Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:A2L-B

Session:

Number:102

Analytical Approach to the Robustness of Strongly Correlated Complex Networks

Toshihiro Tanizawa,  Shlomo Havlin,  H. Eugene Stanley,  

pp.102-105

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.102

PDF download (487.2KB)

The robustness of complex networks against external perturbations, such as node and/or link removal, is critical for the functioning of a complex network and has been studied through various approaches. Most analytical work assumes, for simplicity, that there is no specific correlation in connecting nodes, because of the difficulty and complexity in treating correlation between node connections properly. Since many networks in the real world do have such correlation, we focus on deriving analytical equations for calculating the threshold and the giant component fraction for networks having degree-degree correlations against arbitrary strategies of node removal. As an example of the analyses using these expressions, we show how the vulnerability of scale-free networks against targeted node removal can be significantly improved by taking the structure in which the nodes with almost the same degree are connected to each other. Our analytic calculations are verified by numerical simulations.

[1] R. Albert, H. Jeong, and A.-L. Barabási. Error and attack tolerance of complex networks. Nature (London), 406:378-382, Feb 2000.

[2] D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts. Network Robustness and Fragility: Percolation on Random Graphs. Phys. Rev. Lett., 85:5468-5471, Dec. 2000.

[3] R. Cohen, K. Erez, D. ben Avraham, and S. Havlin. Resilience of the Internet to Random Breakdowns. Phys. Rev. Lett., 85(21):4626-4628, Nov. 2000.

[4] R. Cohen, K. Erez, D. ben Avraham, and S. Havlin. Breakdown of the Internet under Intentional Attack. Phys. Rev. Lett., 86(16):3682-3685, Apr. 2001.

[5] A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes. Percolation on correlated networks. Phys. Rev. E, 78(5):051105, Nov. 2008.

[6] H. J. Herrmann, C. M. Schneider, A. A. Moreira, J. S. Andrade Jr, and S. Havlin. Onion-like network topology enhances robustness against malicious attacks. Journal of Statistical Mechanics: Theory and Experiment, 2011(01):P01027, Jan. 2011.

[7] C. M. Schneider, A. A. Moreira, J. S. Andrade Jr, S. Havlin, and H. J. Herrmann. Mitigation of malicious attacks on networks. PNAS, 108(10):3838-3841, Feb. 2011.

[8] T. Tanizawa, S. Havlin, and H. E. Stanley. Robustness of onion-like correlated networks against targeted attacks. Phys. Rev. E, 85(4):046109, Mar. 2012.