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Books on the topic 'Random Graph'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 March 2023

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1

Random graphs. London: Academic Press, 1985.

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2

Kolchin, V. F. Random graphs. Cambridge, UK: Cambridge University Press, 1999.

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3

Random graphs. 2nd ed. Cambridge: Cambridge University Press, 2001.

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4

Random geometric graphs. Oxford: Oxford University Press, 2003.

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5

Random graph dynamics. Cambridge: Cambridge University Press, 2007.

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6

Evstigneev, V. A. Teorii͡a︡ grafov: Algoritmy obrabotki beskonturnykh grafov. Novosibirsk: "Nauka," Sibirskoe predprii͡a︡tie RAN, 1998.

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7

O'Connell, Neil. Some large deviation results for sparse random graphs. Bristol [England]: Hewlett Packard, 1996.

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8

Orthogonal decompositions and functional limit theorems for random graph statistics. Providence, RI: American Mathematical Society, 1994.

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9

1949-, Rödl Vojtěch, Ruciński Andrzej, and Tetali Prasad, eds. A Sharp threshold for random graphs with a monochromatic triangle in every edge coloring. Providence, R.I: American Mathematical Society, 2006.

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10

Transfiniteness for graphs, electrical networks, and random walks. Boston: Birkhäuser, 1996.

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11

Olsen, Lars. Random geometrically graph directed self-similar multifractals. Harlow, Essex, England: Longman Scientific & Technical, 1994.

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12

Harris, Jenine. An Introduction to Exponential Random Graph Modeling. 2455 Teller Road, Thousand Oaks California 91320 United States: SAGE Publications, Inc., 2014. http://dx.doi.org/10.4135/9781452270135.

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13

Lusher, Dean, Johan Koskinen, and Garry Robins, eds. Exponential Random Graph Models for Social Networks. Cambridge: Cambridge University Press, 2012. http://dx.doi.org/10.1017/cbo9780511894701.

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14

Olsen, Lars. Random geometrically graph directed self-similar multifractals. New York: Longman Scientific & Technical, 1994.

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15

Grimmett, Geoffrey. Probability on graphs: Random processes on graphs and lattices. Cambridge: Cambridge University Press, 2010.

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16

Freĭdlin, M. I. Random perturbations of Hamiltonian systems. Providence, R.I: American Mathematical Society, 1994.

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17

Bonato, Anthony. The game of cops and robbers on graphs. Providence, R.I: American Mathematical Society, 2011.

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18

Reggini, Horacio C. Regular polyhedra: Random generation, Hamiltonian paths, and single chain nets. Buenos Aires: Academia Nacional de Ciencias Exactas, Físicas y Naturales, 1991.

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19

Probability on graphs: Random processes on graphs and lattices. Cambridge: Cambridge University Press, 2010.

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20

Woess, Wolfgang. Random walks on infinite graphs and groups. Cambridge: Cambridge University Press, 2000.

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21

F, Le Gall J., ed. Random trees, Lévy processes, and spatial branching processes. Paris, France: Société mathématique de France, 2002.

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22

Mahmoud, Hosam M. Evolution of random search trees. New York: Wiley, 1992.

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23

Kalyagin, V. A., A. P. Koldanov, P. A. Koldanov, and P. M. Pardalos. Statistical Analysis of Graph Structures in Random Variable Networks. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60293-2.

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24

International Seminar on Random Graphs and Probabilistic Methods in Combinatorics (3rd 1987 Poznaṅ, Poland). Random graphs '87: Based on proceedings of the 3rd International Seminar on Random Graphs and Probabilistic Methods in Combinatorics, June 27 - July 3 1987, Poznaṅ, Poland. Chichester [England]: Wiley, 1990.

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25

Exponential random graph models for social networks: Theories, methods, and applications. Cambridge: Cambridge University Press, 2012.

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26

1957-, Steger Tim, ed. Harmonic analysis for anisotropic random walks on homogeneous trees. Providence, R.I: American Mathematical Society, 1994.

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27

Mikov, Aleksandr. Generalized graphs and grammars. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1013698.

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The textbook deals with ordinary graphs and their generalizations-hypergraphs, hierarchical structures, geometric graphs, random and dynamic graphs. Graph grammars are considered in detail. Meets the requirements of the federal state educational standards of higher education of the latest generation. For master's students studying in the areas of the 02.00.00 group "Computer and Information Sciences", and can also be used in senior bachelor's courses and other areas in the field of computer science and computer engineering.

