Configuring random graph models with fixed degree sequences

SIAM Review

Volumn 60, Issue 2, 2018, Pages 315-355

  Fosdick, Bailey K ^a   Larremore, Daniel B ^b   Nishimura, Joel ^c   Ugander, Johan ^d  

^a Veterinary Dentistry and Oral Surgery   (United States)

^b SANTA FE INSTITUTE   (United States)

^c ARIZONA STATE UNIVERSITY WEST   (United States)

^d Stanford University   (United States)

Author keywords

Complex networks; Configuration model; Graph enumeration; Graph sampling; Markov chain monte carlo; Permutation tests

Indexed keywords

COMPLEX NETWORKS; DIRECTED GRAPHS; GRAPHIC METHODS; IMPORTANCE SAMPLING; MARKOV PROCESSES; NEURONS; PROTEINS;

CONFIGURATION MODEL; GRAPH ENUMERATION; GRAPH SAMPLINGS; MARKOV CHAIN MONTE-CARLO; PERMUTATION TESTS;

GRAPH THEORY;

EID: 85046685956     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/16M1087175     Document Type: Review

References (139)

1. A. Agresti, A survey of exact inference for contingency tables, Statist. Sci., 7 (1992), pp. 131-153. (Cited on p. 322).
2. E. M. Airoldi, D. M. Blei, S. E. Fienberg, and E. P. Xing, Mixed membership stochastic blockmodels, J. Mach. Learn. Res., 9 (2008), pp. 1981-2014. (Cited on p. 340).
3. D. Aldous and U. Vazirani, "Go with the winners"" algorithms, in SFCS 1994 Proceedings of the 35th Annual Symposium on Foundations of Computer Science, IEEE, 1994, pp. 492-501. (Cited on p. 336).
4. Y. Amanatidis, B. Green, and M. Mihail, Graphic Realizations of Joint-Degree Matrices, preprint, https://arxiv.org/abs/1509.07076, 2008. (Cited on p. 339).
5. Y. Artzy-Randrup, S. J. Fleishman, N. Ben-Tal, and L. Stone, Comment on "Network motifs: Simple building blocks of complex networks"" and "Superfamilies of evolved and designed networks, " Science, 305 (2004) p. 1107. (Cited on p. 322).
6. Y. Artzy-Randrup and L. Stone, Generating uniformly distributed random networks, Phys. Rev. E, 72 (2005), art. 056708. (Cited on pp. 322, 325, 326, 329).
7. L. Babai, Graph isomorphism in quasipolynomial time, in Proceedings of the 48th Annual ACM Symposium on Theory of Computing, ACM, 2016, pp. 684-697. (Cited on p. 341).
8. A.-L. Barabasi and R. Albert, Emergence of scaling in random networks, Science, 286 (1999), pp. 509-512. (Cited on p. 339).
9. K. E. Bassler, C. I. Del Genio, P. L. Erdos, I. Miklos, and Z. Toroczkai, Exact sampling of graphs with prescribed degree correlations, New J. Phys., 17 (2015), art. 083052. (Cited on p. 339).
10. M. Bayati, J. H. Kim, and A. Saberi, A sequential algorithm for generating random graphs, Algorithmica, 58 (2010), pp. 860-910. (Cited on pp. 335, 336).
11. A. Bekessy, P. Bekessy, and J. Komlos, Asymptotic enumeration of regular matrices, Stud. Sci. Math. Hungar, 7 (1972), pp. 343-353. (Cited on p. 319).
12. E. A. Bender and E. R. Canfield, The asymptotic number of labeled graphs with given degree sequences, J. Combinatorial Theory Ser. A, 24 (1978), pp. 296-307. (Cited on p. 319).
13. C. Berge, Theory of Graphs and Its Applications, Methuen, London, 1962. (Cited on p. 330).
14. J. Besag and P. Clifford, Generalized Monte Carlo significance tests, Biometrika, 76 (1989), pp. 633-642. (Cited on p. 325).
15. S. Bhamidi, G. Bresler, and A. Sly, Mixing time of exponential random graphs, Ann. Appl. Probab., 21 (2011), pp. 2146-2170. (Cited on p. 340).
16. D. Bienstock and O. Gunluk, A degree sequence problem related to network design, Networks, 24 (1994), pp. 195-205. (Cited on pp. 326, 330, 335, 337).
17. J. Blitzstein and P. Diaconis, A sequential importance sampling algorithm for generating random graphs with prescribed degrees, Internet Math., 6 (2011), pp. 489-522. (Cited on pp. 319, 336).
