Graph Spectra for Complex Networks

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 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.

ISBN 052119458X   Pages 362 ISBN13 9780521194587 (What's this?)   Weight (grammes) 870 Publisher Cambridge University Press   Published in Cambridge Imprint Cambridge University Press   Height (mm) 247 Format Hardback   Width (mm) 174 Publication date 02 Dec 2010   Spine width (mm) 21 DEWEY 511.5   Academic level Postgraduate DEWEY edition DC22

		Preface
		Acknowledgements
		Symbols
1		Introduction		1
1.1		Interpretation and contemplation		2
1.2		Outline of the book		5
1.3		Classes of graphs		7
1.4		Outlook		10
Part I		Spectra of graphs		11
2		Algebraic graph theory		13
2.1		Graph related matrices		13
2.2		Walks and paths		25
3		Eigenvalues of the adjacency matrix		29
3.1		General properties		29
3.2		The number of walks		33
3.3		Regular graphs		43
3.4		Bounds for the largest, positive eigenvalue λ1		46
3.5		Eigenvalue spacings		55
3.6		Additional properties		58
3.7		The stochastic matrix P = Δ-1 A		63
4		Eigenvalues of the Laplacian Q		67
4.1		General properties		67
4.2		Second smallest eigenvalue of the Laplacian Q		80
4.3		Partitioning of a graph		89
4.4		The modularity and the modularity matrix M		96
4.5		Bounds for the diameter		108
4.6		Eigenvalues of graphs and subgraphs		109
5		Spectra of special types of graphs		115
		More...

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