Advertisement

Automatic Discovery of Families of Network Generative Processes

  • Telmo MenezesEmail author
  • Camille Roth
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution processes which will form the basis of the model to be developed. Machine learning techniques have lately been introduced to assist the automatic discovery of generative models. These approaches may more broadly be described as “symbolic regression,” where fundamental network dynamic functions, rather than just parameters, are evolved through genetic programming. This chapter first aims at reviewing the principles, efforts, and the emerging literature in this direction, which is very much aligned with the idea of creating artificial scientists. Our contribution then aims more specifically at building upon an approach recently developed by us (Menezes and Roth, Sci Rep 4:6284, 2014) in order to demonstrate the existence of families of networks that may be described by similar generative processes. In other words, symbolic regression may be used to group networks according to their inferred genotype (in terms of generative processes) rather than their observed phenotype (in terms of statistical/topological features). Our empirical case is based on an original dataset of 238 anonymized ego-centered networks of Facebook friends, further yielding insights on the formation of sociability networks.

Keywords

Network generators Social networks Machine learning Genetic programming Network families Symbolic regression 

Notes

Acknowledgements

We are grateful to the members of our “Algopol” project team (ANR-12-CORD-0018) who organized most of the Facebook survey, including Irène Bastard, Dominique Cardon, Raphaël Charbey, Guilhem Fouetillou, Christophe Prieur, and Stéphane Raux. We further acknowledge interesting discussions with Jean-Philippe Cointet and David Fourquet regarding generative families, as well as the constructive feedback of our anonymous reviewers. This paper has been partially supported by the “Algodiv” grant (ANR-15-CE38-0001) funded by the ANR (French National Agency of Research).

References

  1. 1.
    Acar, E., Dunlavy, D.M., Kolda, T.G.: Link prediction on evolving data using matrix and tensor factorizations. In: Proceedings of ICDMW’09, IEEE International Conference on Data Mining Workshops, pp. 262–269. IEEE, Piscataway (2009)Google Scholar
  2. 2.
    Adar, E., Zhang, L., Adamic, L.A., Lukose, R.M.: Implicit structure and the dynamics of blogspace. In: Workshop on the Weblogging Ecosystem, 13th International World Wide Web Conference (2004)Google Scholar
  3. 3.
    Adolphs, R.: The unsolved problems of neuroscience. Trends Cogn. Sci. 19(4), 173–175 (2015)CrossRefGoogle Scholar
  4. 4.
    Aiello, W., Chung, F., Lu, L.: A random graph model for massive graphs. In: Proceedings ACM 32nd Annual ACM Symposium on Theory of Computing, pp. 171–180. ACM, New York (2000)Google Scholar
  5. 5.
    Al Hasan, M., Chaoji, V., Salem, S., Zaki, M.: Link prediction using supervised learning. In: SDM: Workshop on Link Analysis, Counter-terrorism and Security (2006)Google Scholar
  6. 6.
    Al Hasan, M., Zaki, M.J.: A survey of link prediction in social networks. In: Aggarwal, C.C. (ed) Social Network Data Analytics, pp. 243–275. Springer, Boston (2011)CrossRefGoogle Scholar
  7. 7.
    Amblard, F., Bouadjio-Boulic, A., Gutiérrez, C.S., Gaudou, B.: Which models are used in social simulation to generate social networks? A review of 17 years of publications in JASSS. In: Winter Simulation Conference (WSC), 2015, pp 4021–4032. IEEE, Piscataway (2015)Google Scholar
  8. 8.
    Anderson, C.J., Wasserman, S., Faust, K.: Building stochastic blockmodels. Soc. Net. 14, 137–161 (1992)CrossRefGoogle Scholar
  9. 9.
    Anderson, C.J., Wasserman, S., Crouch, B.: A p* primer: logit models for social networks. Soc. Net. 21, 37–66 (1999)CrossRefGoogle Scholar
  10. 10.
    Arora, V., Ventresca, M.: A multi-objective optimization approach for generating complex networks. In: Companion Proceedings of GECCO’16 18th Genetic and Evolutionary Computation Conference, pp. 15–16. ACM, New York (2016)Google Scholar
  11. 11.