18. M. Boguna, R. Pastor-Satorras, and A. Vespignani, Cut-offs and finite size effects in scale-free networks, Eur. Phys. J. B, 38 (2004), pp. 205-209. (Cited on pp. 320, 342).
19. B. Bollobas, A probabilistic proof of an asymptotic formula for the number of labelled regular graphs, European J. Combin., 1 (1980), pp. 311-316. (Cited on pp. 319, 335).
20. S. Brooks and A. Gelman, Some issues for monitoring convergence of iterative simulations, Comput. Sci. Statist., 1998), pp. 30-36. (Cited on p. 335).
21. Z. Burda and A. Krzywicki, Uncorrelated random networks, Phys. Rev. E, 67 (2003), art. 046118. (Cited on p. 326).
22. S. Cafieri, P. Hansen, and L. Liberti, Loops and multiple edges in modularity maximization of networks, Phys. Rev. E, 81 (2010), art. 046102. (Cited on pp. 326, 347).
23. D. S. Callaway, J. E. Hopcroft, J. M. Kleinberg, M. E. Newman, and S. H. Strogatz, Are randomly grown graphs really random?, Phys. Rev. E, 64 (2001), art. 041902. (Cited on p. 339).
24. D. S. Callaway, M. E. Newman, S. H. Strogatz, and D. J. Watts, Network robustness and fragility: Percolation on random graphs, Phys. Rev. Lett., 85 (2000), pp. 5468-5471. (Cited on p. 320).
25. C. J. Carstens, Proof of uniform sampling of binary matrices with fixed row sums and column sums for the fast curveball algorithm, Phys. Rev. E, 91 (2015), art. 042812, https://doi.org/10.1103/PhysRevE.91.042812. (Cited on p. 338).
26. C. J. Carstens, A. Berger, and G. Strona, Curveball: A New Generation of Sampling Algorithms for Graphs with Fixed Degree Sequence, preprint, https://arxiv.org/abs/1609.05137, 2016. (Cited on p. 338).
27. C. J. Carstens and K. J. Horadam, Switching edges to randomize networks: What goes wrong and how to fix it, J. Complex Networks, 5 (2017), pp. 337-351. (Cited on pp. 317, 338).
28. D. Centola, V. M. Eguluz, and M. W. Macy, Cascade dynamics of complex propagation, Phys. A, 374 (2007), pp. 449-456. (Cited on p. 322).
29. A. G. Chandrasekhar and M. O. Jackson, Tractable and Consistent Random Graph Models, Tech. report, National Bureau of Economic Research, 2014. (Cited on p. 340).
30. S. Chatterjee and P. Diaconis, Estimating and understanding exponential random graph models, Ann. Statist., 41 (2013), pp. 2428-2461.(Cited on p. 340).
31. Y. Chen, P. Diaconis, S. P. Holmes, and J. S. Liu, Sequential Monte Carlo methods for statistical analysis of tables, J. Amer. Statist. Assoc., 100 (2005), pp. 109-120. (Cited on p. 322).
32. F. Chung and L. Lu, The average distances in random graphs with given expected degrees, Proc. Natl. Acad. Sci., 99 (2002), pp. 15879-15882. (Cited on pp. 339, 347).
33. A. Clauset, C. R. Shalizi, and M. E. J. Newman, Power-law distributions in empirical data, SIAM Rev., 51 (2009), pp. 661-703, https://doi.org/10.1137/070710111. (Cited on p. 339).
34. R. Cohen, D. Ben-Avraham, and S. Havlin, Percolation critical exponents in scale-free networks, Phys. Rev. E, 66 (2002), art. 036113. (Cited on p. 320).
35. E. F. Connor and D. Simberloff, The assembly of species communities: Chance or competition?, Ecology, 60 (1979), pp. 1132-1140. (Cited on p. 321).
36. C. Cooper, M. Dyer, and C. Greenhill, Sampling regular graphs and a peer-To-peer network, Combin. Probab. Comput., 16 (2007), pp. 557-593. (Cited on p. 334).
37. E. Czabarka, A. Dutle, P. L. Erdos, and I. Miklos, On realizations of a joint degree matrix, Discrete Appl. Math., 181 (2015), pp. 283-288. (Cited on p. 339).
