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Graph spectra for complex networks / Piet Van Mieghem, Delft University of Technology.

By: Material type: TextLanguage: English Publication details: Cambridge, UK : Cambridge University Press, 2023.Edition: Second editionDescription: xix, 515 pages : illISBN:
  • 9781009366793
Subject(s): Additional physical formats: Print version: : No titleDDC classification:
  • 511.5 23 MIE
Online resources:
Contents:
Introdouction Part I: Spectra of graphs Algebraic graph theory Eigenvalues of the adjacency matrix Eigenvalues of the Laplacian Q Effective resistance matrix Spectra of special types of graphs Density function of the eigenvalues Spectra of complex networks Part II: Eigensystem Topics in linear algebra Eigensystem of a matrix Part III: Polynomials Polynomials with real coefficients Orthogonal polynomials
Summary: This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks. The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.
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Cover image Item type Current library Home library Collection Shelving location Call number Materials specified Vol info URL Copy number Status Notes Date due Barcode Item holds Item hold queue priority Course reserves
General Books CUTN Central Library Sciences Non-fiction 511.5 MIE (Browse shelf(Opens below)) Available 54652

Introdouction
Part I: Spectra of graphs
Algebraic graph theory
Eigenvalues of the adjacency matrix
Eigenvalues of the Laplacian Q
Effective resistance matrix
Spectra of special types of graphs
Density function of the eigenvalues
Spectra of complex networks
Part II: Eigensystem
Topics in linear algebra
Eigensystem of a matrix
Part III: Polynomials
Polynomials with real coefficients
Orthogonal polynomials

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This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks. The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

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