Graph Spectra for Complex Networks

Piet Van Mieghem

ISBN 10: 1009366807 / ISBN 13: 9781009366809

Published by Cambridge University Press, GB, 2023

About this Item

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.

Seller Inventory # LU-9781009366809

Bibliographic Details

• Title: Graph Spectra for Complex Networks
• Publisher: Cambridge University Press, GB
• Publication Date: 2023
• Language: English
• ISBN 10: 1009366807
• ISBN 13: 9781009366809
• Binding: Paperback
• Edition: 2nd Edition
• Condition: New
• Weight: 913 grams

About this title

Synopsis

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.

About the Author

Piet Van Mieghem is Professor at the Delft University of Technology. His research interests lie in network science: the modeling and analysis of complex networks such as infrastructural networks (for example telecommunication, power grids and transportation) as well as biological, brain, social and economic networks.