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  • 1
    Book
    Book
    Graph spectra for complex networks (2011)
    Cambridge [u.a.] : Cambridge University Press
    Details
    UID:
    b3kat_BV041770266
    Format: XI, 346 S. , Ill.
    Edition: 1. publ.
    ISBN: 9780521194587
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    QH 450
    RVK:
    SK 890
    Keywords: Graphentheorie ; Komplexes System
    URL: Inhaltstext
    Library Location Call Number Volume/Issue/Year Availability
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    Book
    UB Potsdam get availability status
    TU Berlin get availability status
  • 2
    Online Resource
    Online Resource
    Graph spectra for complex networks / (2011)
    Cambridge, U.K. :Cambridge University Press,
    Details
    UID:
    almafu_9959242026802883
    Format: 1 online resource (xvi, 346 pages) : , digital, PDF file(s).
    ISBN: 0-511-99364-1 , 1-107-21440-8 , 0-511-99244-0 , 9786612976551 , 0-511-98490-1 , 0-511-98865-6 , 0-511-99145-2 , 0-511-98685-8 , 0-511-99046-4 , 1-282-97655-9 , 0-511-92168-3
    Content: 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.
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , pt. 1. Spectra of graphs -- pt. 2. Eigensystem and polynomials.
    Additional Edition: ISBN 0-521-19458-X
    Additional Edition: ISBN 1-107-41147-5
    Language: English
    URL: https://doi.org/10.1017/CBO9780511921681
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    HU Berlin
    FU Berlin
  • 3
    Online Resource
    Online Resource
    Graph spectra for complex networks (2011)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_883477971
    Format: 1 Online-Ressource (xvi, 346 pages) , digital, PDF file(s)
    ISBN: 9780511921681
    Content: 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
    Note: Title from publisher's bibliographic system (viewed on 05 Oct 2015) , 5.2. A small-world graph -- 5.3. A circuit on N nodes -- 5.4. A path of N -- 1 hops -- 5.5. A path of h hops -- 5.6. The wheel WN+1 -- 5.7. The complete biPartite graph Km, n -- 5.8. A general biPartite graph -- 5.9. Complete multi-Partite graph -- 5.10. An m-fully meshed star topology -- 5.11. A chain of cliques -- 5.12. The lattice -- 6. Density function of the eigenvalues -- 6.1. Definitions -- 6.2. The density when N & rarr; & infin; -- 6.3. Examples of spectral density functions -- 6.4. Density of a sparse regular graph -- 6.5. Random matrix theory -- 7. Spectra of complex networks -- 7.1. Simple observations -- 7.2. Distribution of the Laplacian eigenvalues and of the degree -- 7.3. Functional brain network -- 7.4. Rewiring Watts-Strogatz small-world graphs -- 7.5. Assortativity -- 7.6. Reconstructability of complex networks -- 7.7. Reaching consensus -- 7.8. Spectral graph metrics -- pt. II Eigensystem and polynomials -- 8. Eigensystem of a matrix. , 8.1. Eigenvalues and eigenvectors -- 8.2. Functions of a matrix -- 8.3. Hermitian and real symmetric matrices -- 8.4. Vector and matrix norms -- 8.5. Non-negative matrices -- 8.6. Positive (semi) definiteness -- 8.7. Interlacing -- 8.8. Eigenstructure of the product AB -- 8.9. Formulae of determinants -- 9. Polynomials with real coefficients -- 9.1. General properties -- 9.2. Transforming polynomials -- 9.3. Interpolation -- 9.4. The Euclidean algorithm -- 9.5. Descartes' rule of signs -- 9.6. The number of real zeros in an interval -- 9.7. Locations of zeros in the complex plane -- 9.8. Zeros of complex functions -- 9.9. Bounds on values of a polynomial -- 9.10. Bounds for the spacing between zeros -- 9.11. Bounds on the zeros of a polynomial -- 10. Orthogonal polynomials -- 10.1. Definitions -- 10.2. Properties -- 10.3. The three-term recursion -- 10.4. Zeros of orthogonal polynomials -- 10.5. Gaussian quadrature -- 10.6. The Jacobi matrix. , Machine generated contents note: 1. Introduction -- 1.1. Interpretation and contemplation -- 1.2. Outline of the book -- 1.3. Classes of graphs -- 1.4. Outlook -- pt. I Spectra of graphs -- 2. Algebraic graph theory -- 2.1. Graph related matrices -- 2.2. Walks and paths -- 3. Eigenvalues of the adjacency matrix -- 3.1. General properties -- 3.2. The number of walks -- 3.3. Regular graphs -- 3.4. Bounds for the largest, positive eigenvalue & lambda;1 -- 3.5. Eigenvalue spacings -- 3.6. Additional properties -- 3.7. The stochastic matrix P = & Delta;-1 A -- 4. Eigenvalues of the Laplacian Q -- 4.1. General properties -- 4.2. Second smallest eigenvalue of the Laplacian Q -- 4.3. Partitioning of a graph -- 4.4. The modularity and the modularity matrix M -- 4.5. Bounds for the diameter -- 4.6. Eigenvalues of graphs and subgraphs -- 5. Spectra of special types of graphs -- 5.1. The complete graph.
    Additional Edition: ISBN 9780521194587
    Additional Edition: ISBN 9781107411470
    Additional Edition: Erscheint auch als Druck-Ausgabe ISBN 9780521194587
    Language: English
    DOI: 10.1017/CBO9780511921681
    URL: Volltext
    URL: Inhaltstext
    URL: Inhaltsverzeichnis
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Online Access
    Open Access Request
    UB Potsdam
  • 4
    Online Resource
    Online Resource
    Graph Spectra for Complex Networks (2010)
    Cambridge : Cambridge University Press
    Details
    UID:
    gbv_1653235799
    Format: Online-Ressource (1 online resource (364 p.)) , digital, PDF file(s).
    Edition: Online-Ausg.
    ISBN: 9780511921681
    Content: 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.
    Note: Title from publishers bibliographic system (viewed on 18 Feb 2013)
    Additional Edition: ISBN 9780521194587
    Additional Edition: Erscheint auch als Druck-Ausgabe Mieghem, Piet van, 1964 - Graph spectra for complex networks Cambridge : Cambridge Univ. Press, 2011 ISBN 052119458X
    Additional Edition: ISBN 9780521194587
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    QH 450
    RVK:
    SK 890
    Keywords: Graphentheorie ; Komplexes System
    DOI: 10.1017/CBO9780511921681
    URL: Volltext
    URL: Inhaltstext
    URL: Inhaltsverzeichnis
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Online Resource
    Online Access
    Open Access Request
    UB Potsdam
  • 5
    Book
    Book
    Graph spectra for complex networks / (2012)
    Cambridge [u.a.] :Cambridge University Press,
    Details
    UID:
    almahu_BV040364529
    Format: XI, 346 S. : , Ill.
    Edition: 1. publ., 1. paperback ed.
    ISBN: 978-1-107-41147-0 , 1-107-41147-5 , 978-0-521-19458-7
    Note: Originally published: 2011
    Language: English
    Subjects: Economics , Mathematics
    RVK:
    SK 890
    RVK:
    QH 450
    Keywords: Graphentheorie ; Komplexes System
    URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025218285&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Book
    HU Berlin get availability status
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