38. J. A. Davis and S. Leinhardt, The structure of positive interpersonal relations in small groups, in Sociological Theories in Progress, Vol. 2, J. Berger, M. Zelditch, and B. Anderson, eds., 1971. (Cited on p. 321).
39. D. J. de Solla Price, Networks of scientific papers, Science, 149 (1965), pp. 510-515. (Cited on p. 339).
40. D. J. de Solla Price, A general theory of bibliometric and other cumulative advantage processes, J. Amer. Soc. Inform. Sci., 27 (1976), pp. 292-306. (Cited on p. 339).
41. C. I. Del Genio, H. Kim, Z. Toroczkai, and K. E. Bassler, Efficient and exact sampling of simple graphs with given arbitrary degree sequence, PLoS ONE, 5 (2010), art. e10012. (Cited on p. 336).
42. E. D. Demaine, F. Reidl, P. Rossmanith, F. S. Villaamil, S. Sikdar, and B. D. Sullivan, Structural Sparsity of Complex Networks: Bounded Expansion in Random Models and Real-World Graphs, preprint, https://arxiv.org/abs/1406.2587, 2014. (Cited on p. 339).
43. B. A. Desmarais and S. J. Cranmer, Statistical inference for valued-edge networks: The generalized exponential random graph model, PLoS ONE, 7 (2012), art. e30136. (Cited on p. 340).
44. P. Diaconis and A. Gangolli, Rectangular arrays with fixed margins, in Discrete Probability and Algorithms, D. Aldous, P. Diaconis, J. Spencer, and J. Steele, eds., IMA Vol. Math. Appl. 72, Springer, New York, 1995, pp. 15-41, https://doi.org/10.1007/978-1-4612-0801-33. (Cited on p. 322).
45. J. M. Diamond, Assembly of species communities, in Ecology and Evolution of Communities, J. M. Diamond and M. L. Cody, eds., Harvard University Press, 1975, pp. 342-344. (Cited on p. 321).
46. R. B. Eggleton, Graphic sequences and graphic polynomials: A report, Infinite and Finite Sets, 1 (1973), pp. 385-392. (Cited on p. 330).
47. R. B. Eggleton and D. A. Holton, The Graph of Type (0, ∞ ∞ ) Realizations of a Graphic Sequence, Springer, 1979. (Cited on p. 328).
48. R. B. Eggleton and D. A. Holton, Simple and Multigraphic Realizations of Degree Sequences, Springer, 1981. (Cited on p. 330).
49. D. Eppstein, Z. Galil, G. F. Italiano, and A. Nissenzweig, Sparsification-A technique for speeding up dynamic graph algorithms, J. ACM, 44 (1997), pp. 669-696. (Cited on p. 337).
50. P. L. Erdos, Z. Kiraly, and I. Miklos, On the swap-distances of different realizations of a graphical degree sequence, Combin. Probab. Comput., 22 (2013), pp. 366-383. (Cited on p. 335).
51. P. L. Erdos, S. Z. Kiss, I. Miklos, and L. Soukup, Approximate counting of graphical realizations, PLoS ONE, 10 (2015), art. e0131300. (Cited on p. 334).
52. T. Feder, A. Guetz, M. Mihail, and A. Saberi, A local switch Markov chain on given degree graphs with application in connectivity of peer-To-peer networks, in Proceedings of the 47th Annual IEEE Conference on Foundations of Computer Science, IEEE, 2006, pp. 69-76. (Cited on p. 338).
53. R. A. Fisher, The Design of Experiments, Oliver and Boyd, Edinburgh, 1935. (Cited on p. 320).
54. S. Fortunato, Community detection in graphs, Phys. Rep., 486 (2010), pp. 75-174. (Cited on p. 346).
55. O. Frank and F. Harary, Cluster inference by using transitivity indices in empirical graphs, J. Amer. Statist. Assoc., 77 (1982), pp. 835-840. (Cited on p. 340).
56. M. Gail and N. Mantel, Counting the number of rtimes c contingency tables with fixed margins, J. Amer. Statist. Assoc., 72 (1977), pp. 859-862. (Cited on p. 322).
57. T. Gallai and P. Erdos, Graphs with prescribed degree of vertices (Hungarian), Mat. Lapok, 11 (1960), pp. 264-274. (Cited on p. 336).
58. A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin, Bayesian Data Analysis, 3rd ed., CRC Press, 2014. (Cited on p. 335).
