Advertisement

Individuality in Social Networks

  • Daniel Borchmann
  • Tom Hanika
Chapter
Part of the Lecture Notes in Social Networks book series (LNSN)

Abstract

We consider individuality in bi-modal social networks, a facet that has not been considered before in the mathematical analysis of social networks. We use methods from formal concept analysis to develop a natural definition for individuality, and provide experimental evidence that this yields a meaningful approach for additional insights into the nature of social networks.

Keywords

Formal concept analysis Social network analysis Individuality Small world networks Bipartite graphs Extent distribution 

Notes

Acknowledgements

We thank R. Schaller and B. Ludwig for providing the LNM data set, which is a great addition to this work. Daniel Borchmann gratefully acknowledges support by the Cluster of Excellence “Center for Advancing Electronics Dresden” (cfAED). The computations presented in this paper were conducted by conexp-clj, a general-purpose software for formal concept analysis (https://github.com/exot/conexp-clj). Finally, we would like to thank the reviewers for their insightful comments on this work.

References

  1. 1.
    Andrews, S.: A ‘best-of-breed’ approach for designing a fast algorithm for computing fixpoints of Galois connections. Inf. Sci. 295, 633–649 (2015). doi:10.1016/j.ins.2014.10.011CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Atzmueller, M., Hanika, T., Stumme, G., Schaller, R., Ludwig, B.: Social event network analysis: structure, preferences, and reality. In: Proceedings of IEEE/ACM ASONAM. IEEE Press, Boston, MA (2016)Google Scholar
  3. 3.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Birkhoff, G.: Lattice Theory. Colloquium Publications, vol. 25, 3rd edn. American Mathematical Society, New York (1967)Google Scholar
  5. 5.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006). ISSN: 0370-1573CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Borchmann, D., Hanika, T.: Some experimental results on randomly generating formal contexts. In: Huchard, M., Kuznetsov, S. (eds.) CLA. CEUR Workshop Proceedings, vol. 1624, pp. 57–69. CEUR-WS.org (2016)Google Scholar
  7. 7.
    Freeman, L.C.: Cliques, Galois lattices, and the structure of human social groups. Soc. Netw. 18(3), 173–187 (1996). ISSN: 0378-8733CrossRefGoogle Scholar
  8. 8.
    Freeman, L.C.: Finding social groups: a meta-analysis of the southern women data. In: Dynamic Social Network Modeling and Analysis: Workshop Summary and Papers, pp. 39–97. National Research Council, The National Academies, Washington, DC (2002)Google Scholar
  9. 9.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin/Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  10. 10.
    Gjoka, M., Smith, E., Butts, C.: Estimating clique composition and size distributions from sampled network data. In: 2014 IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), pp. 837–842. IEEE, Toronto (2014)Google Scholar
  11. 11.
    Gkantsidist, C., Mihail, M., Zegura, E.: The Markov chain simulation method for generating connected power law random graphs. In: Proceedings of the 5th Workshop on Algorithm Engineering and Experiments, vol. 111, p. 16. SIAM, Philadelphia (2003)Google Scholar
  12. 12.
    Jäschke, R., Hotho, A., Schmitz, C., Ganter, B., Stumme, G.: Discovering shared conceptualizations in folksonomies. J. Web Semant. 6(1), 38–53 (2008)CrossRefGoogle Scholar
  13. 13.
    Kolaczyk, E.D.: Statistical Analysis of Network Data: Methods and Models. Springer Series in Statistics, p. 386. Springer, New York (2009)Google Scholar
  14. 14.
    KONECT (2016) Club membership network datasetGoogle Scholar
  15. 15.
    Maslov, S., Sneppen, K.: Specificity and stability in topology of protein networks. Science 296(5569), 910 (2002)CrossRefGoogle Scholar
  16. 16.
    Myers, S.A., Sharma, A., Gupta, P., Lin, J.: Information network or social network?: The structure of the Twitter follow graph. In: Proc. WWW (Companion), pp. 493–498. ACM, Seoul (2014). ISBN: 978-1-4503-2745-9Google Scholar
  17. 17.
    Opsahl, T., Panzarasa, P.: Clustering in weighted networks. Soc. Netw. 31(2), 155–163 (2009)CrossRefGoogle Scholar
  18. 18.
    Outrata, J., Vychodil, V.: Fast algorithm for computing fixpoints of Galois connections induced by object-attribute relational data. Inf. Sci. 185(1), 114–127 (2012). doi:10.1016/j.ins.2011.09.023CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Saracco, F., Di Clemente, R., Gabrielli, A., Squartini, T.: Randomizing bipartite networks: the case of the World Trade Web. Sci. Rep. 5, 10595 (2015)CrossRefGoogle Scholar
  20. 20.
    Schaller, R., Harvey, M., Elsweiler, D.: Detecting event visits in urban areas via smartphone GPS data. In: Advances in Information Retrieval. Proc. ECIR. Springer, Cham (2014)CrossRefGoogle Scholar
  21. 21.
    Seierstad, C., Opsahl, T.: For the few not the many? The effects of affirmative action on presence, prominence, and social capital of women directors in Norway. Scand. J. Manag. 27(1), 44–54 (2011)CrossRefGoogle Scholar
  22. 22.
    Slater, N., Itzschack, R., Louzoun, Y.: Mid size cliques are more common in real world networks than triangles. Netw. Sci. 2(3), 387–402 (2014). doi:10. 1017/nws.2014.22Google Scholar
  23. 23.
    Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Internet topology at the router and autonomous system level. In: CoRR (2002). cond-mat/0206084Google Scholar
  24. 24.
    Wasserman, S., Faust, K.: Social Network Analysis. Methods and Applications. Structural Analysis in the Social Sciences. Cambridge University Press, New York (1994)CrossRefzbMATHGoogle Scholar
  25. 25.
    Watts, D.J.: Networks, dynamics, and the small-world phenomenon. Am. J. Sociol. 105, 493–527 (1999)CrossRefGoogle Scholar
  26. 26.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998). ISSN: 0028-0836. doi:10.1038/30918CrossRefzbMATHGoogle Scholar
  27. 27.
    Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets: Proceedings of the NATO Advanced Study Institute, pp. 445–470, Banff, 28 August–12 September 1981. Springer, Dordrecht (1982). ISBN: 978-94-009-7798-3Google Scholar
  28. 28.
    Xiao, W.-K., et al.: Empirical study on clique-degree distribution of networks. Phys. Rev. E 76(3), 037102 (2007)CrossRefGoogle Scholar
  29. 29.
    Zweig, K.A.: How to forget the second side of the story: a new method for the one-mode projection of bipartite graphs. In: International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2010, pp. 200–207, Odense, 9–11 August 2010. doi:10.1109/ASONAM.2010.24Google Scholar
  30. 30.
    Zweig, K.A., Kaufmann, M.: A systematic approach to the one-mode projection of bipartite graphs. Soc. Netw. Anal. Min. 1(3), 187–218 (2011). doi:10.1007/s13278-011-0021-0CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Technische Universität DresdenDresdenGermany
  2. 2.Knowledge & Data Engineering Group, Research Center for Information System Design (ITeG)University of KasselKasselGermany

Personalised recommendations