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The Perceived Assortativity of Social Networks: Methodological Problems and Solutions

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Trends in Social Network Analysis

Abstract

Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections. Social networks are typically thought to be distinct from other networks in being assortative (possessing positive degree correlations); well-connected individuals associate with other well-connected individuals, and poorly connected individuals associate with each other. We review the evidence for this in the literature and find that, while social networks are more assortative than non-social networks, only when they are built using group-based methods do they tend to be positively assortative. Non-social networks tend to be disassortative. We go on to show that connecting individuals due to shared membership of a group, a commonly used method, biases towards assortativity unless a large enough number of censuses of the network are taken. We present a number of solutions to overcoming this bias by drawing on advances in sociological and biological fields. Adoption of these methods across all fields can greatly enhance our understanding of social networks and networks in general.

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References

  1. Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. U. S. A. 99, 7821–7826 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Krause, J., Croft, D.P., James, R.: Social network theory in the behavioural sciences: potential applications. Behav. Ecol. Sociobiol. 62, 15–27 (2007)

    Article  Google Scholar 

  3. Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the Internet. Phys. Rev. Lett. 87, 258701 (2001)

    Article  Google Scholar 

  4. Nemeth, R.J., Smith, D.A.: International trade and world-system structure: a multiple network analysis. Rev. (Fernand Braudel Cent). 8, 517–560 (2010)

    Google Scholar 

  5. Snyder, D., Kick, E.L.: Structural position in the world system and economic growth, 1955–1970: a multiple-network analysis of transactional interactions. Am. J. Sociol. 84, 1096–1126 (1979)

    Article  Google Scholar 

  6. Kapferer, B.: In: Boissevain, J., Mitchell, J.C. (eds.) Norms and the Manipulation of Relationships in a Work Setting, pp. 83–110. Netw. Anal. Stud. Hum. Interact. Mouton, Paris (1969)

    Google Scholar 

  7. Thurman, B.: In the office: networks and coalitions. Soc. Networks. 2, 47–63 (1979)

    Article  Google Scholar 

  8. Voelkl, B., Kasper, C.: Social structure of primate interaction networks facilitates the emergence of cooperation. Biotechnol. Lett. 5, 462–464 (2009)

    Google Scholar 

  9. Zachary, W.W.: An information flow model for conflict and fission in small groups. J. Anthropol. Res. 473, (1977)

    Google Scholar 

  10. Newman, M.: Assortative mixing in networks. Phys. Rev. Lett. 2, 1–5 (2002)

    Google Scholar 

  11. Hasegawa, T., Konno, K., Nemoto, K.: Robustness of correlated networks against propagating attacks. Eur. Phys. J. B. 85, 1–9 (2012)

    Article  Google Scholar 

  12. Jing, Z., Lin, T., Hong, Y., et al.: The effects of degree correlations on network topologies and robustness. Chin. Phys. 16, 3571–3580 (2007)

    Article  Google Scholar 

  13. Di Bernado, M., Garofalo, F., Sorrentino, F.: Effects of degree correlation on the sychronization of networks of oscillators. Int. J. Bifurcation Chaos. 17, 3499–3506 (2007)

    Article  MATH  Google Scholar 

  14. Gallos, L., Song, C., Makse, H.: Scaling of degree correlations and its influence on diffusion in scale-free networks. Phys. Rev. Lett. 100, 248701 (2008)

    Article  Google Scholar 

  15. Newman, M., Park, J.: Why social networks are different from other types of networks. Phys. Rev. E. 68, 036122 (2003)

    Article  Google Scholar 

  16. Whitney, D., Alderson, D.: Are technological and social networks really different? Unifying Themes Complex Syst. 6, 74–81 (2008)

    Google Scholar 

  17. Estrada, E.: Combinatorial study of degree assortativity in networks. Phys. Rev. E. 84, 047101 (2011)

    Article  Google Scholar 

  18. Newman, M.: Mixing patterns in networks. Phys. Rev. E. 67, 026126 (2003)

    Article  MathSciNet  Google Scholar 

  19. Holme, P., Edling, C.R., Liljeros, F.: Structure and time evolution of an Internet dating community. Soc. Networks. 26, 155–174 (2004)

