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Books on the topic 'Graph spectrum'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Spectral graph theory. Published for the Conference Board of the mathematical sciences by the American Mathematical Society, 1997.

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2

Cvetković, Dragoš M. Applications of graph spectra. Edited by Gutman Ivan 1947-. Matematički institut SANU, 2009.

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3

Puppe, Thomas. Spectral Graph Drawing: A Survey. VDM Verlag Dr. Mu ller Aktiengesellschaft & Co. KG, 2008.

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4

Graph spectra for complex networks. Cambridge University Press, 2011.

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5

Al-Doujan, Fawwaz Awwad. Spectra of graphs. University of East Anglia, 1992.

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6

H, Haemers Willem, and SpringerLink (Online service), eds. Spectra of Graphs. Andries E. Brouwer and Willem H. Haemers, 2012.

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7

Brouwer, Andries E., and Willem H. Haemers. Spectra of Graphs. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1939-6.

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8

Spectral analysis on graph-like spaces. Springer-Verlag, 2012.

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9

Post, Olaf. Spectral Analysis on Graph-like Spaces. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23840-6.

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10

Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge University Press, 1997.

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11

Peter, Rowlinson, Simić S. (Slobodan), and London Mathematical Society, eds. An introduction to the theory of graph spectra. Cambridge University Press, 2010.

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12

Obata, Nobuaki. Spectral Analysis of Growing Graphs. Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-3506-7.

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13

Cvetković, Dragoš M. Selected topics on applications of graph spectra. Edited by Gutman Ivan 1947-. Matematički institut SANU, 2011.

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14

Peter, Rowlinson, and Simić S, eds. Spectral generalizations of line graphs: On graphs with least negative eigenvalue -2. Cambridge University Press, 2004.

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15

Cvetković, Dragoš M. Eigenspaces of graphs. Cambridge University Press, 2008.

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16

Cvetković, Dragoš M. Spectra of graphs: Theory and applications. 3rd ed. Johann Ambrosius Barth, 1995.

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17

Guattery, Stephen. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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18

Verdière, Yves Colin de. Spectres de graphes. Société mathématique de France, 1998.

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19

Möller, Manfred, and Vyacheslav Pivovarchik. Direct and Inverse Finite-Dimensional Spectral Problems on Graphs. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60484-4.

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20

1973-, Warzel Simone, ed. Random operators: Disorder effects on quantum spectra and dynamics. American Mathematical Society, 2015.

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21

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Ensembles with hard constraints. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0005.

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This chapter introduces random graph ensembles involving hard constraints such as setting a fixed total number of links or fixed degree sequence, including properties of the partition function. It continues on from the previous chapter’s investigation of ensembles with soft-constrained numbers of two-stars (two-step paths) and soft-constrained total number of triangles, but now combined with a hard constraint on the total number of links. This illustrates phase transitions in a mixed-constrained ensemble – which in this case is shown to be a condensation transition, where the network becomes c

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22

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Definitions and concepts. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0002.

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A network is specified by its links and nodes. However, it can be described by a much wider range of interesting and important topological features. This chapter introduces how a network can be characterized by its microscopic topological features and macroscopic topological features. Microscopic features introduced are degree and clustering coefficients. Macroscopic topological features introduced are the degree distribution; correlation between degrees of connected nodes; modularity; and, the eigenvalue spectrum (which counts the number of closed paths in the graph).

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23

(Foreword), L. Accardi, ed. Quantum Probability and Spectral Analysis of Graphs (Theoretical and Mathematical Physics). Springer, 2007.

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24

Mieghem, Piet Van. Graph Spectra for Complex Networks. Cambridge University Press, 2012.

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25

Chung. Recent Advances in Spectral Graph Theory. American Mathematical Society, 1999.

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26

Stevanovic, Dragan. Spectral Radius of Graphs. Elsevier Science & Technology Books, 2014.

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27

Spectral Radius of Graphs. Elsevier, 2015. http://dx.doi.org/10.1016/c2014-0-02233-2.

