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.
Recenzijas
'This book provides a comprehensive background in the area, especially for researchers and graduate students Highly recommended.' J. T. Saccoman, CHOICE
Papildus informācija
Spectral properties of the adjacency, Laplacian and effective resistance matrices of graphs are derived and applied to complex networks.
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.
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.
Biežāk uzdotie jautājumi par e-grāmatām