Abstract
In a social network, the number of links of a node, or node degree, is often assumed as a proxy for the node’s importance or prominence within the network. It is known that social networks exhibit the (first-order) assortative mixing, i.e. if two nodes are connected, they tend to have similar node degrees, suggesting that people tend to mix with those of comparable prominence. In this paper, we report the second-order assortative mixing in social networks. If two nodes are connected, we measure the degree correlation between their most prominent neighbours, rather than between the two nodes themselves. We observe very strong second-order assortative mixing in social networks, often significantly stronger than the first-order assortative mixing. This suggests that if two people interact in a social network, then the importance of the most prominent person each knows is very likely to be the same. This is also true if we measure the average prominence of neighbours of the two people. This property is weaker or negative in non-social networks. We investigate a number of possible explanations for this property. However, none of them was found to provide an adequate explanation. We therefore conclude that second-order assortative mixing is a new property of social networks.
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References
Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286, 509 (1999)
Barabási, A.L.: Linked: The New Science of Networks. Perseus Publishing (2002)
Boguñá, M., Pastor-Satorras, R., Vespignani, A.: Cut-offs and finite size effects in scale-free networks. Eur. Phys. J. B 38, 205–210 (2004)
Bornholdt, S., Schuster, H.G.: Handbook of Graphs and Networks—From the Genome to the Internet. Wiley-VCH, Weinheim Germany (2002)
Colizza, V., Flammini, A., Maritan, A., Vespignani, A.: Characterization and modeling of protein-protein interaction networks. Physica A 352, 1–27 (2005)
Dorogovtsev, S.N., Goltsev, A.V., Mendes, J.F.F.: Pseudofractal scale-free web. Phys. Rev. E 65, 066122 (2002)
Dorogovtsev, S.N., Mendes, J.F.F.: Evolution of Networks—From Biological Nets to the Internet and WWW. Oxford University Press, Oxford (2003)
Efron, B.: Computers and the theory of statistics thinking the unthinkable. SIAM Rev. 21, 460–480 (1979)
Erdös, P., Rényi, A.: On random graphs. Publ. Math. Debrecen 6, 290 (1959)
Gleiser, P., Danon, L.: Community structure in jazz. Adv. Complex Syst. 6, 565–573 (2003)
Guimera, R., Danon, L., Diaz-Guilera, A., Giralt, F., Arenas, A.: Self-similar community structure in a network of human interactions. Phys. Rev. E 68, 065103 (2003)
Jeong, H., Tombor, B., Albert, R., Oltvai, Z.N., Barabási, A.-L.: The large-scale organization of metabolic networks. Nature 407, 651–654 (2000)
Mahadevan, P., Krioukov, D., Fall, K., Vahdat, A.: Systematic topology analysis and generation using degree correlations. ACM SIGCOMM Comput. Commun. Rev. 36(4), 135–146 (2006)
Maslov, S., Sneppen, K.: Specificity and stability in topology of protein networks. Science 296(5569), 910–913 (2002)
Maslov, S., Sneppenb, K., Zaliznyaka, A.: Detection of topological patterns in complex networks: correlation profile of the internet. Physica A 333, 529–540 (2004)
Newman, M.: Scientific collaboration networks. I. Network construction and fundamental results. Phys. Rev. E 64(016131), 016131 (2001)
Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89(208701), 208701 (2002)
Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the Internet. Phys. Rev. Lett. 87(258701), 258701 (2001)
Pastor-Satorras, R., Vespignani, A.: Evolution and Structure of the Internet—A Statistical Physics Approach. Cambridge University Press, Cambridge (2004)
Ravasz, E., Barabási, A.-L.: Hierarchical organization in complex networks. Phys. Rev. E 67, 026112 (2003)
Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, Cambridge (1994)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440 (1998)
Watts, J.: Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton Univeristy Press, New Jersey, USA (1999)
Zhou, S., Mondragón, R.: Structural constraints in complex networks. New J. Phys. 9(173), 1–11 (2007)
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The authors thank Ole Winther and Sune Lehmann of DTU, Denmark for discussions relating to the clustering coefficient.
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Zhou, S., Cox, I.J., Hansen, L.K. (2017). Second-Order Assortative Mixing in Social Networks. In: Gonçalves, B., Menezes, R., Sinatra, R., Zlatic, V. (eds) Complex Networks VIII. CompleNet 2017. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-54241-6_1
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