    Arora, V., Ventresca, M.: Action-based modeling of complex networks. Sci. Rep. 7, 6673 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    Avena-Koenigsberger, A., Goñi, J., Solé, R., Sporns, O.: Network morphospace. J. R. Soc. Interface 12(103), 20140881 (2015)CrossRefGoogle Scholar
  13. 13.
    Bailey, A., Ventresca, M., Ombuki-Berman, B.: Automatic generation of graph models for complex networks by genetic programming. In: Proceedings GECCO’12 14th ACM Annual Conference on Genetic and Evolutionary Computation, pp. 711–718. ACM, New York (2012)Google Scholar
  14. 14.
    Bailey, A., Ventresca, M., Ombuki-Berman, B.: Genetic programming for the automatic inference of graph models for complex networks. IEEE Trans. Evol. Comput. 18(3), 405–419 (2014)CrossRefGoogle Scholar
  15. 15.
    Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Barabási, A.L., Jeong, H., Ravasz, E., Neda, Z., Vicsek, T., Schubert, A.: Evolution of the social network of scientific collaborations. Physica A 311, 590–614 (2002)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Berger, N., Borgs, C., Chayes, J.T., D’Souza, R.M., Kleinberg, R.D.: Competition-induced preferential attachment. In: Proceedings of the 31st International Colloquium on Automata, Languages and Programming, pp. 208–221 (2004)Google Scholar
  18. 18.
    Betzel, R.F., Avena-Koenigsberger, A., Goñi, J., He, Y., De Reus, M.A., Griffa, A., Vértes, P.E., Mišic, B., Thiran, J.P., Hagmann, P., et al.: Generative models of the human connectome. Neuroimage 124, 1054–1064 (2016)CrossRefGoogle Scholar
  19. 19.
    Bliss, C.A., Frank, M.R., Danforth, C.M., Dodds, P.S.: An evolutionary algorithm approach to link prediction in dynamic social networks. J. Comput. Sci. 5(5), 750–764 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Block, P., Stadtfeld, C., Snijders, T.A.B.: Forms of dependence: comparing SAOMs and ERGMs from basic principles. Sociol. Methods Res. 48(1) (2016)Google Scholar
  21. 21.
    Block, P., Koskinen, J., Hollway, J., Steglich, C., Stadtfeld, C.: Change we can believe in: comparing longitudinal network models on consistency, interpretability and predictive power. Soc. Net. 52, 180–191 (2018)CrossRefGoogle Scholar
  22. 22.
    Borg, I., Groenen, P.J.F.: Modern Multidimensional Scaling: Theory and Applications. Springer Science & Business Media, New York (2005)zbMATHGoogle Scholar
  23. 23.
    Brennecke, J., Rank, O.N.: The interplay between formal project memberships and informal advice seeking in knowledge-intensive firms: a multilevel network approach. Soc. Net. 44, 307–318 (2016)CrossRefGoogle Scholar
  24. 24.
    Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30(1–7), 107–117 (1998)CrossRefGoogle Scholar
  25. 25.
    Caldarelli, G., Capocci, A., De Los Rios, P., Munoz, M.A.: Scale-free networks from varying vertex intrinsic fitness. Phys. Rev. Lett. 89(25), 258702 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    Charbey, R., Prieur, C.: Graphlet-based characterization of many ego networks. hal-01764253v2 (2018)Google Scholar
  27. 27.
    Clauset, A., Moore, C., Newman, M.E.J.: Hierarchical structure and the prediction of missing links in networks. Nature 453, 98–101 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Cointet, J.P., Roth, C.: Local networks, local topics: structural and semantic proximity in blogspace. In: Proceedings 4th ICWSM AAAI International Conference on Weblogs and Social Media, pp. 223–226. AAAI, Menlo Park (2010)Google Scholar
  29. 29.
    Colizza, V., Banavar, J.R., Maritan, A., Rinaldo, A.: Network structures from selection principles. Phys. Rev. Lett. 92(19), 198701 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    Corominas-Murtra, B., Goñi, J., Solé, R.V., Rodríguez-Caso, C.: On the origins of hierarchy in complex networks. PNAS 110(33), 13316–13321 (2013)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    da Fontoura Costa, L., Rodrigues, F.A., Travieso, G., Villas Boas, P.R.: Characterization of complex networks: a survey of measurements. Adv. Phys. 56(1), 167–242 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    de Solla Price, D.J.: A general theory of bibliometric and other cumulative advantage processes. J. Am. Soc. Inf. Sci. 27(5–6), 292–306 (1976)CrossRefGoogle Scholar
  33. 33.
    Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of networks with aging of sites. Phys. Rev. E 62, 1842–1845 (2000)ADSCrossRefGoogle Scholar
  34. 34.
    D’Souza, R.M., Borgs, C., Chayes, J.T., Berger, N., Kleinberg, J.T.: Emergence of tempered preferential attachment from optimization. PNAS 104, 6112–6117 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    Estrada, E.: Topological structural classes of complex networks. Phys. Rev. E 75(1), 016103 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    Fabrikant, A., Koutsoupias, E., Papadimitriou, C.H.: Heuristically optimized trade-offs: a new paradigm for power laws in the internet. In: ICALP ’02: Proceedings of the 29th International Colloquium on Automata, Languages and Programming, London, UK, pp. 110–122, Springer, Berlin (2002). ISBN 3-540-43864-5Google Scholar
  37. 37.
    Fienberg, S.E., Meyer, M.M., Wasserman, S.S.: Statistical analysis of multiple sociometric relations. J. Am. Stat. Assoc. 80(389), 51–67 (1985)CrossRefGoogle Scholar
  38. 38.
    Fortunato, S., Flammini, A., Menczer, F.: Scale-free network growth by ranking. Phys. Rev. Lett. 96, 218701 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    Frank, O., Strauss, D.: Markov graphs. J. Am. Stat. Assoc. 81(395), 832–842 (1986)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Gilbert, N.: A simulation of the structure of academic science. Sociol. Res. Online 2(2), 1–15 (1997)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Gkantsidis, C., Mihail, M., Zegura, E.W.: The markov chain simulation method for generating connected power law random graphs. In: Proceedings 5th Workshop on Algorithm Engineering and Experiments (ALENEX) (2003)Google Scholar
  42. 42.
    Goetz, M., Leskovec, J., McGlohon, M., Faloutsos, C.: Modeling blog dynamics. In: ICWSM 2009 Proceedings 3rd International AAAI Conference on Weblogs and Social Media, AAAI, Menlo Park (2009)Google Scholar
  43. 43.
    Goñi, J., Avena-Koenigsberger, A., de Mendizabal, N.V., van den Heuvel, M.P., Betzel, R.F., Sporns, O.: Exploring the morphospace of communication efficiency in complex networks. PLoS One 8(3), e58070 (2013)ADSCrossRefGoogle Scholar
  44. 44.
    Guimerà, R., Amaral, L.A.N.: Modeling the world-wide airport network. Eur. Phys. J. B 38, 381–385 (2004)ADSCrossRefGoogle Scholar
  45. 45.
    Guimerà, R., Sales-Pardo, M.: Missing and spurious interactions and the reconstruction of complex networks. PNAS 106(52), 22073–22078 (2009)ADSCrossRefGoogle Scholar
  46. 46.
    Guimera, R., Uzzi, B., Spiro, J., Nunes Amaral, L.A.: Team assembly mechanisms determine collaboration network structure and team performance. Science 308, 697–702 (2005)ADSCrossRefGoogle Scholar
  47. 47.
    Guimerà, R., Sales-Pardo, M., Amaral, L.A.N.: Classes of complex networks defined by role-to-role connectivity profiles. Nat. Phys. 3, 63–69 (2007)ADSCrossRefGoogle Scholar
  48. 48.
    Hanneke, S., Fu, W., Xing, E.P.: Discrete temporal models of social networks. Elect. J. Stat. 4, 585–605 (2010)MathSciNetCrossRefGoogle Scholar
  49. 49.
    Harrison, K.R., Ventresca, M., Ombuki-Berman, B.M.: Investigating fitness measures for the automatic construction of graph models. In: Mora, A., Squillero, G. (eds) EvoApplications 2015 Applications of Evolutionary Computation. LNCS, vol. 9028, pp. 189–200. Springer, Berlin (2015)Google Scholar
  50. 50.