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28

Spectra of graphs: Theory and Applications. Huthig Pub Ltd, 1997.

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29

Pierantozzi, Donald. Topics in Spectral Analysis: Algebraic Graph Theory. Independently Published, 2020.

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30

M, Cvetković Dragoš, ed. Recent results in the theory of graph spectra. North-Holland, 1988.

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31

Cvetkovic, Dragos M., Horst Sachs, M. Cvetkovi&cacute, HorstLISTPRICE: 110 00 Sachs, and Michael Doob. Spectra of Graphs: Theory and Applications, 3rd Revised and Enlarged Edition. Vch Verlagsgesellschaft Mbh, 1998.

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32

Recent Results in the Theory of Graph Spectra. Elsevier, 1988. http://dx.doi.org/10.1016/s0167-5060(08)x7010-4.

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33

Spectra of Graphs: Theory and Applications (Pure and Applied Mathematics (Academic Pr)). 3rd ed. Academic Press, 1997.

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34

Center, Langley Research, ed. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. National Aeronautics and Space Administration, Langley Research Center, 1997.

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35

Quantum Probability and Spectral Analysis of Graphs. Springer Berlin Heidelberg, 2007. http://dx.doi.org/10.1007/3-540-48863-4.

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36

Cvetkovic, Dragos, Peter Rowlinson, and Slobodan Simic. Spectral Generalizations of Line Graphs: On Graphs with Least Eigenvalue -2 (London Mathematical Society Lecture Note Series). Cambridge University Press, 2004.

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37

Verbaarschot, Jac. Quantum chaos and quantum graphs. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.33.

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This article examines the origins of the universality of the spectral statistics of quantum chaotic systems in the context of periodic orbit theory. It also considers interesting analogies between periodic orbit theory and the sigma model, along with related work on quantum graphs. The article first reviews some facts and definitions for classically chaotic systems in order to elucidate their quantum behaviour, focusing on systems with two degrees of freedom: one characterized by ergodicity and another by hyperbolicity. It then describes two semiclassical approximation techniques — Gutzwiller’

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38

Spectral Clustering and Biclustering: Learning Large Graphs and Contingency Tables. Wiley, 2013.

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39

Bolla, Marianna. Spectral Clustering and Biclustering: Learning Large Graphs and Contingency Tables. Wiley & Sons, Incorporated, John, 2013.

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40

Obata, Nobuaki. Spectral Analysis of Growing Graphs: A Quantum Probability Point of View. Ingramcontent, 2017.

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41

Quantum Probability and Spectral Analysis of Graphs Theoretical and Mathematical Physics. Springer, 2010.

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42

Newman, Mark. Networks. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.001.0001.

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The study of networks, including computer networks, social networks, and biological networks, has attracted enormous interest in recent years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyse network data on an unprecendented scale, and the development of new theoretical tools has allowed us to extract knowledge from networks of many different kinds. The study of networks is broadly interdisciplinary and developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, an

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43

Rennie, Richard, and Jonathan Law, eds. A Dictionary of Physics. Oxford University Press, 2019. http://dx.doi.org/10.1093/acref/9780198821472.001.0001.

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Over 4,000 entries This new eighth edition has been fully updated to reflect progress in physics and related fields. It sees expansion to the areas of cosmology, astrophysics, condensed matter, quantum technology, and nanotechnology, with 125 new entries including, Deep Underground Neutrino Experiment, kilonova, leptoquark, and muscovium. The dictionary’s range of appendices, updated for the new edition, includes the periodic table, the electromagnetic spectrum, and a detailed chronology of key dates. Seventeen new diagrams add to the clarity and accessibility of the text, with almost 150 line

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44

Introduction to Quantum Graphs (Mathematical Surveys and Monographs). American Mathematical Society, 2012.

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45

Vernizzi, Graziano, and Henri Orland. Complex networks. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.43.

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This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how

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46

T. Wave Phenomena. Courier Dover Publications, 2014.

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