Results 21 to 30 of about 232,364 (309)
Doubling constants and spectral theory on graphs
Discrete Mathematics, 2023 We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph $G$. We show that this constant can be estimated from below by $1+ r(A_G)$, where $r(A_G)$ is the spectral radius of the adjacency matrix of $G$, and study when both quantities coincide.
Estibalitz Durand-Cartagena +2 more
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A theory of spectral partitions of metric graphs [PDF]
, 2020 We introduce an abstract framework for the study of clustering in metric graphs: after suitably metrising the space of graph partitions, we restrict Laplacians to the clusters thus arising and use their spectral gaps to define several notions of ...
Kennedy, James B. +3 more
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Re-imagining Spectral Graph Theory [PDF]
CoRRWe propose a Laplacian based on general inner product spaces, which we call the inner product Laplacian. We show the combinatorial and normalized graph Laplacians, as well as other Laplacians for hypergraphs and directed graphs, are special cases of the inner product Laplacian. After developing the necessary basic theory for the inner product Laplacian,
Sinan G. Aksoy, Stephen J. Young
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A Short Text Clustering Algorithm Based on Spectral Cut [PDF]
Jisuanji gongcheng, 2016 Short text has the characteristics of sparsity and high dimension,and the existing clustering algorithm for the large-scale short text has low accuracy and efficiency.Aiming at this problem,a novel clustering method based on spectral clustering theory ...
LI Xiaohong,XIE Meng,MA Huifang,HE Tingnian
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From Time–Frequency to Vertex–Frequency and Back
Mathematics, 2021 The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided.
Ljubiša Stanković +5 more
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Eigenvalues of multipart matrices and their applications
The American Journal of Combinatorics, 2023 A square matrix is called a multipart matrix if all its diagonal entries are zero and all other entries in each column are constant. In this paper, we describe various interesting spectral properties of multipart matrices. We provide suitable bounds for
Ranjit Mehatari
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The Grone-Merris Conjecture [PDF]
, 2010 In spectral graph theory, Grone and Merris conjecture that the spectrum of the Laplacian matrix of a finite graph is majorized by the conjugate degree sequence of this graph.
Bai, Hua
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Generalized modularity matrices [PDF]
, 2015 Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinatorial functions appearing in the framework of graph clustering problems. In
D. Fasino +12 more
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Frontiers in Neuroscience, 2022 We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of
Ashish Raj +2 more
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Spectral sparsification of graphs [PDF]
Communications of the ACM, 2013 Graph sparsification is the approximation of an arbitrary graph by a sparse graph. We explain what it means for one graph to be a spectral approximation of another and review the development of algorithms for spectral sparsification. In addition to being an interesting concept, spectral sparsification has been an important tool in the design ...
Joshua D. Batson +3 more
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