    Harrison, K.R., Ventresca, M., Ombuki-Berman, B.M.: A meta-analysis of centrality measures for comparing and generating complex network models. J. Comput. Sci. 17, 205–215 (2016)CrossRefGoogle Scholar
  51. 51.
    Holland, P., Leinhardt, S.: A dynamic model for social networks. J. Math. Soc. 5, 5–20 (1977)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Holland, P.W., Leinhardt, S.: An exponential family of probability distributions for directed graphs. J. Am. Stat. Assoc. 76(373), 33–65 (1981)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Holland, P.W., Laskey, K.B., Leinhardt, S.: Stochastic blockmodels: first steps. Soc. Net. 5, 109–137 (1983)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Holme, P., Kim, B.J.: Growing scale-free networks with tunable clustering. Phys. Rev. E 65, 026107 (2002)ADSCrossRefGoogle Scholar
  55. 55.
    Hornby, G., Globus, A., Linden, D., Lohn, J.: Automated antenna design with evolutionary algorithms. In: Space 2006, AIAA SPACE Forum, pp. 1–8 (2006)Google Scholar
  56. 56.
    Jeong, H., Néda, Z., Barabási, A.L.: Measuring preferential attachment for evolving networks. Europhys. Lett. 61(4), 567–572 (2003)ADSCrossRefGoogle Scholar
  57. 57.
    Karrer, B., Newman, M.E.J.: Random graphs containing arbitrary distributions of subgraphs. Phys. Rev. E 82, 066118 (2010)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    Koskinen, J.H., Snijders, T.A.B.: Bayesian inference for dynamic social network data. J. Statist. Plann. Inference 137(12), 3930–3938 (2007)MathSciNetCrossRefGoogle Scholar
  59. 59.
    Kossinets, G., Watts, D.J.: Empirical analysis of an evolving social network. Science 311, 88–90 (2006)ADSMathSciNetCrossRefGoogle Scholar
  60. 60.
    Kumar, R., Raghavan, P., Rajagopalan, S., Sivakumar, D., Tomkins, A., Upfal, E.: Stochastic models for the web graph. In: IEEE 41st Annual Symposium on Foundations of Computer Science (FOCS), p. 57. IEEE Computer Society, Washington (2000)Google Scholar
  61. 61.
    Leskovec, J., Horvitz, E.: Planetary-scale views on a large instant-messaging network. In: Proceedings WWW’08 17th International Conference World Wide Web, pp. 915–924. ACM, New York (2008)Google Scholar
  62. 62.
    Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 177–187. ACM, New York (2005)Google Scholar
  63. 63.
    Leskovec, J., Chakrabarti, D., Kleinberg, J., Faloutsos, C., Ghahramani, Z.: Kronecker graphs: an approach to modeling networks. J. Mach. Learn. Res. 11, 985–1042 (2010)MathSciNetzbMATHGoogle Scholar
  64. 64.
    Lewis, K., Gonzalez, M., Kaufman, J.: Social selection and peer influence in an online social network. PNAS 109(1), 68–72 (2012)ADSCrossRefGoogle Scholar
  65. 65.
    Liben-Nowell, D., Kleinberg, J.: The link prediction problem for social networks. In: CIKM ’03: Proceedings of the 12th International Conference on Information and Knowledge Management, pp. 556–559. ACM Press, New York (2003)Google Scholar
  66. 66.
    Ling, H., Okada, K.: An efficient earth mover’s distance algorithm for robust histogram comparison. IEEE Trans. Pattern Anal. Mach. Intell. 29(5), 840–853 (2007)CrossRefGoogle Scholar
  67. 67.
    Lü, L., Zhou, T.: Link prediction in complex networks: a survey. Physica A 390, 1150–1170 (2011)ADSCrossRefGoogle Scholar
  68. 68.
    Mahadevan, P., Krioukov, D., Fall, K., Vahdat, A.: Systematic topology analysis and generation using degree correlations. In: Proceedings SIGCOMM’06 ACM International Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications, pp. 135–146. ACM, New York (2006)Google Scholar
  69. 69.