59. C. Gkantsidis, M. Mihail, and E. Zegura, The Markov chain simulation method for generating connected power law random graphs, in Proceedings of the 5th Workshop on Algorithm Engineering and Experiments, SIAM, Philadelphia, 2003, pp. 16-25. (Cited on p. 337).
60. L. A. Goodman, Snowball sampling, Ann. Math. Statist., 32 (1961), pp. 148-170. (Cited on p. 337).
61. N. J. Gotelli and G. R. Graves, Null Models in Ecology, Smithsonian Institution Press, Washington, D.C., 1996. (Cited on pp. 321, 326).
62. C. Greenhill, A polynomial bound on the mixing time of a Markov chain for sampling regular directed graphs, Electron. J. Combin., 18 (2011), art. P234. (Cited on p. 334).
63. C. Greenhill, The switch Markov chain for sampling irregular graphs, in Proceedings of the 26th Annual ACM-SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 2015, pp. 1564-1572, https://doi.org/10.1137/1.9781611973730.103. (Cited on pp. 334, 335).
64. S. L. Hakimi, On realizability of a set of integers as degrees of the vertices of a linear graph. I, J. Soc. Indust. Appl. Math., 10 (1962), pp. 496-506, https://doi.org/10.1137/0110037. (Cited on p. 336).
65. S. L. Hakimi, On realizability of a set of integers as degrees of the vertices of a linear graph. II. Uniqueness, J. Soc. Indust. Appl. Math., 11 (1963), pp. 135-147, https://doi.org/10.1137/0111010. (Cited on pp. 321, 326).
66. V. J. Havel, A remark on the existence of finite graphs, Casopis Pest. Mat, 80 (1955), p. 1253. (Cited on pp. 321, 336).
67. P. W. Holland, K. B. Laskey, and S. Leinhardt, Stochastic blockmodels: First steps, Social Networks, 5 (1983), pp. 109-137. (Cited on p. 340).
68. G. C. Homans, The Human Group, Routledge and Kegan Paul, London, 1950. (Cited on p. 321).
69. S. Itzkovitz, R. Milo, N. Kashtan, M. E. Newman, and U. Alon, Reply to Comment on Subgraphs in random networks, Phys. Rev. E, 70 (2004), art. 058102. (Cited on p. 322).
70. S. Itzkovitz, R. Milo, N. Kashtan, G. Ziv, and U. Alon, Subgraphs in random networks, Phys. Rev. E, 68 (2003), art. 026127. (Cited on p. 322).
71. M. Jerrum and A. Sinclair, Fast uniform generation of regular graphs, Theoret. Comput. Sci., 73 (1990), pp. 91-100. (Cited on p. 336).
72. B. Jones, Computational Geometry Database, http://jeffe.cs.illinois.edu/compgeom/biblios.html, 2002 (accessed 7/1/2016). (Cited on p. 342).
73. B. Karrer and M. E. Newman, Stochastic blockmodels and community structure in networks, Phys. Rev. E, 83 (2011), art. 016107. (Cited on p. 340).
74. O. D. King, Comment on "Subgraphs in random networks, "" Phys. Rev. E, 70 (2004), art. 058101. (Cited on p. 322).
75. D. J. Kleitman and D.-L. Wang, Algorithms for constructing graphs and digraphs with given valences and factors, Discrete Math., 6 (1973), pp. 79-88. (Cited on p. 338).
76. T. G. Kolda, A. Pinar, T. Plantenga, and C. Seshadhri, A scalable generative graph model with community structure, SIAM J. Sci. Comput., 36 (2014), pp. C424-C452, https://doi.org/10.1137/130914218. (Cited on p. 340).
77. P. N. Krivitsky, Exponential-family random graph models for valued networks, Electron. J. Statist., 6 (2012), pp. 1100-1128. (Cited on p. 340).
78. M. D. LaMar, Directed 3-cycle anchored digraphs and their application in the uniform sampling of realizations from a fixed degree sequence, in Proceedings of the Winter Simulation Conference, 2011, pp. 3353-3364. (Cited on p. 338).
79. D. B. Larremore, A. Clauset, and C. O. Buckee, A network approach to analyzing highly recombinant malaria parasite genes, PLoS Comput. Biol., 9 (2013), art. e1003268. (Cited on p. 346).