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28

Large networks and graph limits. Providence, Rhode Island: American Mathematical Society, 2012.

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29

Random trees: An interplay between combinatorics and probability. New York: Springer, 2009.

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30

Dimitri, Volchenkov, and SpringerLink (Online service), eds. Random Walks and Diffusions on Graphs and Databases: An Introduction. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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31

Shi, Feng. Learn About Exponential Random Graph Model in R With Data From UK Faculty Dataset (2008). 1 Oliver's Yard, 55 City Road, London EC1Y 1SP United Kingdom: SAGE Publications, Ltd., 2019. http://dx.doi.org/10.4135/9781526487551.

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32

Janson, Svante, Tomasz Łuczak, and Andrzej Rucinski. Random Graphs. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2000. http://dx.doi.org/10.1002/9781118032718.

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33

International Seminar on Random Graphs and Probabilistic Methods in Combinatorics. (2nd 1985 Uniwersytet im. Adama Mickiewicza w Poznaniu. Instytut Matematyki). Random graphs '85. New York: North-Holland, 1987.

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34

Durrett, Rick. Random Graph Dynamics. Cambridge University Press, 2006.

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35

Durrett, Rick. Random Graph Dynamics. Cambridge University Press, 2007.

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36

Durrett, Rick. Random Graph Dynamics. Cambridge University Press, 2007.

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37

Durrett, Rick. Random Graph Dynamics. Cambridge University Press, 2009.

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38

Kolchin, V. F. Random Graphs. Cambridge University Press, 2010.

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39

Kolchin, V. F. Random Graphs. Cambridge University Press, 2011.

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40

Kolchin, V. F. Random Graphs. Cambridge University Press, 2009.

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41

(Editor), Alan Frieze, and Tomasz Łuczak (Editor), eds. Random Graphs: Volume 2 (Random Graphs). Wiley-Interscience, 1992.

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42

Penrose, Mathew. Random Geometric Graphs. Oxford University Press, Incorporated, 2003.

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43

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Random graph ensembles. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0003.

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This chapter presents some theoretical tools for defining random graph ensembles systematically via soft or hard topological constraints including working through some properties of the Erdös-Rényi random graph ensemble, which is the simplest non-trivial random graph ensemble where links appear between two nodes with a fixed probability p. The chapter sets out the central representation of graph generation as the result of a discrete-time Markovian stochastic process. This unites the two flavours of graph generation approaches – because they can be viewed as simply moving forwards or backwards through this representation. It is possible to define a random graph by an algorithm, and then calculate the associated stationary probability. The alternative approach is to specify sampling weights and then to construct an algorithm that will have these weights as the stationary probabilities upon convergence.

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44

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Soft constraints: exponential random graph models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0004.

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Exponential random graph models (ERGMs) provide conceptually elegant recipes for generating soft-constrained random graphs. This chapter begins by explaining the theory and describing how to properly specify an ERGM, including demonstrating Lagrange’s method to derive the values of the model parameters that correspond to the desired constraints. Three ERGMs, all with constraints depending linearly on the adjacency matrix, are solved exactly: the targeted total number of links, targeted individual node degrees and targeted number of two-way links in a directed graph. However, when the controlled features become more complicated, ERGMs have a tendency to produce graphs in extreme phases (very dense or very sparse). The two-star model and the Strauss model are worked through in detail using advanced techniques from statistical mechanics in order to analyze the phase transitions. The chapter closes with a discussion of the strengths and weaknesses of ERGMs as null models.

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45

Durrett, Rick. Random Graph Dynamics. Cambridge University Press, 2007.

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46

Random Graph Dynamics. Cambridge University Press, 2010.

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47

Choi, In-kyeong. On straight line representations of random planar graphs. 1991.

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48

Sobieczky, Florian. Unimodularity in Randomly Generated Graphs. American Mathematical Society, 2018.

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49

Newman, Mark. Random graphs. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805090.003.0011.

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An introduction to the mathematics of the Poisson random graph, the simplest model of a random network. The chapter starts with a definition of the model, followed by derivations of basic properties like the mean degree, degree distribution, and clustering coefficient. This is followed with a detailed derivation of the large-scale structural properties of random graphs, including the position of the phase transition at which a giant component appears, the size of the giant component, the average size of the small components, and the expected diameter of the network. The chapter ends with a discussion of some of the shortcomings of the random graph model.

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50

Brant, el. Random Thoughts: 4x4 Graph. Independently Published, 2021.

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