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AN INTRODUCTION TO SPECTRAL GRAPH THEORY
"... Abstract. Spectral graph theory is the study of properties of the Laplacian matrix or adjacency matrix associated with a graph. In this paper, we focus on the connection between the eigenvalues of the Laplacian matrix and graph ..."
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Abstract. Spectral graph theory is the study of properties of the Laplacian matrix or adjacency matrix associated with a graph. In this paper, we focus on the connection between the eigenvalues of the Laplacian matrix and graph
Introduction to Spectral Graph Theory
, 2011
"... Up to this point in the class, we have been looking at a graph as a collection ..."
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Up to this point in the class, we have been looking at a graph as a collection
Spectral graph theory
, 2010
"... With every graph (or digraph) one can associate several different matrices. We have already seen the vertexedge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall concentrate mainly on the adjacency matrix of (undirected) graphs, and also discuss briefly the Laplacia ..."
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the Laplacian. We shall show that spectral properies (the eigenvalues and eigenvectors) of these matrices provide useful information about the structure of the graph. It turns out that for regular graphs, the information one can deduce from one matrix representation (e.g., the adjacency matrix) is similar
TWO SHORTER PROOFS IN SPECTRAL GRAPH THEORY
 UNIV. BEOGRAD. PUBL. ELEKTROTEHN. FAK. SER. MAT. 14 (2003), 94–98.
, 2003
"... We give shorter proofs of two inequalities already known in spectral graph theory. ..."
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Cited by 1 (0 self)
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We give shorter proofs of two inequalities already known in spectral graph theory.
Finiteness theorems in spectral graph theory
, 2014
"... The purpose of this paper is to classify finite graphs satisfying certain spectral bounds and give explicit methods for understanding asymptotic behavior of the spectrum. Let X be a finite kregular graph and µ1(X) the second largest eigenvalue of its adjacency matrix. It follows from the wellknow ..."
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The purpose of this paper is to classify finite graphs satisfying certain spectral bounds and give explicit methods for understanding asymptotic behavior of the spectrum. Let X be a finite kregular graph and µ1(X) the second largest eigenvalue of its adjacency matrix. It follows from the well
Spectral Graph Theory Lecture 1
, 2015
"... These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. I sometimes edit the notes after class to make ..."
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These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. I sometimes edit the notes after class to make
Spectral Graph Theory Lecture 19
, 2012
"... 19.1 About these notes These notes are not necessarily an accurate representation of what happened in class. The notes written before class say what I think I should say. The notes written after class way what I wish I said. Eigen style. 19.2 Overview Preconditioning is an approach to solving linear ..."
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. This will not be a problem, as every positivedefinite matrix has a square root. Let ΨΛΨ T = A be the spectral factorization of A with eigenvectors contained in the columns of Ψ and the eigenvalues on the diagonals of Λ. Then, A 1/2 def
Algorithm Design Using Spectral Graph Theory
, 2013
"... necessarily reflect the views of the funding parties. Keywords: Combinatorial Preconditioning, Linear System Solvers, Spectral Graph Theory, Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix, a ..."
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Cited by 3 (3 self)
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necessarily reflect the views of the funding parties. Keywords: Combinatorial Preconditioning, Linear System Solvers, Spectral Graph Theory, Spectral graph theory is the interplay between linear algebra and combinatorial graph theory. Laplace’s equation and its discrete form, the Laplacian matrix
Spectral graph theory and the inverse eigenvalue of a graph
, 2005
"... Spectral Graph Theory is the study of the spectra of certain matrices defined from a given graph, including the adjacency matrix, the Laplacian matrix and other related matrices. Graph spectra have been studied extensively for more than fifty years. In the last fifteen years, interest has develope ..."
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Cited by 20 (2 self)
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Spectral Graph Theory is the study of the spectra of certain matrices defined from a given graph, including the adjacency matrix, the Laplacian matrix and other related matrices. Graph spectra have been studied extensively for more than fifty years. In the last fifteen years, interest has
Results 1  10
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842,070