80. D. B. Larremore, A. Clauset, and A. Z. Jacobs, Efficiently inferring community structure in bipartite networks, Phys. Rev. E, 90 (2014), art. 012805. (Cited on p. 340).
81. D. B. Larremore, W. L. Shew, and J. G. Restrepo, Predicting criticality and dynamic range in complex networks: Effects of topology, Phys. Rev. Lett., 106 (2011), art. 58101. (Cited on p. 320).
82. J. Leskovec, K. J. Lang, A. Dasgupta, and M. W. Mahoney, Community structure in large networks: Natural cluster sizes and the absence of large well-defined clusters, Internet Math., 6 (2009), pp. 29-123. (Cited on p. 346).
83. J. Leskovec and R. Sosic, SNAP: A general purpose network analysis and graph-mining library, ACM Trans. Intell. Syst. Technol., 8 (2016), art. 1, https://doi.org/10.1145/2898361. (Cited on p. 336).
84. D. A. Levin, Y. Peres, and E. L. Wilmer, Markov Chains and Mixing Times, AMS, Providence, RI, 2009. (Cited on p. 334).
85. I. I. Levin, D. M. Zonana, J. M. Burt, and R. J. Safran, Performance of encounternet tags: Field tests of miniaturized proximity loggers for use on small birds, PLoS ONE, 10 (2015), art. e0137242. (Cited on p. 344).
86. I. I. Levin, D. M. Zonana, B. K. Fosdick, S. J. Song, R. Knight, and R. J. Safran, Stress response, gut microbial diversity and sexual signals correlate with social interactions, Biology Lett., 12 (2016), https://doi.org/10.1098/rsbl.2016.0352. (Cited on p. 344).
87. X. Liu, T. Murata, and K. Wakita, Detecting network communities beyond assortativityrelated attributes, Phys. Rev. E, 90 (2014), art. 012806. (Cited on p. 322).
88. P. Mahlmann and C. Schindelhauer, Peer-To-peer networks based on random transformations of connected regular undirected graphs, in Proceedings of the 17th Annual ACM Symposium on Parallelism in Algorithms and Architectures, ACM, 2005, pp. 155-164. (Cited on p. 337).
89. R. D. Malmgren, J. M. Ottino, and L. A. N. Amaral, The role of mentorship in protege performance, Nature, 465 (2010), pp. 622-626. (Cited on p. 322).
90. S. Maslov and K. Sneppen, Specificity and stability in topology of protein networks, Science, 296 (2002), pp. 910-913. (Cited on p. 322).
91. S. Maslov, K. Sneppen, and A. Zaliznyak, Detection of topological patterns in complex networks: Correlation profile of the internet, Phys. A, 333 (2004), pp. 529-540. (Cited on pp. 322, 337).
92. C. P. Massen and J. P. Doye, Identifying communities within energy landscapes, Phys. Rev. E, 71 (2005), art. 046101. (Cited on p. 347).
93. R. Mathon, A note on the graph isomorphism counting problem, Inform. Process. Lett., 8 (1979), pp. 131-136. (Cited on p. 341).
94. B. D. McKay and N. C. Wormald, Uniform generation of random regular graphs of moderate degree, J. Algorithms, 11 (1990), pp. 52-67. (Cited on p. 335).
95. I. Miklos, P. L. Erd\H os, and L. Soukup, Towards random uniform sampling of bipartite graphs with given degree sequence, Electron. J. Combin., 20 (2013), art. P16. (Cited on p. 334).
96. I. Miklos and J. Podani, Randomization of presence-Absence matrices: Comments and new algorithms, Ecology, 85 (2004), pp. 86-92. (Cited on pp. 325, 329).
97. R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, and U. Alon, Response to comment on Network motifs: Simple building blocks of complex networks" and "Superfamilies of evolved and designed networks, "" Science, 305 (2004), p. 1107, https://doi.org/10.1126/science.1100519, https://arxiv.org/abs/http://science.sciencemag.org/content/305/5687/1107.4.full.pdf. (Cited on p. 322).
