Advertisement

Uncovering the nucleus of a massive reciprocal network

  • Braulio Dumba
  • Zhi-Li Zhang
Article
Part of the following topical collections:
  1. Special Issue on Social Computing and Big Data Applications

Abstract

Google+ is a directed online social network where nodes have either reciprocal (bidirectional) edges or parasocial (one-way) edges. As reciprocal edges play an important role in the structural properties, formation and evolution of online social networks, we study the core structure of the subgraph formed by them, referred to as the reciprocal network of Google+ — in a sense, a reciprocal network can be viewed as the stable “skeleton” network of a directed online social network that holds it together. We develop an effective three-step procedure to hierarchically extract and unfold the core structure of a network by building up and generalizing ideas from the existing k-shell decomposition and clique percolation approaches. Our scheme produces higher-level representations of the core structure of the Google+ reciprocal network and it reveals that there are ten subgraphs (“communities”) comprising of dense clusters of cliques lying at the center of the core structure of the Google+ reciprocal network. Together they form the core to which “peripheral” sparse subgraphs are attached. Furthermore, our analysis shows that the core structure of the Google+ reciprocal network is very stable as the network evolves. Our results have implications in the design of algorithms for information flow, and in development of techniques for analyzing the vulnerability or robustness of online social networks.

Keywords

Google+ Reciprocal network K-Shell decomposition Network core Dependence Hypergraph 

Notes

Acknowledgments

This research was supported in part by DoD ARO MURI Award W911NF-12-1-0385, DTRA grant HDTRA1- 14-1-0040, NSF grant CNS-1411636, CNS-1618339 and CNS-1617729.

