Graph Spectra for Complex Networks

by Piet van Mieghem

Overview

Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

Product Details

ISBN-13:	9780511993640
Publisher:	Cambridge University Press
Publication date:	12/02/2010
Sold by:	Barnes & Noble
Format:	eBook
File size:	20 MB
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About the Author

Piet Van Mieghem is a Professor at the Delft University of Technology with a chair in telecommunication networks, and chairman of the Network Architectures and Services (NAS) section. His main research interests lie in the modeling and analysis of complex networks (such as biological, brain, social, infrastructural, etc. networks) and in new Internet-like architectures and algorithms for future communications networks.

Table of Contents

Preface; Acknowledgements; 1. Introduction; Part I. Spectra of Graphs: 2. Algebraic graph theory; 3. Eigenvalues of the adjacency matrix; 4. Eigenvalues of the Laplacian Q; 5. Spectra of special types of graphs; 6. Density function of the eigenvalues; 7. Spectra of complex networks; Part II. Eigensystem and Polynomials: 8. Eigensystem of a matrix; 9. Polynomials with real coefficients; 10. Orthogonal polynomials; List of symbols; Bibliography; Index.