Dense Subgraphs in Biological Networks

  • Mohammad Mehdi HosseinzadehEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12011)


A fundamental problem in analysing biological networks is the identification of dense subgraphs, since they are considered to be related to relevant parts of networks, like communities. Many contributions have been focused mainly in computing a single dense subgraph, but in many applications we are interested in finding a set of dense, possibly overlapping, subgraphs. In this paper we consider the Top-k-Overlapping Densest Subgraphs problem, that aims at finding a set of k dense subgraphs, for some integer \(k \ge 1\), that maximize an objective function that consists of the density of the subgraphs and the distance among them. We design a new heuristic for the Top-k-Overlapping Densest Subgraphs and we present an experimental analysis that compares our heuristic with an approximation algorithm developed for Top-k-Overlapping Densest Subgraphs (called DOS) on biological networks. The experimental result shows that our heuristic provides solutions that are denser than those computed by DOS, while the solutions computed by DOS have a greater distance. As for time-complexity, the DOS algorithm is much faster than our method.


Biological networks Graph algorithms Heuristics Dense subgraph 


  1. 1.
    Alba, R.D.: A graph-theoretic definition of a sociometric clique. J. Math. Sociol. 3, 113–126 (1973)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Asahiro, Y., Iwama, K., Tamaki, H., Tokuyama, T.: Greedily finding a dense subgraph. In: Karlsson, R., Lingas, A. (eds.) SWAT 1996. LNCS, vol. 1097, pp. 136–148. Springer, Heidelberg (1996). Scholar
  3. 3.
    Balalau, O.D., Bonchi, F., Chan, T.H., Gullo, F., Sozio, M.: Finding subgraphs with maximum total density and limited overlap. In: Cheng, X., Li, H., Gabrilovich, E., Tang, J. (eds.) Proceedings of the Eighth ACM International Conference on Web Search and Data Mining, WSDM 2015, pp. 379–388. ACM (2015).
  4. 4.
    Charikar, M.: Greedy approximation algorithms for finding dense components in a graph. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 84–95. Springer, Heidelberg (2000). Scholar
  5. 5.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)zbMATHGoogle Scholar
  6. 6.
    Dondi, R., Hosseinzadeh, M.M., Mauri, G., Zoppis, I.: Top-k overlapping densest subgraphs: approximation and complexity. In: Proceeding in 20th Italian Conference on Theoretical Computer Science (2019, to appear)Google Scholar
  7. 7.
    Dondi, R., Mauri, G., Sikora, F., Zoppis, I.: Covering a graph with clubs. J. Graph Algorithms Appl. 23(2), 271–292 (2019). Scholar
  8. 8.
    Fratkin, E., Naughton, B.T., Brutlag, D.L., Batzoglou, S.: MotifCut: regulatory motifs finding with maximum density subgraphs. Bioinformatics 22(14), 156–157 (2006). Scholar
  9. 9.
    Galbrun, E., Gionis, A., Tatti, N.: Top-k overlapping densest subgraphs. DataMin. Knowl. Discov. 30(5), 1134–1165 (2016). Scholar
  10. 10.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman & Co., Stuttgart (1979)zbMATHGoogle Scholar
  11. 11.
    Goldberg, A.V.: Finding a Maximum Density Subgraph. University of California Berkeley, CA (1984)Google Scholar
  12. 12.
    Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds.) Complexity of Computer Computations. IRSS, pp. 85–103. Plenum Press, New York (1972). Scholar
  13. 13.
    Komusiewicz, C.: Multivariate algorithmics for finding cohesive subnetworks. Algorithms 9(1), 21 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Leskovec, J., Lang, K.J., Dasgupta, A., Mahoney, M.W.: Community structure in large networks: natural cluster sizes and the absence of large well-defined clusters. Internet Math. 6(1), 29–123 (2009). Scholar
  15. 15.
    Ma, X., Zhou, G., Shang, J., Wang, J., Peng, J., Han, J.: Detection of complexes in biological networks through diversified dense subgraph mining. J. Comput. Biol. 24(9), 923–941 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mokken, R.: Cliques, clubs and clans. Qual. Quant. Int. J. Methodol. 13(2), 161–173 (1979)CrossRefGoogle Scholar
  17. 17.
    Nasir, M.A.U., Gionis, A., Morales, G.D.F., Girdzijauskas, S.: Fully dynamic algorithm for top-k densest subgraphs. In: Lim, E., et al. (eds.) Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, CIKM 2017, pp. 1817–1826. ACM (2017).
  18. 18.
    Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence (2015).

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Università degli Studi di BergamoBergamoItaly

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