Graph Spectra for Complex Networks

Spectral properties of the adjacency, Laplacian and effective resistance matrices of graphs are derived and applied to complex networks.

Piet Van Mieghem (Author)

9781009366809, Cambridge University Press

Paperback / softback, published 21 September 2023

536 pages
24.2 x 17 x 3.1 cm, 0.92 kg

'This book provides a comprehensive background in the area, especially for researchers and graduate students … Highly recommended.' J. T. Saccoman, CHOICE

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.

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.

Subject Areas: Algorithms & data structures [UMB]