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Entanglement in Multiplex Networks: Understanding Group Cohesion in Homophily Networks

  • Benjamin RenoustEmail author
  • Guy Melançon
  • Marie-Luce Viaud
Chapter
Part of the Lecture Notes in Social Networks book series (LNSN)

Abstract

The analysis and exploration of a social network depends on the type of relations at play. Homophily (similarity) relationships form an important category of relations linking entities whenever they exhibit similar behaviors. Examples of homophily networks examined in this paper are: co-authorship, where homophily between two persons follows from having co-published a paper on a given topic; movie actors having played under the supervision of the same movie director; members of a entrepreneur network having exchanged ideas through discussion threads. Homophily is often embodied through a bipartite network where entities (authors, movie directors, members) connect through attributes (papers, actors, discussion threads). A common strategy is then to project this bipartite graph onto a single-type network. The resulting single-type network can then be studied using standard techniques such as community detection or by computing various centrality indices. We revisit this type of approach and introduce a homogeneity measure inspired from past work by Burt and Schøtt. Instead of considering a projection in a bipartite network, we consider a multiplex network which preserves both entities and attributes as our core object of study. The homogeneity of a subgroup depends on how intensely and how equally interactions occur between layers of edges giving rise to the subgroup. The measure thus differentiates between subgroups of entities exhibiting similar topologies depending on the interaction patterns of the underlying layers. The method is first validated using two widely used datasets. A first example looks at authors of the IEEE InfoVis Conference (InfoVis 2007 Contest). A second example looks at homophily relations between movie actors that have played under the direction of a same director (IMDB). A third example shows the capability of the methodology to deal with weighted homophily networks, pointing at subtleties revealed from the analysis of weights associated with interactions between attributes.

Keywords

Group cohesion Homophily Entanglement index Bipartite graph Community reliability 

Notes

Acknowledgments

We would like to thank the European project FP7 FET ICT-2011.9.1 Emergence by Design (MD) Grant agreement no: 284625.