References

  1. 1.
    Alvarez-Hamelin, J.I., Dall’Asta, L., Barrat, A., Vespignani, A.: K-core decomposition of internet graphs: hierarchies, self-similarity and measurement biases. arXiv:cs/0511007 (2005)
  2. 2.
    Alvarez-Hamelin, J.I., Dall’Asta, L., Barrat, A., Vespignani, A.: Large scale networks fingerprinting and visualization using the k-core decomposition. Advances in neural information processing systems, 41–50 (2006)Google Scholar
  3. 3.
    Borgatti, S., Everett, M.: Models of core/periphery structures. Soc. Networks 21(4), 375–395 (2000)CrossRefGoogle Scholar
  4. 4.
    Carmi, S., Havlin, S., Kirkpatrick, S., Shavitt, Y., Shir, E.: A model of Internet topology using k-shell decomposition. PNAS 104, 11150–11154 (2007)CrossRefGoogle Scholar
  5. 5.
    Cazals, F., Karande, C.: A note on the problem of reporting maximal cliques. Theor. Comput. Sci. 407(1), 564–568 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Da Silva, M.R., Ma, H., Zeng, A.: Centrality, network capacity, and modularity as parameters to analyze the core-periphery structure in metabolic networks. Proc. IEEE 96(8), 1411–1420 (2008)CrossRefGoogle Scholar
  8. 8.
    Dumba, B., Zhang, Z.: Unfolding the core structure of the reciprocal graph of a massive online social network. In: Proceedings of the 10th annual international conference on combinatorial optimization and applications (COCOA’16), pp. 16–18 (2016)Google Scholar
  9. 9.
    Dumba, B., Golnari, G., Zhang, Z.: Analysis of a reciprocal network using Google+ : structural properties and evolution. In: Proceedings of the 5th international conference on computational social networks (CSoNet’16), pp. 14–26 (2016)Google Scholar
  10. 10.
    Fitting Power Law Distribution, http://tuvalu.santafe.edu/~aaronc/powerlaws/
  11. 11.
    Fortunato, S.: Community detection in graphs. Phys. Rep. 486(3), 75–174 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Garas, A., Argyrakis, P., Rozenblat, C., Tomassini, M., Havlin, S.: Worldwide spreading of economic crisis. New J. Phys. 12(11), 113043 (2010)CrossRefGoogle Scholar
  13. 13.
    Garlaschelli, D., Loffredo, M.I.: Patterns of link reciprocity in directed networks. Phys. Rev. Lett. 93, 268–701 (2004)Google Scholar
  14. 14.
    Gong, N.Z., Xu, W.: Reciprocal versus parasocial relationships in online social networks. Soc. Netw. Anal. Min. 4(1), 184–197 (2014)CrossRefGoogle Scholar
  15. 15.
    Gong, N.Z., Xu, W., Huang, L., Mittal, P., Stefanov, E., Sekar, V., Song, D.: Evolution of the social-attribute networks: measurements, modeling, and implications using Google+ . In: IMC 2015, pp. 131–144. ACM (2015)Google Scholar
  16. 16.
    Gonzalez, R., Cuevas, R., Motamedi, R., Rejaie, R., Cuevas, A.: Google+ or Google-? dissecting the evolution of the new OSN in its first year. In: WWW 2013, pp. 483–494. ACM (2013)Google Scholar
  17. 17.
  18. 18.
  19. 19.
    Hai, P.H., Shin, H.: Effective Clustering of dense and concentrated online communities. In: Asia-Pacific Web conference (APWEB) 2010, pp. 133–139. IEEE (2010)Google Scholar
  20. 20.
    Holme, P.: Core-periphery organization of complex networks. Phys. Rev. E 72 (4), 046111 (2005)CrossRefGoogle Scholar
  21. 21.
    Jamali, M., Haffari, G., Ester, M.: Modeling the temporal dynamics of social rating networks using bidirectional effects of social relations and rating patterns. In: WWW 2011, pp. 527–536. ACM (2011)Google Scholar
  22. 22.
    Jiang, B., Zhang, Z. -L., Towsley, D.: Reciprocity in social networks with capacity constraints. In: KDD 2015, pp. 457–466. ACM (2015)Google Scholar
  23. 23.
    Kitsak, M., Gallos, L.K., Havlin, S., Liljeros, F., Muchnik, L., Stanley, H.E., A Makse, H.: Identification of influential spreaders in complex networks. Nat. Phys. 6(11), 888–893 (2010)CrossRefGoogle Scholar
  24. 24.
    Li, Y., Zhang, Z.-L., Bao, J.: Mutual or unrequited love: identifying stable clusters in social networks with Uni- and Bi-Directional links. In: Bonato, A., Janssen, J (eds.) WAW 2012. LNCS, vol. 7323, pp 113–125. Springer, Heidelberg (2012)Google Scholar
  25. 25.
    Magno, G., Comarela, G., Saez-Trumper, D., Cha, M., Almeida, V.: New kid on the block: exploring the Google+ social graph. In: IMC 2012, pp. 159–170. ACM (2012)Google Scholar
  26. 26.
    Mislove, A., Marcon, M., Gummadi, K.P., Druschel, P., Bhattacharjee, B.: Measurement and analysis of online social networks. In: Proceedings of the 7th ACM SIGCOMM conference on internet measurement, pp. 29–42. ACM (2007)Google Scholar
  27. 27.
    Palla, G., Derényi, I., Farkas, I., Vicsek, T.: Uncovering the overlapping community structure of complex networks in nature and society. Nature 435(7043), 814–818 (2005)CrossRefGoogle Scholar
  28. 28.
    Rossa, F.D., Dercole, F., Piccardi, C.: Profiling coreperiphery network structure by random walkers. Sci. Rep. 3, 1467 (2013)CrossRefGoogle Scholar
  29. 29.
    Schiberg, D., Schneider, F., Schiberg, H., Schmid, S., Uhlig, S., Feldmann, A.: Tracing the Birth of an OSN: social graph and profile analysis in Google+ . In: Websci 2012, pp. 265–274. ACM (2012)Google Scholar
  30. 30.
    Shanahan, M., Wildie, M.: Knotty-centrality: finding the connective core of a complex network. PLoS One 7(5), e36579 (2012)CrossRefGoogle Scholar
  31. 31.
    Siganos, G., Tauro, S.L., Faloutsos, M.: Jellyfish: a conceptual model for the as internet topology. Commun. Netw. 8(3), 339–350 (2006)CrossRefGoogle Scholar
  32. 32.
    Wang, L., Hopcroft, J., He, J., Liang, H., Suwajanakorn, S.: Extracting the core structure of social networks using (α β) communities. Internet Math. 9(1), 58–81 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Wolfe, A.: Social network analysis: methods and applications. Am. Ethnol. 24 (1), 219–220 (1997)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science & EngineeringUniversity of MinnesotaTwin CitiesUSA

Personalised recommendations