Line Graph for Weighted Networks toward Overlapping Community Discovery

  • Tetsuya Yoshida
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 16)


We propose generalized line graph for weighted networks toward overlapping community discovery from the networks. Community discovery from a network has often been conducted by assigning each node in a network only to one community. However, in real world networks, a node (e.g., user) might belong to several communities. For undirected networks without self-loops, we propose to generalize line graph by defining the weights in the line graph based on the weights in the original network. Based on the line graph representation, a node can be assigned to more than one community by assigning the links adjacent to the node to the corresponding communities. Various properties of the proposed generalized line graph are clarified, and the properties indicate that our proposal is a natural extension of the conventional line graph. Preliminary experiments are conducted over several real-world networks, and the results indicate that the proposed generalized line graph can improve the quality of the discovered overlapping communities.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dempster, A., Laird, N., Rubin, D.: Maximum Likelihood from Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 39(2), 1–38 (1977)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Diestel, R.: Graph Theory. Springer (2006)Google Scholar
  3. 3.
    Evans, T., Lambiotte, R.: Line graphs, link partitions, and overlapping communities. Physical Review E 80(1), 016105, 1–8 (2009)Google Scholar
  4. 4.
    Harville, D.A.: Matrix Algebra From a Statistican’s Perspective. Springer (2008)Google Scholar
  5. 5.
    Mika, P.: Social Networks and the Semantic Web. Springer (2007)Google Scholar
  6. 6.
    Newman, M.: Finding community structure using the eigenvectors of matrices. Physical Review E 76(3), 036104 (2006)Google Scholar
  7. 7.
    Newman, M.: Networks: An Introduction. Oxford University Press (2010)Google Scholar
  8. 8.
    Pons, P., Latapy, M.: Computing communities in large networks using random walks. Journal of Graph Algorithms 10(2), 191–218 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Raghavan, U., Albert, R., Kumara, S.: Near linear time algorithm to detect community structures in large-scale networks. Physical Review E 76, 036106 (2007)Google Scholar
  10. 10.
    von Luxburg, U.: A tutorial on spectral clustering. Statistics and Computing 17(4), 395–416 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Watts, D.J.: Six Degrees: The Science of a Connected Age. W W Norton & Co., Inc. (2004)Google Scholar
  12. 12.
    Whitney, H.: Congruent graphs and the connectivity of graphs. American Journal of Mathematics 54, 150–168 (1932)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Yoshida, T.: Toward finding hidden communities based on user profile. Journal of Intelligent Information Systems (2011) (accepted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan

Personalised recommendations