References

  1. 1.
    Aral S, Muchnik L, Sundararajan A (2009) Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks. Proc Natl Acad Sci 106(51):21544–21549CrossRefGoogle Scholar
  2. 2.
    Auber D, Chiricota Y, Jourdan F, Melançon G (2003) Multiscale navigation of small world networks. In: IEEE symposium on information visualisation. IEEE Computer Science Press, pp 75–81Google Scholar
  3. 3.
    Bakshy E, Rosenn I, Marlow C, Adamic L (2012) The role of social networks in information diffusion. In: 21st international conference on world wide web. ACM, pp 519–528Google Scholar
  4. 4.
    Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech: Theory Exp 2008(10):P10008CrossRefGoogle Scholar
  5. 5.
    Borgatti SP (2012) Two-mode concepts in social network analysis. In: Meyers RA (ed) Computational complexity—theory, techniques, and applications. Springer, New York, pp 2912–2924Google Scholar
  6. 6.
    Borgatti SP, Everett MG (1997) Network analysis of 2-mode data. Soc Netw 19(3):243–269CrossRefMathSciNetGoogle Scholar
  7. 7.
    Borgatti SP, Mehra A, Brass DJ, Labianca G (2009) Network analysis in the social sciences. Science 323(5916):892–895CrossRefGoogle Scholar
  8. 8.
    Buja A, Cook D, Swayne DF (1996) Interactive high-dimensional data visualization. J Comput Graph Stat 5(1):78–99Google Scholar
  9. 9.
    Burt R, Scott T (1985) Relation content in multiple networks. Soc Sci Res 14:287–308CrossRefGoogle Scholar
  10. 10.
    De Domenico M, Solè-Ribalta A, Cozzo E, Kivelä M, Moreno Y, Porter MA, Gòmez S, Arenas A (2013) Mathematical formulation of multi-layer networks. arXiv preprint arXiv:1307.4977 [physics.soc-ph]
  11. 11.
    Didimo W, Liotta G, Romeo SA (2011) A graph drawing application to web site traffic analysis. J Graph Algorithms Appl 15(2):229–251CrossRefMathSciNetGoogle Scholar
  12. 12.
    Ding J, Zhou A (2009) Nonnegative matrices, positive operators and applications. World Scientific, SingaporeCrossRefzbMATHGoogle Scholar
  13. 13.
    Easley D, Kleinberg J (2010) Networks in their surrounding contexts. In: Networks, crowds, and markets—reasoning about a highly connected world. Cambridge University Press, Cambridge, pp 77–106Google Scholar
  14. 14.
    Everett MG, Borgatti SP (1998) Anal Clique Overlap Connect 21(1):49–61Google Scholar
  15. 15.
    Fortunato S (2010) Community detection in graphs. Phys Rep 486(3D5):75–174CrossRefMathSciNetGoogle Scholar
  16. 16.
    Fujimoto K, Chou CP, Valente TW (2011) The network autocorrelation model using two-mode data: affiliation exposure and potential bias in the autocorrelation parameter. Soc Netw 33(3):231–243CrossRefGoogle Scholar
  17. 17.
    Guillaume JL, Latapy M (2005) Bipartite graphs as models of complex networks. Lecture Notes in Computer Science, vol 3405. Springer, pp 127–139Google Scholar
  18. 18.
    Guimera R, Mossa S, Turtschi A, Amaral LAN (2005) The worldwide air transportation network: anomalous centrality, community structure, and cities global roles. Proc Natl Acad Sci USA 102(22):7794–7799CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
  20. 20.
    Jackson MO (2010) Social and economic networks. Princeton University Press, PrincetonzbMATHGoogle Scholar
  21. 21.
    Jain AK (2010) Data clustering: 50 years beyond k-means. Pattern Recogn Lett 31(8):651–666CrossRefGoogle Scholar
  22. 22.
    Kaski S, Nikkila J, Oja M, Venna J, Toronen P, Castren E (2003) Trustworthiness and metrics in visualizing similarity of gene expression. BMC Bioinform 4(1):48CrossRefGoogle Scholar
  23. 23.
    Ke W, Borner K, Viswanath L (2004) Major information visualization authors, papers and topics in the ACM library. In: IEEE symposium on information visualization 2004. IEEEGoogle Scholar
  24. 24.
    Kivelä M, Arenas A, Barthelemy M, Gleeson JP, Moreno Y, Porter MA (2013) Multilayer networks. arXiv preprint arXiv:1309.7233
  25. 25.
    Latapy M, Magnien C, Vecchio ND (2008) Basic notions for the analysis of large two-mode networks. Soc Netw 30(1):31–48CrossRefGoogle Scholar
  26. 26.
    Lee B, Plaisant C, Parr CS, Fekete JD, Henry N (2006) Task taxonomy for graph visualization. In: Proceedings of the 2006 AVI workshop on beyond time and errors: novel evaluation methods for information visualization. ACM, pp 1–5Google Scholar
  27. 27.
    Manski CF (1993) Identification of endogenous social effects: the reflection problem. Rev Econ Stud 60(3):531–542CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    McPherson M, Smith-Lovin L, Cook JM (2001) Birds of a feather: homophily in social networks. Annu Rev Sociol 27(1):415–444CrossRefGoogle Scholar
  29. 29.
    Neal Z (2013) Identifying statistically significant edges in one-mode projections. Soc Netw Anal Mining pp 1–10Google Scholar
  30. 30.
    Newman MEJ (2003) The structure and function of complex networks. SIAM Rev 45:167–256CrossRefzbMATHMathSciNetGoogle Scholar
  31. 31.
    Opsahl T (2013) Triadic closure in two-mode networks: redefining the global and local clustering coefficients. Soc Netw 35(2):159–167CrossRefGoogle Scholar
  32. 32.
    Peeters R (2003) The maximum edge biclique problem is np-complete. Discret Appl Math 131(3):651–654CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Podolny JM, Baron JN (1997) Resources and relationships: social networks and mobility in the workplace. Am Sociol Rev 62(5):673–693CrossRefGoogle Scholar
  34. 34.
    Renoust B, Melançon G, Viaud ML (2013) Assessing group cohesion in homophily networks. In: Advances in social network analysis and mining (ASONAM) 2013. ACM/IEEE, Niagara Falls, Canada, pp 149–155Google Scholar
  35. 35.
    Renoust B, Melançon G, Viaud ML (2013) Measuring group cohesion in document collections. In: IEEE/WIC/ACM international conference on web intelligenceGoogle Scholar
  36. 36.
    Robins G, Alexander M (2004) Small worlds among interlocking directors: network structure and distance in bipartite graphs. Comput Math Organ Theory 10(1):69–94CrossRefzbMATHGoogle Scholar
  37. 37.
    Shalizi CR, Thomas AC (2011) Homophily and contagion are generically confounded in observational social network studies. Sociol Methods Res 40(2):211–239CrossRefMathSciNetGoogle Scholar
  38. 38.
    Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(379–423):623–656CrossRefMathSciNetGoogle Scholar
  39. 39.
    The EdgeRyders community. http://edgeryders.eu/
  40. 40.
    The internet movie database (IMDB). http://www.imdb.com
  41. 41.
    Yi JS, ah Kang Y, Stasko JT, Jacko JA (2007) Toward a deeper understanding of the role of interaction in information visualization. IEEE Trans Vis Comput Graph 13(6):1224–1231CrossRefGoogle Scholar
  42. 42.
    Zhou T, Ren J, Medo M, Zhang Y (2007) Bipartite network projection and personal recommendation. Phys Rev E 76(4):046115CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Benjamin Renoust
    • 1
    • 2
    Email author
  • Guy Melançon
    • 1
  • Marie-Luce Viaud
    • 2
  1. 1.CNRS UMR 5800 LaBRI, INRIA Bordeaux Sud-OuestCampus Université Bordeaux ITalenceFrance
  2. 2.Institut National de L’Audiovisuel (INA)ParisFrance

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