    Article  Google Scholar 

  20. Mac Carron, P., Kenna, R.: Universal properties of mythological networks. EPL Europhys. Lett. 99, 28002 (2012)

    Article  Google Scholar 

  21. Lusseau, D., Newman, M.: Identifying the role that animals play in their social networks. Proc. R. Soc. B Biol. Sci. 271, S477–S481 (2004)

    Article  Google Scholar 

  22. Hu, H.-B., Wang, X.-F.: Disassortative mixing in online social networks. EPL Europhys. Lett. 86, 18003 (2009)

    Article  Google Scholar 

  23. Araújo, E.B., Moreira, A.A., Furtado, V., et al.: Collaboration networks from a large CV database: dynamics, topology and bonus impact. PLoS One. 9, e90537 (2014)

    Article  Google Scholar 

  24. Furtenbacher, T., Arendás, P., Mellau, G., Császár, A.G.: Simple molecules as complex systems. Sci. Rep. 4, 4654 (2014)

    Article  Google Scholar 

  25. Litvak, N., van der Hofstad, R.: Uncovering disassortativity in large scale-free networks. Phys. Rev. E. 87, 022801 (2013)

    Article  Google Scholar 

  26. Mac Carron P, Kenna R. A quantitative approach to comparative mythology. nestor.coventry.ac.uk (2013)

  27. Palathingal, B., Chirayath, J.: Clustering similar questions in social question answering services. In: Shan, L.P., Cao, T.H. (eds.) The 16th Pacific Asia Conference on Information Systems (PACIS), USA, 13–15 July 2012 (2012)

    Google Scholar 

  28. Thedchanamoorthy, G., Piraveenan, M., Kasthuriratna, D., Senanayake, U.: Node assortativity in complex networks: an alternative approach. Proc. Comput. Sci. 29, 2449–2461 (2014)

    Article  Google Scholar 

  29. Franks, D.W., Ruxton, G.D., James, R.: Sampling animal association networks with the gambit of the group. Behav. Ecol. Sociobiol. 64, 493–503 (2009)

    Article  Google Scholar 

  30. Piraveenan, M., Prokopenko, M., Zomaya, A.: Assortative mixing in directed biological networks. IEEE/ACM Trans. Comput. Biol. Bioinf. 9, 66–78 (2012)

    Article  MATH  Google Scholar 

  31. Ciotti, V., Bianconi, G., Capocci, A., et al.: Degree correlations in signed social networks. Phys. A Stat. Mech. Appl. 422, 25–39 (2015)

    Article  Google Scholar 

  32. Ugander J, Karrer B, Backstrom L, Marlow C. The anatomy of the facebook social graph. arXiv Prepr arXiv. 1–17 (2011)

    Google Scholar 

  33. Manno, T.G.: Social networking in the Columbian ground squirrel, Spermophilus columbianus. Anim. Behav. 75, 1221–1228 (2008)

    Article  Google Scholar 

  34. Wang G, Wang B, Wang T, et al.. Whispers in the dark. In: Proceedings of the 2014 Conference on Internet Measurement Conference—IMC ’14, ACM Press, New York, NY, pp. 137–150 (2014)

    Google Scholar 

  35. Shan, W., Liu, C., Yu, J.: Features of the discipline knowledge network: evidence from China. Technol. Econ. Dev. Econ. 20, 45–64 (2014)

    Article  Google Scholar 

  36. Sosa, S.: Structural architecture of the social network of a non-human primate (Macaca sylvanus): a study of its topology in La Forêt des Singes, Rocamadour. Folia Primatol. (Basel). 85, 154–163 (2014)

    Article  Google Scholar 

  37. Lima A, Rossi L, Musolesi M. Coding Together at Scale: GitHub as a Collaborative Social Network. In: Proceedings of 8th AAAI International Conference on Weblogs and Social Media (ICWSM) (2014)

    Google Scholar 

  38. Wiszniewski, J., Lusseau, D., Möller, L.M.: Female bisexual kinship ties maintain social cohesion in a dolphin network. Anim. Behav. 80, 895–904 (2010)

