Social Network Analysis and Mining

, Volume 3, Issue 4, pp 939–952 | Cite as

Quantifying topological robustness of networks under sustained targeted attacks

  • Mahendra Piraveenan
  • Gnana Thedchanamoorthy
  • Shahadat Uddin
  • Kon Shing Kenneth Chung
Original Article


In this paper, we introduce a measure to analyse the structural robustness of complex networks, which is specifically applicable in scenarios of targeted, sustained attacks. The measure is based on the changing size of the largest component as the network goes through disintegration. We argue that the measure can be used to quantify and compare the effectiveness of various attack strategies. Applying this measure, we confirm the result that scale-free networks are comparatively less vulnerable to random attacks and more vulnerable to targeted attacks. Then we analyse the robustness of a range of real world networks, and show that most real world networks are least robust to attacks based on betweenness of nodes. We also show that the robustness values of some networks are more sensitive to the attack strategy as compared to others. Furthermore, robustness coefficient computed using two centrality measures may be similar, even when the computational complexities of calculating these centrality measures may be different. Given this disparity, the robustness coefficient introduced potentially plays a key role in choosing attack and defence strategies for real world networks. While the measure is applicable to all types of complex networks, we clearly demonstrate its relevance to social network analysis.


Complex networks Robustness Social networks 


  1. Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97CrossRefMATHGoogle Scholar
  2. Albert R, Jeong H, Barabási AL (2000) Error and attack tolerance of complex networks. Nature 406:378–382CrossRefGoogle Scholar
  3. Alon U (2007) Introduction to systems biology: design principles of biological circuits. Chapman and Hall, LondonGoogle Scholar
  4. Baumbach J (2007) Coryneregnet 4.0-a reference database for corynebacterial gene regulatory networks. BMC Bioinf 8Google Scholar
  5. Bonacich P (2001) Eigenvector-like measures of centrality for asymmetric relations. Soc Netw 23(3):191–201MathSciNetCrossRefGoogle Scholar
  6. Cazabet R, Takeda H, Hamasaki M, Amblard F (2012) Using dynamic community detection to identify trends in user-generated content. Soc Netw Anal Min 2(4):361–371CrossRefGoogle Scholar
  7. Colizza V, Flammini A, Serrano MA, Vespignani A (2006) Detecting rich-club ordering in complex networks. Nat Phys 2:110–115CrossRefGoogle Scholar
  8. Collations of connectivity data on the Macaque brain (2009) URL:
  9. Costa LDF, Rodrigues FA, Travieso G, Villas Boas PR (2007) Characterization of complex networks: a survey of measurements. Adv Phys 56(1):167–242CrossRefGoogle Scholar
  10. Crucittia P, Latora V, Marchiori M, Rapisarda A (2004) Error and attack tolerance of complex networks. Phys A 340:388–394MathSciNetCrossRefGoogle Scholar
  11. Dekker AH, Colbert BD (2004) Network robustness and graph topology. In: Proceedings of the 27th Australasian conference on computer science. ACSC ’04, vol 26, Australian Computer Society Inc., Darlinghurst, pp 359–368Google Scholar
  12. Dorogovtsev SN, Mendes JFF (2003) Evolution of networks: from biological nets to the internet and WWW. Oxford University Press, OxfordGoogle Scholar
  13. Gilbert F, Simonetto P, Zaidi F, Jourdan F, Bourqui R (2011) Communities and hierarchical structures in dynamic social networks: analysis and visualization. Soc Netw Anal Min 1(2):83–95CrossRefGoogle Scholar
  14. Gleiser P, Danon L (2003) Adv Complex Syst 6:565CrossRefGoogle Scholar
  15. Hanley JA, Mcneil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143(1):29–36Google Scholar
  16. Junker BH, Schreiber F (2008) Analysis of biological networks (Wiley Series in Bioinformatics). Wiley, New YorkGoogle Scholar
  17. Kepes F (2007) (ed) Biological networks. World Scientific, SingaporeGoogle Scholar
  18. Kreyszig E (2005) Advanced engineering mathematics, 9th edn. Wiley, New YorkGoogle Scholar
  19. Lusseau D, Schneider K, Boisseau OJ, Haase P, Slooten E, Dawson SM (2003) Dolphin social network. Behav Ecol Sociobiol 54Google Scholar
  20. Michigan Molecular Interaction Database (2008) University of Michigan URL:
  21. Milgram S (1967) The small world problem. Psychol Today 1:61Google Scholar
  22. Newman MEJ (2002) Assortative mixing in networks. Phys Rev Lett 89(20):208–701CrossRefGoogle Scholar
  23. Newman MEJ (2005) A measure of betweenness centrality based on random walks. Soc Netw 27(1):39–54CrossRefGoogle Scholar
  24. Ng AKS, Efstathiou J (2006) Structural robustness of complex networks. Phys Rev 3:175–188Google Scholar
  25. Noh JD Rieger H (2004) Random walks on complex networks. Phys Rev Lett 92:118–701CrossRefGoogle Scholar
  26. Piraveenan M, Prokopenko M, Zomaya AY (2008) Local assortativeness in scale-free networks. Europhys Lett 84(2):28–002CrossRefGoogle Scholar
  27. Piraveenan M, Prokopenko M, Zomaya AY (2009) Assortativity and growth of Internet. Eur Phys J B 70:275–285CrossRefGoogle Scholar
  28. Piraveenan M, Prokopenko M, Zomaya AY (2010) Local assortativeness in scale-free networks—addendum. Europhys Lett 89(4):49–901CrossRefGoogle Scholar
  29. Rees BS, Gallagher KB (2012) Overlapping community detection using a community optimized graph swarm. Soc Netw Anal Min 2(4):405–417CrossRefGoogle Scholar
  30. Solé RV, Valverde S (2004) Information theory of complex networks: on evolution and architectural constraints. Complex networks In: Ben-Naim E, Frauenfelder H, Toroczkai Z (eds) Lecture notes in physics, vol 650. Springer, BerlinGoogle Scholar
  31. Tang A, Honey C, Hobbs J, Sher A, Litke A, Sporns O, Beggs J (2008) Information flow in local cortical networks is not democratic. BMC Neurosc 9(Suppl 1):O3Google Scholar
  32. Venkatasubramanian V, Katare S, Patkar PR, Mu F (2004) Spontaneous emergence of complex optimal networks through evolutionary adaptation. CoRR nlin.AO/0402046Google Scholar
  33. Watts DJ, Strogatz SH (1998) Collective dynamics of small-world networks. Nature 393(6684):440–442CrossRefGoogle Scholar
  34. Zachary W (1977) An information flow model for conflict and fission in small groups. J Anthropol Res 33:452–473Google Scholar
  35. Zaidi F (2013) Small world networks and clustered small world networks with random connectivity. Soc Netw Anal Min 3(1):51–63CrossRefGoogle Scholar
  36. Zhou S, Mondragón RJ (2004) The rich-club phenomenon in the internet topology. IEEE Commun Lett 8:180–182CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Mahendra Piraveenan
    • 1
  • Gnana Thedchanamoorthy
    • 1
  • Shahadat Uddin
    • 1
  • Kon Shing Kenneth Chung
    • 1
  1. 1.Centre for Complex Systems Research, Faculty of Engineering and ITThe University of SydneySydney Australia

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