Can Everybody Sit Closer to Their Friends Than Their Enemies?

  • Anne-Marie Kermarrec
  • Christopher Thraves
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)

Abstract

Signed graphs are graphs with signed edges. They are commonly used to represent positive and negative relationships in social networks. While balance theory and clusterizable graphs deal with signed graphs, recent empirical studies have proved that they fail to reflect some current practices in real social networks. In this paper we address the issue of drawing signed graphs and capturing such social interactions. We relax the previous assumptions to define a drawing as a model in which every vertex has to be placed closer to its neighbors connected through a positive edge than its neighbors connected through a negative edge in the resulting space. Based on this definition, we address the problem of deciding whether a given signed graph has a drawing in a given ℓ-dimensional Euclidean space. We focus on the 1-dimensional case, where we provide a polynomial time algorithm that decides if a given complete signed graph has a drawing, and provides it when applicable.

Keywords

Signed graphs graph embedding graph drawing structural balance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Antal, T., Krapivsky, P.L., Redner, S.: Dynamics of social balance on networks. Phys. Rev. E 72(3), 036121 (2005)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56(1-3), 89–113 (2004)CrossRefMATHGoogle Scholar
  3. 3.
    Brandes, U., Fleischer, D., Lerner, J.: Summarizing dynamic bipolar conflict structures. IEEE Trans. Vis. Comput. Graph. 12(6), 1486–1499 (2006)CrossRefGoogle Scholar
  4. 4.
    Cartwright, D., Harary, F.: Structural balance: a generalization of heider’s theory. Psychological Review 63(5), 277–293 (1956)CrossRefGoogle Scholar
  5. 5.
    Davis, J.A.: Clustering and structural balance in graphs. Human Relations 20(2), 181 (1967)CrossRefGoogle Scholar
  6. 6.
    Habib, M., McConnell, R.M., Paul, C., Viennot, L.: Lex-bfs and partition refinement, with applications to transitive orientation, interval graph recognition and consecutive ones testing. Theor. Comput. Sci. 234(1-2), 59–84 (2000)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Harary, F.: On the notion of balance of a signed graph. Michigan Mathematical Journal 2(2), 143 (1953)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Harary, F., Kabell, J.A.: A simple algorithm to detect balance in signed graphs. Mathematical Social Sciences 1(1), 131–136 (1980)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Harary, F., Kabell, J.A.: Counting balanced signed graphs using marked graphs. In: Proceedings of the Edinburgh Mathematical Society, vol. 24(2), pp. 99–104 (1981)Google Scholar
  10. 10.
    Harary, F., Palmer, E.: On the number of balanced signed graphs. Bulletin of Mathematical Biology 29, 759–765 (1967)MATHGoogle Scholar
  11. 11.
    Kunegis, J., Schmidt, S., Lommatzsch, A., Lerner, J., De Luca, E.W., Albayrak, S.: Spectral analysis of signed graphs for clustering, prediction and visualization. In: SDM, page 559 (2010)Google Scholar
  12. 12.
    Lauterbach, D., Truong, H., Shah, T., Adamic, L.A.: Surfing a web of trust: Reputation and reciprocity on couchsurfing.com. In: CSE (4), pp. 346–353 (2009)Google Scholar
  13. 13.
    Leskovec, J., Huttenlocher, D.P., Kleinberg, J.M.: Governance in social media: A case study of the wikipedia promotion process. In: ICWSM 2010 (2010)Google Scholar
  14. 14.
    Leskovec, J., Huttenlocher, D.P., Kleinberg, J.M.: Predicting positive and negative links in online social networks. In: WWW 2010, pp. 641–650 (2010)Google Scholar
  15. 15.
    Leskovec, J., Huttenlocher, D.P., Kleinberg, J.M.: Signed networks in social media. In: CHI 2010, pp. 1361–1370 (2010)Google Scholar
  16. 16.
    Szell, M., Lambiotte, R., Thurner, S.: Multirelational organization of large-scale social networks in an online world. PNAS 107(31), 13636–13641 (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Anne-Marie Kermarrec
    • 1
  • Christopher Thraves
    • 2
  1. 1.INRIA Rennes – Bretagne AtlantiqueFrance
  2. 2.LADyR, GSyC, Universidad Rey Juan CarlosSpain

Personalised recommendations