Identification of crucial elements for network integrity: a perturbation approach through graph spectral method

  • Vasundhara Gadiyaram
  • Anasuya Dighe
  • Saraswathi VishveshwaraEmail author


The complex behaviour of a network emerges as a product of all the interactions between its components as a single entity. The aim of system level investigations has been to identify emergent properties of a network. Identifying crucial components which are responsible for maintaining integrity of networks is essential, to understand or control them. This study presents a method to rank the participation of nodes and edges in a network using perturbation analysis to identify crucial players that contribute to the integrity of the network. The spectra of a network capture maximal features with minimal loss of information. Unlike earlier methods which evaluate perturbation in a network, based on the change in centralities or paths, the present method uses a network comparison score (Network Similarity Score) which quantifies changes at edge level to global entity level using graph spectral properties. The method is evaluated on realistic complex networks of protein structures of Muscarinic acetylcholine receptors. The important amino acid residues (nodes) and their interactions (edges) derived from the study have been correlated with experimental findings. The potential of perturbation score as a predictive tool for any real-world network is also discussed.


Network comparison Centrality measures Perturbation Structural analysis of networks Biological and molecular networks Muscarinic acetylcholine receptors 



SV thanks National Academy of Sciences (NASI), Allahabad, India, for Senior Scientist Fellowship. VG thanks IISc for Research Associate fellowship. We also thank SERC and MBU for computational facilities.

Supplementary material

12572_2018_236_MOESM1_ESM.xls (313 kb)
Supplementary material 1 (XLS 313 kb)


  1. 1.
    Albert, R., Jeong, H., Barabási, A.-L.: Error and attack tolerance of complex networks. Nature 406, 378 (2000)CrossRefGoogle Scholar
  2. 2.
    Carmi, S., et al.: A model of Internet topology using k-shell decomposition. Proc. Natl. Acad. Sci. 104(27), 11150 (2007)CrossRefGoogle Scholar
  3. 3.
    Colizza, V., et al.: Detecting rich-club ordering in complex networks. Nat. Phys. 2, 110 (2006)CrossRefGoogle Scholar
  4. 4.
    Pastor-Satorras, R., Vespignani, A.: Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86(14), 3200–3203 (2001)CrossRefGoogle Scholar
  5. 5.
    Kintali, S.: Betweenness centrality: Algorithms and lower bounds. arXiv preprint arXiv:0809.1906 (2008)
  6. 6.
    Freeman, L.C.: Centrality in social networks conceptual clarification. Soc. Netw. 1(3), 215–239 (1978)CrossRefGoogle Scholar
  7. 7.
    Austin, D.: How Google finds your needle in the web’s haystack. Am. Math. Soc. Feature Column 10, 12 (2006)Google Scholar
  8. 8.
    Chung, A., et al.: Characterising brain network topologies: a dynamic analysis approach using heat kernels. Neuroimage 141, 490–501 (2016)CrossRefGoogle Scholar
  9. 9.
    Escolano, F., Hancock, E.R., Lozano, M.A.: Heat diffusion: thermodynamic depth complexity of networks. Phys. Rev. E 85(3), 036206 (2012)CrossRefGoogle Scholar
  10. 10.
    Gadiyaram, V., Ghosh, S., Vishveshwara, S.: A graph spectral-based scoring scheme for network comparison. J. Complex Netw. 5(2), 219–244 (2017)Google Scholar
  11. 11.
    Haggarty, S.J., Clemons, P.A., Schreiber, S.L.: Chemical genomic profiling of biological networks using graph theory and combinations of small molecule perturbations. J. Am. Chem. Soc. 125(35), 10543–10545 (2003)CrossRefGoogle Scholar
  12. 12.
    Ghosh, S., Gadiyaram, V., Vishveshwara, S.: Validation of protein structure models using network similarity score. Proteins 85(9), 1759–1776 (2017)CrossRefGoogle Scholar
  13. 13.
    Liu, F., et al.: Global spectral clustering in dynamic networks. In: Proceedings of the National Academy of Sciences (2018)Google Scholar
  14. 14.
    Chavez, M., Valencia, M., Navarro, V., Latora, V., Martinerie, J.: Functional modularity of background activities in normal and epileptic brain networks. Phys. Rev. Lett. 104(11), 118701 (2010). CrossRefGoogle Scholar
  15. 15.
    Sistla, R.K., Brinda, K.V., Vishveshwara, S.: Identification of domains and domain interface residues in multidomain proteins from graph spectral method. Proteins 59(3), 616–626 (2005)CrossRefGoogle Scholar
  16. 16.
    Noh, J.D., Rieger, H.: Random walks on complex networks. Phys. Rev. Lett. 92(11), 118701 (2004)CrossRefGoogle Scholar
  17. 17.
    Tran, T.-D., Kwon, Y.-K.: Hierarchical closeness efficiently predicts disease genes in a directed signaling network. Comput. Biol. Chem. 53, 191–197 (2014)CrossRefGoogle Scholar
  18. 18.
    Trzaskowski, B., et al.: Action of molecular switches in GPCRs-theoretical and experimental studies. Curr. Med. Chem. 19(8), 1090–1109 (2012)CrossRefGoogle Scholar
  19. 19.
    Gregory, K.J., Sexton, P.M., Christopoulos, A.: Allosteric modulation of muscarinic acetylcholine receptors. Curr. Neuropharmacol. 5(3), 157–167 (2007)CrossRefGoogle Scholar
  20. 20.
    Wess, J., Eglen, R.M., Gautam, D.: Muscarinic acetylcholine receptors: mutant mice provide new insights for drug development. Nat. Rev. Drug Discov. 6(9), 721 (2007)CrossRefGoogle Scholar
  21. 21.
    Kruse, A.C., et al.: Activation and allosteric modulation of a muscarinic acetylcholine receptor. Nature 504(7478), 101 (2013)CrossRefGoogle Scholar
  22. 22.
    Haga, K., et al.: Structure of the human M2 muscarinic acetylcholine receptor bound to an antagonist. Nature 482(7386), 547 (2012)CrossRefGoogle Scholar
  23. 23.
    Berman, H.M., et al.: The protein data bank, 1999. In: Rossmann, M.G., Arnold, E. (eds.) International tables for crystallography volume F: crystallography of biological macromolecules, pp. 675–684. Springer, Dordrecht (2006)CrossRefGoogle Scholar
  24. 24.
    Kannan, N., Vishveshwara, S.: Identification of side-chain clusters in protein structures by a graph spectral method. J. Mol. Biol. 292(2), 441–464 (1999)CrossRefGoogle Scholar

Copyright information

© Indian Institute of Technology Madras 2018

Authors and Affiliations

  1. 1.Molecular Biophysics UnitIndian Institute of ScienceBangaloreIndia
  2. 2.IISc Mathematics Initiative (IMI)Indian Institute of ScienceBangaloreIndia

Personalised recommendations