    Märtens, M., Kuipers, F., Mieghem, P.V.: Symbolic regression on network properties. In: McDermott, J., Castelli, M., Sekanina, L., Haasdijk, E., García-Sánchez, P., (edts.) Proceedings EuroGP 2017 Genetic Programming. LNCS, vol. 10196. Springer, Berlin (2017)Google Scholar
  70. 70.
    Menczer, F.: Evolution of document networks. PNAS 101(S1), 5261–5265 (2004)ADSCrossRefGoogle Scholar
  71. 71.
    Menezes, T.: Evolutionary modeling of a blog network. In: Proceedings CEC’2011 IEEE Congress on Evolutionary Computation, pp. 909–916. IEEE, Piscataway (2011)Google Scholar
  72. 72.
    Menezes, T., Roth, C.: Automatic discovery of agent-based models: an application to social anthropology. Advances in Complex Systems 16(7), 1350027 (2013)MathSciNetCrossRefGoogle Scholar
  73. 73.
    Menezes, T., Roth, C.: Symbolic regression of generative network models. Sci. Rep. 4, 6284 (2014)ADSCrossRefGoogle Scholar
  74. 74.
    Menezes, T., Gargiulo, F., Roth, C., Hamberger, K.: New simulation techniques in kinship network analysis. Struct. Dynam. e-J. Anthropol. Related Sci. 9(2), 180–209 (2016)Google Scholar
  75. 75.
    Milo, R., Itzkovitz, S., Kashtan, N., Levitt, R., Shen-Orr, S., Ayzenshtat, I., Sheffer, M., Alon, U.: Superfamilies of evolved and designed networks. Science 303(5663), 1538–1542 (2004)ADSCrossRefGoogle Scholar
  76. 76.
    Ming, L., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  77. 77.
    Newman, M.E.J., Strogatz, S., Watts, D.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64(026118) (2001)Google Scholar
  78. 78.
    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs models of social networks. PNAS 99, 2566–2572 (2002)ADSCrossRefGoogle Scholar
  79. 79.
    Onnela, J.P., Fenn, D.J., Reid, S., Porter, M.A., Mucha, P.J., Fricker, M.D., Jones, N.S.: Taxonomies of networks from community structure. Phys. Rev. E 86, 036104 (2012)ADSCrossRefGoogle Scholar
  80. 80.
    Papadopoulos, F., Kitsak, M., Serrano, M.Á., Boguná, M., Krioukov, D.: Popularity versus similarity in growing networks. Nature 489, 537–540 (2012)ADSCrossRefGoogle Scholar
  81. 81.
    Perra, N., Gonçalves, B., Pastor-Satorras, R., Vespignani, A.: Activity driven modeling of time varying networks. Sci. Rep. 2(469) (2012)Google Scholar
  82. 82.
    Powell, W.W., White, D.R., Koput, K.W., Owen-Smith, J.: Network dynamics and field evolution: the growth of interorganizational collaboration in the life sciences. Am. J. Sociol. 110(4), 1132–1205 (2005)CrossRefGoogle Scholar
  83. 83.
    Pujol, J.M., Flache, A., Delgado, J., Sangüesa, R.: How can social networks ever become complex? Modelling the emergence of complex networks from local social exchanges. J. Art. Soc. Soc. Sim. 8(4) (2005)Google Scholar
  84. 84.
    Rao, A., Jana, R., Bandyopadhyay, S.: A markov chain Monte Carlo method for generating random (0,1)-matrices with given marginals. Sankhya: The Indian J. Stat. A 58, 225–242 (1996)MathSciNetzbMATHGoogle Scholar
  85. 85.
    Robins, G., Pattison, P., Kalish, Y., Lusher, D.: An introduction to Exponential Random Graph (p*) Models for social networks. Soc. Net. 29(2), 173–191 (2007)CrossRefGoogle Scholar
  86. 86.
    Roth, C.: Generalized preferential attachment: towards realistic socio-semantic network models. In: ISWC 4th International Semantic Web Conference, Workshop on Semantic Network Analysis, CEUR-WS Series (ISSN 1613-0073), vol. 171, pp. 29–42. Galway, Ireland (2005)Google Scholar
  87. 87.
    Roth, C.: Co-evolution in epistemic networks – reconstructing social complex systems. Struct. Dynam. e-J. Anthropol. Related Sci. 1(3). Article 2 (2006)Google Scholar
  88. 88.
