Graph Spectra for Complex Networks
2nd Edition
Published on 6. September 2023
978-1-009-36678-6 (ISBN)
Description
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.
Reviews / Votes
'This book provides a comprehensive background in the area, especially for researchers and graduate students ... Highly recommended.' J. T. Saccoman, CHOICE 'This book provides a comprehensive background in the area, especially for researchers and graduate students ... Highly recommended.' J. T. Saccoman, CHOICEMore details
Edition
2nd Revised edition
Language
English
Place of publication
Cambridge
United Kingdom
Target group
College/higher education
Edition type
Revised edition
Illustrations
Worked examples or Exercises
File size
7,36 MB
ISBN-13
978-1-009-36678-6 (9781009366786)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Piet Van Mieghem
Graph Spectra for Complex Networks
Book
09/2023
2nd Edition
Cambridge University Press
€64.50
Shipment within 15-20 days
Person
Content
Symbols; 1. Introduction; Part I. Spectra of Graphs: 2. Algebraic graph theory; 3. Eigenvalues of the adjacency matrix; 4. Eigenvalues of the Laplacian Q; 5. Effective resistance matrix; 6. Spectra of special types of graphs; 7. Density function of the eigenvalues; 8. Spectra of complex networks; Part II. Eigensystem: 9. Topics in linear algebra; 10. Eigensystem of a matrix; Part III. Polynomials: 11. Polynomials with real coefficients; 12. Orthogonal polynomials; References; Index.
