Balancing a Complete Signed Graph by Editing Edges and Deleting Nodes

Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 20)


A signed graph is a simple undirected graph in which each edge is either positive or negative. A signed graph is balanced if every cycle has even numbers of negative edges. In this paper we study the problem of balancing a complete signed graph by minimum editing cost, in which the editing operations includes inserting edges, deleting edges, and deleting nodes. We design a branch-and-bound algorithm, as well as a heuristic algorithm. By experimental results we show that the branch-and-bound algorithm is much efficient than a trivial one and the heuristic algorithm performs well.


algorithm social network analysis signed graph balanced graph 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Böcker, S., Damaschke, P.: Even faster parameterized cluster deletion and cluster editing. Information Processing Letters 111(14), 717–721 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Böcker, S., Briesemeister, S., Bui, Q.B.A., Truss, A.: Going weighted: Parameterized algorithm for cluster editing. Theor. Comput. Sci. 410(52), 5467–5480 (2009)MATHCrossRefGoogle Scholar
  3. 3.
    Chen, J., Meng, J.: A 2k Kernel for the Cluster Editing Problem. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 459–468. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Damaschke, P.: Bounded-Degree Techniques Accelerate Some Parameterized Graph Algorithms. In: Chen, J., Fomin, F.V. (eds.) IWPEC 2009. LNCS, vol. 5917, pp. 98–109. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Damaschke, P.: Fixed-parameter enumerability of cluster editing and related problems. Theory Computing Syst. 46, 261–283 (2010)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Fellows, M.R., Guo, J., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Graph-based data clustering with overlaps. Discrete Optimization 8(1), 2–17 (2011)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Graph-modeled data clustering: Fixedparameter algorithms for clique generation. Theory Computing Syst. 38, 373–392 (2005)MATHCrossRefGoogle Scholar
  8. 8.
    Gramm, J., Guo, J., Hüffner, F., Niedermeier, R.: Automated generation of search tree algorithms for hard graph modification problems. Algorithmica 39, 321–347 (2004)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Guo, J.: A more effective linear kernelization for cluster editing. Theor. Comput. Sci. 410, 718–726 (2009)MATHCrossRefGoogle Scholar
  10. 10.
    Harary, F.: On the notion of balance of a signed graph. Michigan Mathematical Journal, 143–146 (1953)Google Scholar
  11. 11.
    Hüffner, F., Komusiewicz, C., Moser, H., Niedermeier, R.: Fixed-parameter algorithms for cluster vertex deletion. Theory of Computing Systems 47(1), 196–217 (2010)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press (2006)Google Scholar
  13. 13.
    Shamir, R., Sharan, R., Tsur, D.: Cluster Graph Modification Problems. In: Kučera, L. (ed.) WG 2002. LNCS, vol. 2573, pp. 379–390. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Wasserman, S., Faust, K.: Social Network Analysis. Cambridge University Press, Cambridge (1994)Google Scholar
  15. 15.
    Wei, P.-S., Wu, B.Y.: Balancing a complete signed graph by changing minimum number of edge signs. In: Proceedings of the 29th Workshop on Combinatorial Mathematics and Computation Theory, Taiwan, (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.National Chung Cheng UniversityChiaYiTaiwan, R.O.C.

Personalised recommendations