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 pow...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
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Cambridge :
Cambridge University Press,
2011.
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| Subjects: | |
| Online Access: | CONNECT |
MARC
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| 100 | 1 | |a Van Mieghem, Piet, |e author. | |
| 245 | 1 | 0 | |a Graph spectra for complex networks / |c Piet Van Mieghem. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2011. | |
| 300 | |a 1 online resource (xvi, 346 pages) : |b digital, PDF file(s). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015). | ||
| 505 | 0 | 0 | |g Machine generated contents note: |g 1. |t Introduction -- |g 1.1. |t Interpretation and contemplation -- |g 1.2. |t Outline of the book -- |g 1.3. |t Classes of graphs -- |g 1.4. |t Outlook -- |g pt. I |t Spectra of graphs -- |g 2. |t Algebraic graph theory -- |g 2.1. |t Graph related matrices -- |g 2.2. |t Walks and paths -- |g 3. |t Eigenvalues of the adjacency matrix -- |g 3.1. |t General properties -- |g 3.2. |t The number of walks -- |g 3.3. |t Regular graphs -- |g 3.4. |t Bounds for the largest, positive eigenvalue & lambda;1 -- |g 3.5. |t Eigenvalue spacings -- |g 3.6. |t Additional properties -- |g 3.7. |t The stochastic matrix P = & Delta;-1 A -- |g 4. |t Eigenvalues of the Laplacian Q -- |g 4.1. |t General properties -- |g 4.2. |t Second smallest eigenvalue of the Laplacian Q -- |g 4.3. |t Partitioning of a graph -- |g 4.4. |t The modularity and the modularity matrix M -- |g 4.5. |t Bounds for the diameter -- |g 4.6. |t Eigenvalues of graphs and subgraphs -- |g 5. |t Spectra of special types of graphs -- |g 5.1. |t The complete graph. |
| 505 | 0 | 0 | |g 5.2. |t A small-world graph -- |g 5.3. |t A circuit on N nodes -- |g 5.4. |t A path of N -- 1 hops -- |g 5.5. |t A path of h hops -- |g 5.6. |t The wheel WN+1 -- |g 5.7. |t The complete biPartite graph Km, n -- |g 5.8. |t A general biPartite graph -- |g 5.9. |t Complete multi-Partite graph -- |g 5.10. |t An m-fully meshed star topology -- |g 5.11. |t A chain of cliques -- |g 5.12. |t The lattice -- |g 6. |t Density function of the eigenvalues -- |g 6.1. |t Definitions -- |g 6.2. |t The density when N & rarr; & infin; -- |g 6.3. |t Examples of spectral density functions -- |g 6.4. |t Density of a sparse regular graph -- |g 6.5. |t Random matrix theory -- |g 7. |t Spectra of complex networks -- |g 7.1. |t Simple observations -- |g 7.2. |t Distribution of the Laplacian eigenvalues and of the degree -- |g 7.3. |t Functional brain network -- |g 7.4. |t Rewiring Watts-Strogatz small-world graphs -- |g 7.5. |t Assortativity -- |g 7.6. |t Reconstructability of complex networks -- |g 7.7. |t Reaching consensus -- |g 7.8. |t Spectral graph metrics -- |g pt. II |t Eigensystem and polynomials -- |g 8. |t Eigensystem of a matrix. |
| 505 | 0 | 0 | |g 8.1. |t Eigenvalues and eigenvectors -- |g 8.2. |t Functions of a matrix -- |g 8.3. |t Hermitian and real symmetric matrices -- |g 8.4. |t Vector and matrix norms -- |g 8.5. |t Non-negative matrices -- |g 8.6. |t Positive (semi) definiteness -- |g 8.7. |t Interlacing -- |g 8.8. |t Eigenstructure of the product AB -- |g 8.9. |t Formulae of determinants -- |g 9. |t Polynomials with real coefficients -- |g 9.1. |t General properties -- |g 9.2. |t Transforming polynomials -- |g 9.3. |t Interpolation -- |g 9.4. |t The Euclidean algorithm -- |g 9.5. |t Descartes' rule of signs -- |g 9.6. |t The number of real zeros in an interval -- |g 9.7. |t Locations of zeros in the complex plane -- |g 9.8. |t Zeros of complex functions -- |g 9.9. |t Bounds on values of a polynomial -- |g 9.10. |t Bounds for the spacing between zeros -- |g 9.11. |t Bounds on the zeros of a polynomial -- |g 10. |t Orthogonal polynomials -- |g 10.1. |t Definitions -- |g 10.2. |t Properties -- |g 10.3. |t The three-term recursion -- |g 10.4. |t Zeros of orthogonal polynomials -- |g 10.5. |t Gaussian quadrature -- |g 10.6. |t The Jacobi matrix. |
| 520 | |a 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. | ||
| 650 | 0 | |a Graph theory. | |
| 650 | 0 | |a System analysis. | |
| 730 | 0 | |a Cambridge EBA Collection | |
| 776 | 0 | 8 | |i Print version: |z 9780521194587 |
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