98. R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, S. Shen-Orr, I. Ayzenshtat, M. Sheffer, and U. Alon, Superfamilies of evolved and designed networks, Science, 303 (2004), pp. 1538-1542. (Cited on p. 322).
99. R. Milo, N. Kashtan, S. Itzkovitz, M. E. Newman, and U. Alon, On the Uniform Generation of Random Graphs with Prescribed Degree Sequences, preprint, https://arxiv.org/abs/cond-mat/0312028, 2003. (Cited on pp. 322, 334, 336).
100. R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, Network motifs: Simple building blocks of complex networks, Science, 298 (2002), pp. 824-827. (Cited on p. 322).
101. M. Mitzenmacher, A brief history of generative models for power law and lognormal distributions, Internet Math., 1 (2004), pp. 226-251. (Cited on p. 339).
102. M. Molloy and B. Reed, A critical point for random graphs with a given degree sequence, Random Structures Algorithms, 6 (1995), pp. 161-180. (Cited on pp. 339, 349).
103. J. L. Moreno, Who Shall Survive?, Nervous and Mental Disease Publishing Co., 1934. (Cited on p. 320).
104. J. L. Moreno and H. H. Jennings, Statistics of social configurations, Sociometry, 1938), pp. 342-374. (Cited on p. 320).
105. M. E. Newman, Assortative mixing in networks, Phys. Rev. Lett., 89 (2002), art. 208701. (Cited on pp. 342, 344, 346).
106. M. E. Newman, Mixing patterns in networks, Phys. Rev. E, 67 (2003), art. 026126. (Cited on pp. 325, 326, 328, 334, 342, 344).
107. M. E. Newman, Networks: An Introduction, Oxford University Press, Oxford, 2010. (Cited on p. 347).
108. M. E. Newman and M. Girvan, Finding and evaluating community structure in networks, Phys. Rev. E, 69 (2004), art. 026113. (Cited on pp. 322, 346, 349).
109. M. E. Newman, S. H. Strogatz, and D. J. Watts, Random graphs with arbitrary degree distributions and their applications, Phys. Rev. E, 64 (2001), art. 026118. (Cited on pp. 320, 322, 339).
110. J. Nishimura, Swap Connectivity for Two Graph Spaces between Simple and Pseudo Graphs and Disconnectivity for Triangle Constraints, preprint, https://arxiv.org/abs/1704.01951, 2017. (Cited on pp. 331, 340).
111. J. Nishimura, Uniformly Sampling Graphs with Self-Loops and a Given Degree Sequence, preprint, https://arxiv.org/abs/1701.04888v1, 2017. (Cited on pp. 337, 344).
112. C. Orsini, M. M. Dankulov, A. Jamakovic, P. Mahadevan, A. Vahdat, K. E. Bassler, Z. Toroczkai, M. Boguna, G. Caldarelli, S. Fortunato, et al., Quantifying randomness in real networks, Nature Communications, 6 (2015), p. 8627. (Cited on p. 340).
113. M. Patefield, Algorithm AS 159: An efficient method of generating random rtimes c tables with given row and column totals, Applied Statistics, 30 (1981), pp. 91-97. (Cited on p. 322).
114. T. P. Peixoto, Hierarchical block structures and high-resolution model selection in large networks, Phys. Rev. X, 4 (2014), art. 011047. (Cited on p. 340).
115. J. Petersen, Die theorie der regularen graphs, Acta Math., 15 (1891), pp. 193-220. (Cited on p. 326).
116. E. A. Power, Religious Practice and Social Support in Rural South India, Ph.D. thesis, Stanford University, https://searchworks.stanford.edu/view/11381251, 2015. (Cited on p. 347).
117. A. R. Rao, R. Jana, and S. Bandyopadhyay, A Markov chain Monte Carlo method for generating random (0, 1)-matrices with given marginals, Sankhya Ser. A, 58 (1996), pp. 225- 242. (Cited on pp. 325, 326, 338).
118. J. G. Restrepo, E. Ott, and B. R. Hunt, Onset of synchronization in large networks of coupled oscillators, Phys. Rev. E, 71 (2005), art. 036151. (Cited on p. 320).
119. H. J. Ryser, Combinatorial properties of matrices of zeros and ones, Canad. J. Math., 9 (1957), pp. 371-377. (Cited on p. 326).
