Group-Level Analysis and Visualization of Social Networks

  • Michael Baur
  • Ulrik Brandes
  • Jürgen Lerner
  • Dorothea Wagner
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5515)

Abstract

Social network analysis investigates the structure of relations amongst social actors. A general approach to detect patterns of interaction and to filter out irregularities is to classify actors into groups and to analyze the relational structure between and within the various classes. The first part of this paper presents methods to define and compute structural network positions, i. e., classes of actors dependent on the network structure. In the second part we present techniques to visualize a network together with a given assignment of actors into groups, where specific emphasis is given to the simultaneous visualization of micro and macro structure.

Keywords

Adjacency Matrix Social Network Analysis Role Assignment Layout Algorithm Quotient Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Achlioptas, D., Fiat, A., Karlin, A., McSherry, F.: Web Search Via Hub Synthesis. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2001), pp. 500–509 (2001)Google Scholar
  2. 2.
    Alon, N., Kahale, N.: A Spectral Technique for Coloring Random 3-Colorable Graphs. SIAM Journal on Computation 26, 1733–1748 (1997)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Archambault, D., Munzner, T., Auber, D.: TopoLayout: Multi-Level Graph Layout by Topological Features. IEEE Transactions on Visualization and Computer Graphics 13(2), 305–317 (2007)CrossRefGoogle Scholar
  4. 4.
    Azar, Y., Fiat, A., Karlin, A., McSherry, F., Saia, J.: Spectral Analysis of Data. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC), pp. 619–626 (2001)Google Scholar
  5. 5.
    Bachmaier, C.: A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information. IEEE Transactions on Visualization and Computer Graphics 13(3), 585–594 (2007)CrossRefGoogle Scholar
  6. 6.
    Balzer, M., Deussen, O.: Level-of-Detail Visualization of Clustered Graph Layouts. In: Asia-Pacific Symposium on Visualisation 2007, APVIS 2007 (2007)Google Scholar
  7. 7.
    Batagelj, V., Doreian, P., Ferligoj, A.: An Optimizational Approach to Regular Equivalence. Social Networks 14, 121–135 (1992)CrossRefGoogle Scholar
  8. 8.
    Baur, M., Brandes, U.: Crossing Reduction in Circular Layouts. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 332–343. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Borgatti, S.P., Everett, M.G.: Notions of Position in Social Network Analysis. Sociological Methodology 22, 1–35 (1992)CrossRefGoogle Scholar
  10. 10.
    Brandes, U.: On Variants of Shortest-Path Betweenness Centrality and their Generic Computation. Social Networks 30(2), 136–145 (2008)CrossRefGoogle Scholar
  11. 11.
    Brandes, U., Erlebach, T. (eds.): Network Analysis: Methodological Foundations. Springer, Heidelberg (2005)MATHGoogle Scholar
  12. 12.
    Brandes, U., Fleischer, D., Lerner, J.: Summarizing Dynamic Bipolar Conflict Structures. IEEE Transactions on Visualization and Computer Graphics, special issue on Visual Analytics 12(6), 1486–1499 (2006)CrossRefGoogle Scholar
  13. 13.
    Brandes, U., Lerner, J.: Structural Similarity in Graphs. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 184–195. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Brandes, U., Lerner, J.: Coloring Random 3-Colorable Graphs with Non-uniform Edge Probabilities. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 202–213. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Brandes, U., Lerner, J.: Visualization of Conflict Networks. In: Kauffmann, M. (ed.) Building and Using Datasets on Armed Conflicts. NATO Science for Peace and Security Series E: Human and Societal Dynamics, vol. 36. IOS Press, Amsterdam (2008)Google Scholar
  16. 16.
    Coja-Oghlan, A.: A Spectral Heuristic for Bisecting Random Graphs. In: Proceeding of the 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 850–859 (2005)Google Scholar
  17. 17.
    Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, 2nd edn. Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton (2001)MATHGoogle Scholar
  18. 18.
    Cvetković, D.M., Doob, M., Sachs, H.: Spectra of Graphs. Johann Ambrosius Barth Verlag (1995)Google Scholar
  19. 19.
    Doreian, P., Batagelj, V., Ferligoj, A.: Generalized Blockmodeling. Structural Analysis in the Social Sciences, vol. 25. Cambridge University Press, Cambridge (2005)MATHGoogle Scholar
  20. 20.
    Duncan, C.A., Efrat, A., Kobourov, S.G., Wenk, C.: Drawing with Fat Edges. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 162–177. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Eades, P., Kelly, D.: Heuristics for Reducing Crossings in 2-Layered Networks. Ars Combinatoria 21(A), 89–98 (1986)MathSciNetMATHGoogle Scholar
  22. 22.
    Everett, M.G., Borgatti, S.P.: Regular Equivalence: General Theory. Journal of Mathematical Sociology 18(1), 29–52 (1994)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Fiala, J., Paulusma, D.: The Computational Complexity of the Role Assignment Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 817–828. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  24. 24.
    Fleischer, D.: Theory and Applications of the Laplacian. Ph.D thesis (2007)Google Scholar
  25. 25.
    Freeman, L.C.: Visualizing Social Networks. Journal of Social Structure 1(1) (2000)Google Scholar
  26. 26.
    Fruchterman, T.M.J., Reingold, E.M.: Graph Drawing by Force-Directed Placement. Software - Practice and Experience 21(11), 1129–1164 (1991)CrossRefGoogle Scholar
  27. 27.
