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Graph Spectra for Complex Networks

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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.

Author(s): Piet Van Mieghem
Edition: 2
Publisher: Cambridge University Press
Year: 2023

Language: English
Pages: 535
City: Cambridge, United Kingdom
Tags: Graph Theory; System Analysis; Algorithmics; Complexity; Computer Algebra; Computational Geometry; Communications Processing; Signal Processing; Engineering; Computer Science

Frontmatter
Dedication
Contents
Preface to the second edition
Preface to the first edition
Acknowledgements
Symbols
1 Introduction
Part I Spectra of graphs
Part II Eigensystem
Part III Polynomials
Bibliography
Index