Graph Spectra for Complex Networks

Piet van Mieghem

doi:10.1017/CBO9780511921681

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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-viii
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Preface
pp ix-xii
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Acknowledgements
pp xiii-xiv
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Symbols
pp xv-xvi
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1 - Introduction
pp 1-10
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Part I - Spectra of graphs
pp 11-12
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2 - Algebraic graph theory
pp 13-28
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3 - Eigenvalues of the adjacency matrix
pp 29-66
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4 - Eigenvalues of the Laplacian Q
pp 67-114
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5 - Spectra of special types of graphs
pp 115-158
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6 - Density function of the eigenvalues
pp 159-178
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7 - Spectra of complex networks
pp 179-208
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Part II - Eigensystem and polynomials
pp 209-210
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8 - Eigensystem of a matrix
pp 211-262
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9 - Polynomials with real coefficients
pp 263-312
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10 - Orthogonal polynomials
pp 313-338
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References
pp 339-344
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Index
pp 345-346
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Graph Spectra for Complex Networks

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Contents

Frontmatter
pp i-iv

Contents
pp v-viii

Preface
pp ix-xii

Acknowledgements
pp xiii-xiv

Symbols
pp xv-xvi

1 - Introduction
pp 1-10

Part I - Spectra of graphs
pp 11-12

2 - Algebraic graph theory
pp 13-28

3 - Eigenvalues of the adjacency matrix
pp 29-66

4 - Eigenvalues of the Laplacian Q
pp 67-114

5 - Spectra of special types of graphs
pp 115-158

6 - Density function of the eigenvalues
pp 159-178

7 - Spectra of complex networks
pp 179-208

Part II - Eigensystem and polynomials
pp 209-210

8 - Eigensystem of a matrix
pp 211-262

9 - Polynomials with real coefficients
pp 263-312

10 - Orthogonal polynomials
pp 313-338

References
pp 339-344

Index
pp 345-346

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Graph Spectra for Complex Networks

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