In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.
 R. Albert and A.-L. Barabási, “Statistical mechanics of complex networks,” Reviews of Modern Physics, vol. 74, pp. 47-97, 2002.
 U. Alon, Introduction to Systems Biology: Design Principles of Biological Circuits. London: Chapman and Hall, 2007.
 S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks: From Biological Nets to the Internet andWWW. Oxford: Oxford University Press, January 2003.
 F. Kepes (Ed), Biological Networks. Singapore: World Scientific, 2007.
 J. Park and M. E. J. Newman, “Statistical mechanics of networks,” Physical Review E, vol. 70, no. 6, pp. 066 117+, Dec 2004. [Online]. Available: http://dx.doi.org/10.1103/PhysRevE.70.066117
 M. Piraveenan, M. Prokopenko, and A. Y. Zomaya, “Assortative mixing in directed biological networks,” IEEE/ACM Transactions on computational biology and bioinformatics, vol. 9(1), pp. 66-78, 2012.
 M. Piraveenan, M. Prokopenko, and L. Hossain, “Percolation centrality: Quantifying graphtheoretic impact of nodes during percolation in networks,” PloS one, vol. 8, no. 1, p. e53095, 2013.
 M. Piraveenan, M. Prokopenko, and A. Zomaya, “On congruity of nodes and assortative information content in complex networks,” Networks and Heterogeneous Media (NHM), vol. 3, no. 10.3934/nhm.2012.7.441, pp. 441-461, 2012.
 R. V. Sol´e and S. Valverde, “Information theory of complex networks: on evolution and architectural constraints,” in Complex Networks, ser. Lecture Notes in Physics, E. Ben-Naim, H. Frauenfelder, and Z. Toroczkai, Eds. Springer, 2004, vol. 650.
 R. Albert, H. Jeong, and A.-L. Barab´asi, “Error and attack tolerance of complex networks,” Nature, vol. 406, pp. 378-382, 2000.
 A.-L. Barabáasi, “Scale-free networks: A decade and beyond,” Science, vol. 325, no. 5939, pp. 412-413, 2009.
 A.-L. Barabáasi, R. Albert, and H. Jeong, “Scalefree characteristics of random networks: The topology of the world-wide web,” Physica A, vol. 281, pp. 69-77, 2000.
 A.-L. Barabáasi and E. Bonabeau, “Scale-free networks,” Scientific American, vol. 288, pp. 50-59, 2003.
 A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini, and M. Viale, “Scale-free correlations in bird flocks,” 2009, arXiv:0911.4393. [Online]. Available: http://arxiv.org/abs/0911.4393
 M. Mitchell, “Complex systems: Network thinking,” Artificial Intelligence, vol. 170, no. 18, pp. 1194-1212, 2006.
 D. J. Watts and S. H. Strogatz, “Collective dynamics of ’small-world’ networks,” Nature, vol. 393, pp. 440-442, 1998.
 A. Jamakovic and S. Uhlig, “Influence of the network structure on robustness,” in Networks, 2007. ICON 2007. 15th IEEE International Conference on. IEEE, 2007, pp. 278-283.
 M. E. J. Newman, “Mixing patterns in networks,” Physical Review E, vol. 67, no. 2, p. 026126, 2003.
 M. Piraveenan, M. Prokopenko, and A. Y. Zomaya, “Local assortativeness in scale-free networks,” Europhysics Letters, vol. 84, no. 2, p. 28002, 2008.
 --, “Local assortativeness in scale-free networks - addendum,” Europhysics Letters, vol. 89, no. 4, p. 49901, 2010.
 V. Latora and M. Marchiori, “Efficient behavior of small-world networks,” Physical Review Letters, vol. 87, no. 19, p. 198701, 2001.
 M. E. J. Newman, “Models of the small world,” Journal of Statistical Physics, vol. 101, no. 3, pp. 819-841, November 2000. [Online]. Available: http://dx.doi.org/10.1023/A:1026485807148
 D. J. Watts and S. H. Strogatz, “Collective dynamics of small-world networks,” Nature, vol. 393, no. 6684, pp. 440-442, June 1998. [Online]. Available: http://dx.doi.org/10.1038/30918
 R. Albert, H. Jeong, and A.-L. Barab´asi, “Error and attack tolerance of complex networks,” Nature, vol. 406, no. 6794, pp. 378-382, 2000.
 P. Crucittia, V. Latora, M. Marchiori, and A. Rapisarda, “Error and attack tolerance of complex networks,” Physica A, vol. 340, p. 388394, 2004.
 A. H. Dekker and B. D. Colbert, “Network robustness and graph topology,” in Proceedings of the 27th Australasian conference on Computer science - Volume 26, ser. ACSC ’04. Darlinghurst, Australia, Australia: Australian Computer Society, Inc., 2004, pp. 359-368.
 M. Piraveenan, G. Thedchanamoorthy, S. Uddin, and K. S. K. Chung, “Quantifying topological robustness of networks under sustained targeted attacks,” Social Network Analysis and Mining, 2013. [Online]. Available: 10.1007/s13278-013-0118-8
 J. A. Hanley and B. J. Mcneil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve.” Radiology, vol. 143, no. 1, pp. 29-36, Apr. 1982.
 E. Kreyszig, Advanced Engineering Mathematics, 9th Edition. John Wiley, December 2005.
 M. E. J. Newman, “Assortative mixing in networks,” Physical Review Letters, vol. 89, no. 20, p. 208701, 2002.
 M. Piraveenan, S. Uddin, and K. S. K. Chung, “Measuring topological robustness of networks under sustained targeted attacks,” in 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining. New York: IEEE Computer Society, 2012.
 S. Sarkar and A. Dong, “Characterizing modularity, hierarchy and module interfacing in complex design systems,” in ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2011), vol. 9: 23rd International Conference on Design Theory and Methodology; 16th Design for Manufacturing and the Life Cycle Conference. New York: ASME, 2011, pp. 375-384.
 J. T. Lizier, M. Piraveenan, D. Pradhana, M. Prokopenko, and L. S. Yaeger, “Functional and structural topologies in evolved neural networks,” in Advances in Artificial Life: Tenth European Conference on Artificial Life (ECAL ’09), ser. LNCS/LNAI. Springer, 2009, vol. 5777-5778.
 S. Milgram, “The small world problem,” Psychology Today, vol. 1, p. 61, 1967.