    Gaertler, M.: Algorithmic Aspects of Clustering – Theory, Experimental Evaluation and Applications in Network Analysis and Visualization. Ph.D thesis, Universität Karlsruhe (TH), Fakultät für Informatik (2007)Google Scholar
  28. 28.
    Gansner, E.R., Koren, Y.: Improved Circular Layouts. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 386–398. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  29. 29.
    Gansner, E.R., North, S.C.: Improved Force-Directed Layouts. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 364–373. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  30. 30.
    Gkantsidis, C., Mihail, M., Zegura, E.W.: Spectral Analysis of Internet Topologies. In: Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications Societies (Infocom), vol. 1, pp. 364–374. IEEE Computer Society Press, Los Alamitos (2003)Google Scholar
  31. 31.
    Godsil, C., Royle, G.: Algebraic Graph Theory. Graduate Texts in Mathematics. Springer, Heidelberg (2001)CrossRefMATHGoogle Scholar
  32. 32.
    Golub, G.H., van Loan, C.F.: Matrix Computations. John Hopkins University Press, Baltimore (1996)MATHGoogle Scholar
  33. 33.
    Harel, D., Koren, Y.: Drawing Graphs with Non-Uniform Vertices. In: Proceedings of the 6th Working Conference on Advanced Visual Interfaces (AVI 2002), pp. 157–166. ACM Press, New York (2002)CrossRefGoogle Scholar
  34. 34.
    Holten, D.: Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data. IEEE Transactions on Visualization and Computer Graphics 12(5), 741–748 (2006)CrossRefGoogle Scholar
  35. 35.
    Kannan, R., Vempala, S., Vetta, A.: On clusterings: Good, Bad and Spectral. Journal of the ACM 51(3), 497–515 (2004)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Kaufmann, M., Wiese, R.: Maintaining the Mental Map for Circular Drawings. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 12–22. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  37. 37.
    Krebs, V.E.: Visualizing Human Networks. Release 1.0, pp. 1–25 (1996)Google Scholar
  38. 38.
    Krempel, L.: Visualisierung komplexer Strukturen. Grundlagen der Darstellung mehrdimensionaler Netzwerke. Campus (2005)Google Scholar
  39. 39.
    Lerner, J.: Role Assignments. In: Brandes, U., Erlebach, T. (eds.) Network Analysis. LNCS, vol. 3418, pp. 216–252. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  40. 40.
    Lerner, J.: Structural Similarity of Vertices in Networks. Ph.D thesis (2007)Google Scholar
  41. 41.
    Lorrain, F., White, H.C.: Structural Equivalence of Individuals in Social Networks. Journal of Mathematical Sociology 1, 49–80 (1971)CrossRefGoogle Scholar
  42. 42.
    Luczkovich, J.J., Borgatti, S.P., Johnson, J.C., Everett, M.G.: Defining and Measuring Trophic Role Similarity in Food Webs Using Regular Equivalence. Journal of Theoretical Biology 220(3), 303–321 (2003)MathSciNetCrossRefGoogle Scholar
  43. 43.
    Masuda, S., Kashiwabara, T., Nakajima, K., Fujisawa, T.: On the \(\mathcal{NP}\)-Completeness of a Computer Network Layout Problem. In: Proceedings of the 20th IEEE International Symposium on Circuits and Systems 1987, pp. 292–295. IEEE Computer Society, Los Alamitos (1987)Google Scholar
  44. 44.
    Matuszewski, C., Schönfeld, R., Molitor, P.: Using Sifting for k-Layer Straightline Crossing Minimization. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 217–224. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  45. 45.
    McSherry, F.: Spectral Partitioning of Random Graphs. In: Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2001), pp. 529–537 (2001)Google Scholar
  46. 46.
    Papadimitriou, C., Raghavan, P., Tamaki, H., Vempala, S.: Latent Semantic Indexing: A Probabilistic Analysis. Journal of Computer and System Sciences 61(2), 217–235 (2000)MathSciNetCrossRefMATHGoogle Scholar
  47. 47.
    Rudell, R.: Dynamic Variable Ordering for Ordered Binary Decision Diagrams. In: Proceedings of the 1993 IEEE/ACM International Conference on Computer-Aided Design, pp. 42–47. IEEE Computer Society Press, Los Alamitos (1993)Google Scholar
  48. 48.
    Sailer, L.D.: Structural Equivalence: Meaning and Definition, Computation and Application. Social Networks 1, 73–90 (1978)CrossRefGoogle Scholar
  49. 49.
    Schrodt, P.A., Davis, S.G., Weddle, J.L.: Political Science: KEDS - A Program for the Machine Coding of Event Data. Social Science Computer Review 12(3), 561–588 (1994)CrossRefGoogle Scholar
  50. 50.
    Six, J.M., Tollis, I.G.: A Framework for User-Grouped Circular Drawings. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 135–146. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  51. 51.
    Stewart, G.W., Sun, J.-G.: Matrix Perturbation Theory. Academic Press, London (1990)MATHGoogle Scholar
  52. 52.
    Vempala, S., Wang, G.: A Spectral Algorithm for Learning Mixtures of Distributions. In: Proceedings of the 43rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2002 (2002)Google Scholar
  53. 53.
    Wang, X., Miyamoto, I.: Generating Customized Layouts. In: Brandenburg, F.J. (ed.) GD 1995. LNCS, vol. 1027, pp. 504–515. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  54. 54.
    Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)CrossRefMATHGoogle Scholar
  55. 55.
    White, D.R., Reitz, K.P.: Graph and Semigroup Homomorphisms on Networks of Relations. Social Networks 5, 193–234 (1983)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michael Baur
    • 1
  • Ulrik Brandes
    • 2
  • Jürgen Lerner
    • 2
  • Dorothea Wagner
    • 1
  1. 1.Faculty of InformaticsUniversität Karlsruhe (TH), KITGermany
  2. 2.Department of Computer & Information ScienceUniversity of KonstanzGermany

Personalised recommendations