    Article  Google Scholar 

  39. Farine, D.R., Aplin, L.M., Sheldon, B.C., Hoppitt, W.: Interspecific social networks promote information transmission in wild songbirds. Proc. R. Soc. B. 282, 20142804 (2015)

    Article  Google Scholar 

  40. Illenberger, J., Flötteröd, G.: Estimating network properties from snowball sampled data. Soc. Networks. 34(4), 701–711 (2012)

    Article  Google Scholar 

  41. Kossinets, G.: Effects of missing data in social networks. Soc. Networks. 28, 247–268 (2006)

    Article  Google Scholar 

  42. Whitehead, H.: Analysing Animal Societies: Quantatitive Methods for Vertebrate Social Analysis. The University Chigaco Press, Chicago (2008)

    Book  Google Scholar 

  43. Lusseau, D., Wilson, B., Hammond, P.S., et al.: Quantifying the influence of sociality on population structure in bottlenose dolphins. J. Anim. Ecol. 75, 14–24 (2006)

    Article  Google Scholar 

  44. Croft, D.P., James, R., Thomas, P.O.R., et al.: Social structure and co-operative interactions in a wild population of guppies (Poecilia reticulata). Behav. Ecol. Sociobiol. 59, 644–650 (2006)

    Article  Google Scholar 

  45. Tsouchnika, M., Argyrakis, P.: Network of participants in European research: accepted versus rejected proposals. Eur. Phys. J. B. 87, 292 (2014)

    Article  Google Scholar 

  46. Mena-Chalco, J.P., Digiampietri, L.A., Lopes, F.M., Cesar, R.M.: Brazilian bibliometric coauthorship networks. J. Assoc. Inf. Sci. Technol. 65, 1424–1445 (2014)

    Article  Google Scholar 

  47. Mohman, Y.T., Wang, A., Chen, H.: Statistical analysis of the airport network of Pakistan. Pramana. 85, 173–183 (2015)

    Article  Google Scholar 

  48. Im, K., Paldino, M.J., Poduri, A., et al.: Altered white matter connectivity and network organization in polymicrogyria revealed by individual gyral topology-based analysis. Neuroimage. 86, 182–193 (2014)

    Article  Google Scholar 

  49. Lee, I., Kim, E., Marcotte, E.M.: Modes of interaction between individuals dominate the topologies of real world networks. PLoS One. 10, e0121248 (2015)

    Article  Google Scholar 

  50. Spitz, A., Horvát, E.-Á.: Measuring long-term impact based on network centrality: unraveling cinematic citations. PLoS One. 9, e108857 (2014)

    Article  Google Scholar 

  51. Aguirre-von-Wobeser, E., Soberón-Chávez, G., Eguiarte, L.E., et al.: Two-role model of an interaction network of free-living γ-proteobacteria from an oligotrophic environment. Environ. Microbiol. 16, 1366–1377 (2014)

    Article  Google Scholar 

  52. Jiang, B., Duan, Y., Lu, F., et al.: Topological structure of urban street networks from the perspective of degree correlations. Environ. Plan. B Plan. Des. 41, 813–828 (2014)

    Article  Google Scholar 

  53. Mussmann S, Moore J, Pfeiffer JJ, Neville J. Assortativity in Chung Lu random graph models. In: Proceedings of the 8th Workshop on Social Network Mining and Analysis—SNAKDD’14, ACM Press, New York, NY, pp. 1–8 (2014)

    Google Scholar 

  54. Yang R.. Modifying network assortativity with degree preservation. In: 29th International Conference on Computers and Their Applications. CATA 2014, International Society for Computers and Their Applications, Winona, MN, pp. 35–40 (2014)

    Google Scholar 

  55. Croft, D.P., James, R., Krause, J.: Exploring Animal Social Networks. Princeton University Press, Oxford (2008)

    Book  Google Scholar 

  56. Gleiser, P.M., Danon, L.: Community structure in jazz. Adv. Complex Syst. 06, 565–573 (2003)

    Article  Google Scholar 

  57. Newman, M.E.: The structure of scientific collaboration networks. Proc. Natl. Acad. Sci. U. S. A. 98, 404–409 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  58. Watts, D.J., Strogatz, S.H.: Collective dynamics of “small-world” networks. Nature. 393, 440–442 (1998)

