A Review on Network Robustness from an Information Theory Perspective

  • Tiago SchieberEmail author
  • Martín Ravetti
  • Panos M. Pardalos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9869)


The understanding of how a networked system behaves and keeps its topological features when facing element failures is essential in several applications ranging from biological to social networks. In this context, one of the most discussed and important topics is the ability to distinguish similarities between networks. A probabilistic approach already showed useful in graph comparisons when representing the network structure as a set of probability distributions, and, together with the Jensen-Shannon divergence, allows to quantify dissimilarities between graphs. The goal of this article is to compare these methodologies for the analysis of network comparisons and robustness.


Cluster Coefficient Betweenness Centrality Distance Distribution Average Path Length Closeness Centrality 
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.



Research is partially by supported by the Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, CNPq and FAPEMIG, Brazil.


  1. 1.
    Bunke, H.: Recent developments in graph matching. In: Proceedings of the 15th International Conference on Pattern Recognition, vol. 2 (2000).
  2. 2.
    Dehmer, M., Emmert-Streib, F., Kilian, J.: A similarity measure for graphs with low computational complexity. Appl. Math. Comput. 182(1), 447–459 (2006)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Rodrigues, L., Travieso, G., Boas, P.R.V.: Characterization of complex networks: a survey of measurements. Adv. Phys. 56(1), 167–242 (2006)Google Scholar
  4. 4.
    Schaeffer, S.E.: Survey: graph clustering. Comput. Sci. Rev. 1(1), 27–64 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bai, L., Hancock, E.R.: Graph kernels from the Jensen-Shannon divergence. J. Math. Imaging Vis. 47(1–2), 60–69 (2013)CrossRefzbMATHGoogle Scholar
  6. 6.
    Schieber, T.A., Ravetti, M.G.: Simulating the dynamics of scale-free networks via optimization. PLoS ONE 8(12), e80783 (2013)CrossRefGoogle Scholar
  7. 7.
    Babai, L.: Graph isomorphism in quasipolynomial time. Arxiv, January 2016.
  8. 8.
    Carpi, L.C., Saco, P.M., Rosso, O.A., Ravetti, M.G.: Structural evolution of the tropical pacific climate network. Eur. Phys. J. B 85(11), 1–7 (2012). CrossRefGoogle Scholar
  9. 9.
    Schieber, T.A., Carpi, L., Frery, A.C., Rosso, O.A., Pardalos, P.M., Ravetti, M.: Information theory perspective on network robustness. Phys. Lett. A 380(3), 359–364 (2016)CrossRefGoogle Scholar
  10. 10.
    Schieber, T.A., Carpi, L., Ravetti, M., Pardalos, P.M., Massoler, C., Diaz Guilera, A.: A size independent network difference measure based on information theory quantifiers (2016, Unpublished)Google Scholar
  11. 11.
    Carpi, L.C., Rosso, O.A., Saco, P.M., Ravetti, M.: Analyzing complex networks evolution through information theory quantifiers. Phys. Lett. A 375(4), 801–804 (2011). CrossRefzbMATHGoogle Scholar
  12. 12.
    Newman, M.E.J., Strogatz, S.H., Watts, D.J.: Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E 64, 026118 (2001)CrossRefGoogle Scholar
  13. 13.
    Deza, M.M., Deza, E.: Encyclopedia of Distances, p. 590. Springer, Heidelberg (2009)Google Scholar
  14. 14.
    Lewis, T.G.: Network Science: Theory and Applications. Wiley Publishing, Hoboken (2009)CrossRefzbMATHGoogle Scholar
  15. 15.
    Erdös, P., Rényi, A.: On random graphs. Publ. Math. 6(290), 290–297 (1959)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Albert, R., Barabási, A.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002).
  17. 17.
    Frank, O., Strauss, D.: Markov graphs. J. Am. Stat. Assoc. 81(395), 832–842 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(1), 440–442 (1998)CrossRefGoogle Scholar
  19. 19.
    Cox, T.F., Cox, T.F.: Multidimensional Scaling, 2nd edn. Chapman and Hall/CRC, Boca Raton (2000). zbMATHGoogle Scholar
  20. 20.
    Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009). MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Dinh, T.N., Xuan, Y., Thai, M.T., Pardalos, P.M., Znati, T.: On new approaches of assessing network vulnerability: hardness and approximation. IEEE/ACM Trans. Netw. 20(2), 609–619 (2012)CrossRefGoogle Scholar
  22. 22.
    Walteros, J.L., Pardalos, P.M.: A decomposition approach for solving critical clique detection problems. In: Klasing, R. (ed.) SEA 2012. LNCS, vol. 7276, pp. 393–404. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Kunegis, J.: KONECT - the Koblenz network collection. In: Proceedings of International Web Observatory Workshop (2013)Google Scholar
  24. 24.
    Isella, L., Stehlé, J., Barrat, A., Cattuto, C., Pinton, J.F., den Broeck, W.V.: What’s in a crowd? analysis of face-to-face behavioral networks. J. Theor. Biol. 271(1), 166–180 (2011)CrossRefGoogle Scholar
  25. 25.
    Iyer, S., Killingback, T., Sundaram, B., Wang, Z.: Attack robustness and centrality of complex networks. PLoS ONE 8(4), e59613 (2013)CrossRefGoogle Scholar
  26. 26.
    Train bombing network dataset - KONECT, January 2016Google Scholar
  27. 27.
    Hayes, B.: Connecting the dots. Can the tools of graph theory and social-network studies unravel the next big plot? Am. Sci. 94(5), 400–404 (2006)CrossRefGoogle Scholar
  28. 28.
    Lin, J.: Divergence measures based on the Shannon entropy. IEEE Trans. Inf. Theory 37(1), 145–151 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Opsahl, T., Agneessens, F., Skvoretz, J.: Node centrality in weighted networks: generalizing degree and shortest paths. Soc. Netw. 32(3), 245–251 (2010)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Tiago Schieber
    • 1
    • 2
    Email author
  • Martín Ravetti
    • 1
  • Panos M. Pardalos
    • 3
    • 4
  1. 1.Departamento de Engenharia de ProduçãoUniversidade Federal de Minas GeraisBelo HorizonteBrazil
  2. 2.Departamento de Engenharia de ProduçãoPontifícia Universidade Católica de Minas GeraisBelo HorizonteBrazil
  3. 3.Center for Applied Optimization, Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  4. 4.Laboratory of Algorithms and Technologies for Network AnalysisNational Research University Higher School of EconomicsNizhny NovgorodRussia

Personalised recommendations