    Rowe, M., Stankovic, M., Alani, H.: Who will follow whom? Exploiting semantics for link prediction in attention-information networks. In: Cudré-Mauroux, P., Heflin, J., Sirin, E., Tudorache, T., Euzenat, J., Hauswirth, M., Parreira, J.X., Hendler, J., Schreiber, G., Bernstein, A., Blomqvist, E. (eds) Proceedings ISWC’12 11th International Semantic Web Conference Part I. LNCS, vol. 7649, pp. 476–491. Springer, Berlin (2012)Google Scholar
  89. 89.
    Sarkar, P., Chakrabarti, D., Jordan, M.: Nonparametric link prediction in large scale dynamic networks. Electron. J. Stat. 8(2), 2022–2065 (2014)MathSciNetCrossRefGoogle Scholar
  90. 90.
    Schmidt, M., Lipson, H.: Distilling free-form natural laws from experimental data. Science 324(5923), 81–85 (2009)ADSCrossRefGoogle Scholar
  91. 91.
    Snijders, T.A.B.: The statistical evaluation of social networks dynamics. Sociol. Methodol. 31, 361–395 (2001)CrossRefGoogle Scholar
  92. 92.
    Snijders, T.A.B., Steglich, C., Schweinberger, M.: Modeling the co-evolution of networks and behavior. In: van Montfort, K., Oud, H., Satorra, A. (eds) Longitudinal Models in the Behavioral and Related Sciences, pp. 41–71. Lawrence Erlbaum, Mahwah (2007)Google Scholar
  93. 93.
    Tabourier, L., Roth, C., Cointet, J.P.: Generating constrained random graphs using multiple edge switches. ACM J. Exp. Algorithmics 16(1.7) (2011)Google Scholar
  94. 94.
    Vázquez, A.: Growing network with local rules: preferential attachment, clustering hierarchy, and degree correlations. Phys. Rev. E 67, 056104 (2003)ADSCrossRefGoogle Scholar
  95. 95.
    Wang, P., Robins, G., Pattison, P., Lazega, E.: Exponential Random Graph Models for multilevel networks. Soc. Net. 35, 96–115 (2013)CrossRefGoogle Scholar
  96. 96.
    Wasserman, S.: Analyzing social networks as stochastic processes. J. Am. Stat. Assoc. 75(370), 280–294 (1980)CrossRefGoogle Scholar
  97. 97.
    Wasserman, S., Pattison, P.: Logit models and logistic regressions for social networks: I. an introduction to markov graphs and p*. Psychometrika 61(3), 401–425 (1996)Google Scholar
  98. 98.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998)ADSCrossRefGoogle Scholar
  99. 99.
    Yang, Y., Lichtenwalter, R.N., Chawla, N.V.: Evaluating link prediction methods. Knowl. Inf. Syst. 45(3), 751–782 (2015)CrossRefGoogle Scholar
  100. 100.
    Yaveroglu, Ö.N., Malod-Dognin, N., Devis, D., Levnajic, Z., Janjic, V., Karapandza, R., Stojmirovic, A., Przulj, N.: Revealing the hidden language of complex networks. Sci. Rep. 4(4547) (2014)Google Scholar
  101. 101.
    Yook, S.H., Jeong, H., Barabási, A.L.: Modeling the internet’s large-scale topology. PNAS 99(21), 13382–13386 (2002)ADSCrossRefGoogle Scholar
  102. 102.
    Yuan, G., Murukannaiah, P.K., Zhang, Z., Singh, M.P.: Exploiting sentiment homophily for link prediction. In: Proceedings RecSys ’14 8th ACM Conference on Recommender Systems, pp. 17–24. ACM, New York (2014)Google Scholar
  103. 103.
    Zheleva, E., Sharara, H., Getoor, L.: Co-evolution of social and affiliation networks. In: Proceedings ACM SIGKDD’09 15th International Conference on Knowledge Discovery and Data Mining, pp. 1007–1015. ACM, New York (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Centre Marc Bloch (UMIFRE CNRS/MAE)Computational Social Science TeamBerlinGermany
  2. 2.CNRSParisFrance

Personalised recommendations