    Article  Google Scholar 

  59. Aplin, L.M., Farine, D.R., Morand-Ferron, J., Sheldon, B.C.: Social networks predict patch discovery in a wild population of songbirds. Proc. Biol. Sci. 279, 4199–4205 (2012)

    Article  Google Scholar 

  60. Lusseau, D.: The emergent properties of a dolphin social network. Proc. Biol. Sci. 270, 186–188 (2003)

    Article  Google Scholar 

  61. Mourier, J., Vercelloni, J., Planes, S.: Evidence of social communities in a spatially structured network of a free-ranging shark species. Anim. Behav. 83, 389–401 (2012)

    Article  Google Scholar 

  62. Newman, M.: Coauthorship networks and patterns of scientific collaboration. Proc. Natl. Acad. Sci. U. S. A. 101, 5200–5205 (2004)

    Article  Google Scholar 

  63. Whitehead, H., Dufault, S.: Techniques for analyzing vertebrate social structure using identified individuals: review and recommendations. Adv. Study Behav. 28, 33–73 (1999)

    Google Scholar 

  64. R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing. Vienna (2013)

    Google Scholar 

  65. Perreault, C.: A note on reconstructing animal social networks from independent small-group observations. Anim. Behav. 80, 551–562 (2010)

    Article  Google Scholar 

  66. Bejder, L., Fletcher, D., Bräger, S.: A method for testing association patterns of social animals. Anim. Behav. 56, 719–725 (1998)

    Article  Google Scholar 

  67. Sundaresan, S.R., Fischhoff, I.R., Dushoff, J.: Avoiding spurious findings of nonrandom social structure in association data. Anim. Behav. 77, 1381–1385 (2009)

    Article  Google Scholar 

  68. Krause, S., Mattner, L., James, R., et al.: Social network analysis and valid Markov chain Monte Carlo tests of null models. Behav. Ecol. Sociobiol. 63, 1089–1096 (2009)

    Article  Google Scholar 

  69. Aplin, L.M., Farine, D.R., Morand-Ferron, J., et al.: Individual personalities predict social behaviour in wild networks of great tits (Parus major). Ecol. Lett. 16, 1365–1372 (2013)

    Article  Google Scholar 

  70. Wey, T.W., Burger, J.R., Ebensperger, L.A., Hayes, L.D.: Reproductive correlates of social network variation in plurally breeding degus (Octodon degus). Anim. Behav. 85, 1407–1414 (2013)

    Article  Google Scholar 

  71. Krackhardt, D.: Predicting with networks: nonparametric multiple regression analysis of dyadic data. Soc. Networks. 10, 359–381 (1988)

    Article  MathSciNet  Google Scholar 

  72. Hanhijarvi S, Garriga GC, Puolmakai K. Randomization techniques for graphs. In: Proceedings of the 9th SIAM International Conference on Data Mining (SDM ‘09), pp. 780–791 (2009)

    Google Scholar 

  73. La Fond T, Neville J. Randomization tests for distinguishing social influence and homophily effects. In: Proceedings of the 19th international conference on World wide web—WWW ‘10, ACM Press, New York, NY, p. 601 (2010)

    Google Scholar 

  74. Farine, D.R.: Measuring phenotypic assortment in animal social networks: weighted associations are more robust than binary edges. Anim. Behav. 89, 141–153 (2014)

    Article  Google Scholar 

  75. Granovetter, M.: The strength of weak ties. Am. J. Sociol. 78, 1360–1380 (1973)

    Article  Google Scholar 

  76. Garton, L., Haythornthwaite, C., Wellman, B.: Studying online social networks. J. Comput. Mediated Commun. (2006). doi:10.1111/j.1083-6101.1997.tb00062.x

    Google Scholar 

  77. Rowe R, Creamer G, Hershkop S, Stolfo SJ. Automated social hierarchy detection through email network analysis. In: Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 workshop on Web mining and social network analysis–WebKDD/SNA-KDD ‘07, ACM Press, New York, NY, pp. 109–117 (2007)

