of the adjacency matrix 6. Laplacian eigenvalues 7. Signless Laplacian eigenvalues 8. … Expand. 56. Save. Alert. Steiner Trees in Graphs and Hypergraphs. M. Brazil ... the Steiner tree problem in graphs and the Steiner tree problem in hypergraphs. Also, we consider the minimum ... people\u0027s republic of china pharmacopoeiaWeb14 de jun. de 2015 · Joel Friedman and Avi Wigderson, On the second eigenvalue of hypergraphs, Combinatorica 15 (1995), no. 1, 43--65. Google Scholar; Patrick Girard, L Guiller, C Landrault, and Serge Pravossoudovitch, Low power bist design by hypergraph partitioning: methodology and architectures, Test Conference, 2000. tokyo drift car drawingWebSinceG is of orderp(p−1), the correspondingt-uniform Cayley hypergraph has essentially optimal second eigenvalue for this degree and size of the graph (see [2] for definitions). … tokyo drift first raceWeb@MISC{Friedman89onthe, author = {Joel Friedman and Avi Wigderson}, title = {On the second eigenvalue of hypergraphs}, year = {1989}} Share. OpenURL . ... absolute value 3-uniform hypergraph second eigenvalue undirected d-regular graph uniform hypergraphs general notion adjacency matrix people\u0027s republic of china中文WebKey words: H-eigenvalue, clique, coclique, hypergraph, tensor, signless Laplacian, Laplacian, adjacency MSC (2010): 05C65; 15A18 1 Introduction In the current combinatorics and graph theory associative literatures, a growing number of them studied hypergraphs and their applications in various ﬁelds [1,3,7] because hypergraphs tokyo drift experience japan