120. R. J. Safran, C. R. Neuman, K. J. McGraw, and I. J. Lovette, Dynamic paternity allocation as a function of male plumage color in barn swallows, Science, 309 (2005), pp. 2210-2212. (Cited on p. 344).
121. A. Sinclair, Improved bounds for mixing rates of Markov chains and multicommodity flow, Combin. Probab. Comput., 1 (1992), pp. 351-370. (Cited on p. 334).
122. T. A. Snijders, Markov chain Monte Carlo estimation of exponential random graph models, J. Social Structure, 3 (2002), pp. 1-40. (Cited on p. 340).
123. O. Sporns and R. Kotter, Motifs in brain networks, PLoS Biol., 2 (2004), art. e369. (Cited on p. 322).
124. G. St-Onge, J.-G. Young, E. Laurence, C. Murphy, and L. J. Dube, Susceptible-Infected- Susceptible Dynamics on the Rewired Configuration Model, preprint, https://arxiv.org/abs/1701.01740 2017. (Cited on p. 322).
125. I. Stanton and A. Pinar, Constructing and sampling graphs with a prescribed joint degree distribution, J. Experimental Algorithmics, 17 (2012), pp. 3-5. (Cited on p. 339).
126. L. Stone and A. Roberts, The checkerboard score and species distributions, Oecologia, 85 (1990), pp. 74-79. (Cited on p. 326).
127. D. B. Stouffer, J. Camacho, W. Jiang, and L. A. N. Amaral, Evidence for the existence of a robust pattern of prey selection in food webs, Proc. Roy. Soc. Ser. B, 274 (2007), pp. 1931-1940. (Cited on p. 322).
128. D. Strauss, On a general class of models for interaction, SIAM Rev., 28 (1986), pp. 513-527, https://doi.org/10.1137/1028156. (Cited on p. 340).
129. A. Sundararajan, Local network effects and complex network structure, B. E. J. Theor. Econ., 7 (2007), art. 46. (Cited on p. 322).
130. L. Tabourier, C. Roth, and J.-P. Cointet, Generating constrained random graphs using multiple edge switches, J. Experimental Algorithmics, 16 (2011), pp. 1-7. (Cited on p. 339).
131. R. Taylor, Constrained switchings in graphs, Springer, 1981, in Combinatorial Mathematics VIII, pp, 314-336. (Cited on pp. 326, 330, 337).
132. J. Ugander, L. Backstrom, and J. Kleinberg, Subgraph frequencies: Mapping the empirical and extremal geography of large graph collections, in Proceedings of the 22nd International Conference on World Wide Web, ACM, 2013, pp. 1307-1318. (Cited on p. 340).
133. J. Ugander, B. Karrer, L. Backstrom, and J. Kleinberg, Graph cluster randomization: Network exposure to multiple universes, in Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM, 2013, pp. 329-337. (Cited on p. 346).
134. A. Verbeek and P. M. Kroonenberg, A survey of algorithms for exact distributions of test statistics in rtimes c contingency tables with fixed margins, Comput. Statist. Data Anal., 3 (1985), pp. 159-185. (Cited on pp. 322, 325).
135. N. D. Verhelst, An efficient MCMC algorithm to sample binary matrices with fixed marginals, Psychometrika, 73 (2008), pp. 705-728. (Cited on p. 326).
136. F. Viger and M. Latapy, Efficient and simple generation of random simple connected graphs with prescribed degree sequence, in Computing and Combinatorics, Springer, 2005, pp. 440-449. (Cited on p. 337).
137. D. J. Watts and P. S. Dodds, Influentials, networks, and public opinion formation, J. Consumer Res., 34 (2007), pp. 441-458. (Cited on p. 322).
138. J. B. Wilson, Methods for detecting non-randomness in species co-occurrences: A contribution, Oecologia, 73 (1987), pp. 579-582. (Cited on p. 321).
139. G.-Q. Zhang, Traversability of graph space with given degree sequence under edge rewiring, Electron. Lett., 46 (2010), pp. 351-352. (Cited on p. 330).