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.
References
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.2014.10.011
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)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Birkhoff, G.: Lattice Theory. Colloquium Publications, vol. 25, 3rd edn. American Mathematical Society, New York (1967)
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: 0370-1573
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)
Freeman, L.C.: Cliques, Galois lattices, and the structure of human social groups. Soc. Netw. 18(3), 173–187 (1996). ISSN: 0378-8733
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)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Berlin/Heidelberg (1999)
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)
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)
Jäschke, R., Hotho, A., Schmitz, C., Ganter, B., Stumme, G.: Discovering shared conceptualizations in folksonomies. J. Web Semant. 6(1), 38–53 (2008)
Kolaczyk, E.D.: Statistical Analysis of Network Data: Methods and Models. Springer Series in Statistics, p. 386. Springer, New York (2009)
KONECT (2016) Club membership network dataset
Maslov, S., Sneppen, K.: Specificity and stability in topology of protein networks. Science 296(5569), 910 (2002)
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: 978-1-4503-2745-9
Opsahl, T., Panzarasa, P.: Clustering in weighted networks. Soc. Netw. 31(2), 155–163 (2009)
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.2011.09.023
Saracco, F., Di Clemente, R., Gabrielli, A., Squartini, T.: Randomizing bipartite networks: the case of the World Trade Web. Sci. Rep. 5, 10595 (2015)
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)
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)
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.2014.22
Vázquez, A., Pastor-Satorras, R., Vespignani, A.: Internet topology at the router and autonomous system level. In: CoRR (2002). cond-mat/0206084
Wasserman, S., Faust, K.: Social Network Analysis. Methods and Applications. Structural Analysis in the Social Sciences. Cambridge University Press, New York (1994)
Watts, D.J.: Networks, dynamics, and the small-world phenomenon. Am. J. Sociol. 105, 493–527 (1999)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393(6684), 440–442 (1998). ISSN: 0028-0836. doi:10.1038/30918
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: 978-94-009-7798-3
Xiao, W.-K., et al.: Empirical study on clique-degree distribution of networks. Phys. Rev. E 76(3), 037102 (2007)
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.2010.24
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/s13278-011-0021-0
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.
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Borchmann, D., Hanika, T. (2017). Individuality in Social Networks. In: Missaoui, R., Kuznetsov, S., Obiedkov, S. (eds) Formal Concept Analysis of Social Networks. Lecture Notes in Social Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-64167-6_2
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