    Google Scholar 

  78. Opsahl, T., Agneessens, F., Skvoretz, J.: Node centrality in weighted networks: Generalizing degree and shortest paths. Soc. Networks. 32, 245–251 (2010)

    Article  Google Scholar 

  79. Noldus, R., Van Mieghem, P.: Assortativity in complex networks. J. Complex Networks. 3, 507–542 (2015)

    Article  MathSciNet  Google Scholar 

  80. Iturria-Medina, Y., Canales-Rodríguez, E.J., Melie-García, L., et al.: Characterizing brain anatomical connections using diffusion weighted MRI and graph theory. Neuroimage. 36, 645–660 (2007)

    Article  Google Scholar 

  81. Krivitsky, P.: Exponential-family random graph models for valued networks. Electron. J. Stat. 6, 1100–1128 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  82. Krivitsky P., ergm.count: Fit, simulate and diagnose exponential-family models for networks with count edges. The Statnet Project (2015). http://www.statnet.org. R package version 3.2.2. http://CRAN.R-project.org/package=ergm.count

  83. De Choudhury M, Mason W. Inferring relevant social networks from interpersonal communication. In: Proceedings of the 19th International Conference on World wide web, pp. 301–310 (2010)

    Google Scholar 

  84. Expert, P., Evans, T.S., Blondel, V.D., Lambiotte, R.: Uncovering space-independent communities in spatial networks. Proc. Natl. Acad. Sci. U. S. A. 7663–7668 (2011)

    Google Scholar 

  85. Peruani, F., Tabourier, L.: Directedness of information flow in mobile phone communication networks. PLoS One. 6, e28860 (2011)

    Article  Google Scholar 

  86. Wey, T.W., Blumstein, D.T.: Social cohesion in yellow-bellied marmots is established through age and kin structuring. Anim. Behav. 79, 1343–1352 (2010)

    Article  Google Scholar 

  87. Krause, J., Krause, S., Arlinghaus, R., et al.: Reality mining of animal social systems. Trends Ecol. Evol. 28, 1–11 (2013)

    Article  Google Scholar 

  88. Eagle, N., Pentland, A.: Reality mining: sensing complex social systems. Pers. Ubiquitous Comput. 10, 255–268 (2005)

    Article  Google Scholar 

  89. Böhm, M., Hutchings, M.R., White, P.C.L.: Contact networks in a wildlife-livestock host community: identifying high-risk individuals in the transmission of bovine TB among badgers and cattle. PLoS One. 4, e5016 (2009)

    Article  Google Scholar 

  90. Hamede, R.K., Bashford, J., McCallum, H., Jones, M.: Contact networks in a wild Tasmanian devil (Sarcophilus harrisii) population: using social network analysis to reveal seasonal variability in social behaviour and its implications for transmission of devil facial tumour disease. Ecol. Lett. 12, 1147–1157 (2009)

    Article  Google Scholar 

  91. Rutz, C., Burns, Z.T., James, R., et al.: Automated mapping of social networks in wild birds. Curr. Biol. 22, R669–R671 (2012)

    Article  Google Scholar 

  92. Boyland, N.K., James, R., Mlynski, D.T., et al.: Spatial proximity loggers for recording animal social networks: consequences of inter-logger variation in performance. Behav. Ecol. Sociobiol. 67, 1877–1890 (2013)

    Article  Google Scholar 

  93. Drewe, J.A., Weber, N., Carter, S.P., et al.: Performance of proximity loggers in recording intra- and inter-species interactions: a laboratory and field-based validation study. PLoS One. 7, e39068 (2012)

    Article  Google Scholar 

  94. Zhou, S., Mondragón, R.: The rich-club phenomenon in the Internet topology. IEEE Commun. Lett. 1–3 (2004)

    Google Scholar 

  95. Colizza, V., Flammini, A., Serrano, M.A., Vespignani, A.: Detecting rich-club ordering in complex networks. Nat. Phys. 2, 1–18 (2006)

    Article  Google Scholar 

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Fisher, D.N., Silk, M.J., Franks, D.W. (2017). The Perceived Assortativity of Social Networks: Methodological Problems and Solutions. In: Missaoui, R., Abdessalem, T., Latapy, M. (eds) Trends in Social Network Analysis. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-53420-6_1

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