Topic
Spectral graph theory
About: Spectral graph theory is a research topic. Over the lifetime, 1334 publications have been published within this topic receiving 77373 citations.
Papers published on a yearly basis
Papers
More filters
24 Aug 2014
TL;DR: A spectral invariant which is based on the wave kernel trace to characterize graphs is explored, which can be used to translate equations from continuous analysis to the discrete graph theoretic domain, that have no meanings if defined if defined using vertex-based Laplacian.
Abstract: Graph based methods have been successfully used in computer vision for classification and matching. This is due to the fact that shapes can be conveniently represented using graph structures. In this paper we explore the use of a spectral invariant which is based on the wave kernel trace to characterize graphs. The wave kernel is the solution of wave equation defined using the Edge-based Laplacian of a graph. The advantage of using the edge-based Laplacian over its vertex-based counterpart is that it can be used to translate equations from continuous analysis to the discrete graph theoretic domain, that have no meanings if defined using vertex-based Laplacian. To illustrate the utility of the proposed method we apply it to graphs extracted from both three-dimensional shapes and images.
1 citations
Posted Content•
TL;DR: In this article, an upper bound on the maximal eigenvalue of the adjacency matrix of a connected graph in terms of its maximum degree, diameter and order is given, which is best possible up to a constant factor.
Abstract: We give an upper bound on the maximal eigenvalue of the adjacency matrix of a connected graph in terms of its maximum degree, diameter and order This bound is best possible up to a constant factor and improves prevoius results of Stevanovic, Zhang, and Alon and Sudakov
1 citations
TL;DR: It is proposed to use the methods of the spectral graph theory and the graph signal processing as tools for analyzing the ANN structure to solve the problem of detecting an ANN structure.
Abstract: In the paper, the problem of the possibility of recovering the unknown structure of artificial neural networks (ANNs) using the theory of graphs is investigated. The key ANN concepts, their typical architectures, and differences are considered. The application of the theory of the graph tool for solving the problem of detecting an ANN structure is substantiated, and examples of comparing different ANN architectures and graph types are presented. It is proposed to use the methods of the spectral graph theory and the graph signal processing as tools for analyzing the ANN structure.
1 citations
TL;DR: In this paper , the spectral theory of discrete structures such as graphs, simplicial complexes and hypergraphs is discussed, in particular on the corresponding Laplace operators, and the motivation to model and study real data with these tools is discussed.
Abstract: In this chapter we discuss the spectral theory of discrete structures such as graphs, simplicial complexes and hypergraphs. We focus, in particular, on the corresponding Laplace operators. We present the theoretical foundations, but we also discuss the motivation to model and study real data with these tools.
1 citations
Journal Article•
TL;DR: To tackle the inefficiency problem of the current partial retrieval methods for 3DCAD models, a new partial retrieval approach based on graph indexing and filtering mechanism was proposed and proved, which satisfied the requirements of engineering practice.
1 citations