近年來，複雜網路的強健性成為了一個非常熱門且重要的研究題目。在這篇論文裡，我們利用了幾種傳統的複雜網路模型對現實中的網路進行分類。並使用了臨界值對網路在遭遇各種不同形式攻擊的強健性進行評估。最後，我們使用了循序防禦對各種攻擊進行防禦，並使用不同的防禦順序，再分析每種防禦順序的效能。在攻擊的方面Degree與Ego指標能取得一個不錯的效能。而在偵測層面，Degree是一個比較泛用的防禦順序。

In recent year, network robustness against attack is an important research. In this paper, we find some canonical complex network models and use them to group some real-world networks. The network robustness is evaluated under some different attack schemes by critical value. We use real-world networks data to compare each network models and attack schemes. Degree Centrality attack and Ego Centrality attack have unexpectedly great performances. Next we use the sequential defense with different centrality to detect the different attack scheme. Degree Centrality attack is generic defense order.

[1] R. Albert and A.-L. Barabási, “Statistical mechanics of complex networks,”
Rev. of Modern Phys., vol. 74, no. 1, pp. 47–97, Jan. 2002.
[2] M. E. J. Newman, “The structure and function of complex networks,” SIAM
Rev., vol. 45, no. 2, pp. 167–256, Mar. 2003.
[3] X. F. Wang and G. Chen, “Complex networks: small-world, scale-free and
beyond,” IEEE Circuits Syst. Mag., vol. 3, no. 1, pp. 6–20, Sept. 2003.
[4] T. F. Coleman and J. J. Moré, “Estimation of sparse jacobian matrices and
graph coloring blems,” SIAM Journal on Numerical Analysis, vol. 20, no. 1,
pp. 187–209, Feb. 1983.
[5] R. Albert, H. Jeong, and A.-L. Barabśi, “Error and attack tolerance of complex
networks,” Nature, vol. 406, no. 6794, pp. 378–382, July 2000.
[6] 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.,
vol. 85, no. 25, pp. 5468–5471, Dec. 2000.
[7] M. Molloy and B. Reed, “A critical point for random graphs with a given degree
sequence,” Random Struct. Algorithms, vol. 6, pp. 161–179, Mar. 1995.
[8] B. R. da Cunha, J. C. González-Avella, and S. Gonçalves, “Complex networks
vulnerability to module-based attacks,” arXiv:1502.00353 [physics.soc-ph], Feb.
2015.
[9] V. D. Blondel, J.-L. Guillaume, R. Lambiotte, and E. Lefebvre, “Fast unfolding
of communities in large networks,” journal of statistical mechanics: theory and
experiment, vol. 2008, no. 10, p. P10008, Oct. 2008.
[10] P.-Y. chen and S.-M. Cheng, “Sequential defense against random and inten-
tional attacks in complex networks,” Phys. Rev. E, vol. 91, p. 022805, Feb.
2015.
[11] P.-Y. Chen and K.-C. Chen, “Intentional attack and fusion-based defense strat-
egy in complex networks,” in IEEE GLOBECOM 2011, Dec. 2011, pp. 1–5.
[12] P. Erdös and A. Rényi, “On random graphs, I,” Publicationes Mathematicae
(Debrecen), vol. 6, pp. 290–297, Jan. 1959.
[13] J.-P. Onnela, J. Saramäki, J. Hyvönen, G. Szabó, D. Lazer, K. Kaski,
J. Kertész, and A.-L. Barabási, “Structure and tie strengths in mobile com-
munication networks,” in Proc. PNAS 2007, vol. 104, no. 18, Jan. 2007, pp.
7332–7336.
[14] A.-L. Barabási and R. Albert, “Emergence of scaling in random networks,”
Science, vol. 286, no. 5439, pp. 509–512, Oct. 1999.
[15] M. Faloutsos, P. Faloutsos, and C. Faloutsos, “On power-law relationships of
the Internet topology,” in Proc. ACM SIGCOMM, Oct. 1999, pp. 251–262.
[16] R. V. Solé, M. Rosas-Casals, B. Corominas-Murtra, and S. Valverde, “Robust-
ness of the European power grids under intentional attack,” Phys. Rev. E,
vol. 77, p. 026102, Feb. 2008.
[17] L. Freeman, “A set of measures of centrality based on betweenness,” Sociometry,
vol. 40, pp. 35–41, Mar. 1977.
[18] G. Sabidussi, “The centrality index of a graph,” Psychometrika, vol. 31, no. 4,
pp. 581–603, Feb. 1966.
[19] M. Everett and S. P. Borgatti, “Ego network betweenness,” Social Networks,
vol. 27, no. 1, pp. 31–38, Jan. 2005.
[20] P.-Y. Chen and A. O. Hero, “Local fiedler vector centrality for detection of deep
and overlapping communities in networks,” in Proc. IEEE ICASSP 2014, May
2014, pp. 1120–1124.
[21] A. Wald, Sequential analysis, 1973.
[22] “Caida network dataset – KONECT,” Jan. 2016. [Online]. Available:
http://konect.uni-koblenz.de/networks/as-caida20071105
[23] J.
Kunegis,
“KONECT
–
The
Koblenz
Network
Collection,”
in
Proc. Int. Conf. on World Wide Web Companion, 2013, pp. 1343–
1350. [Online]. Available:
http://userpages.uni-koblenz.de/~kunegis/paper/
kunegis-koblenz-network-collection.pdf
[24] J. Leskovec and A. Krevl, “SNAP Datasets: Stanford large network dataset
collection,” June 2014. [Online]. Available: http://snap.stanford.edu/data
[25] “Protein network dataset – KONECT,” Jan. 2016. [Online]. Available:
http://konect.uni-koblenz.de/networks/moreno_propro
[26] S. Coulomb, M. Bauer, D. Bernard, and M.-C. Marsolier-Kergoat, “Gene es-
sentiality and the topology of protein interaction networks,” Proceedings of the
Royal Society B: Biological Sciences, vol. 272, no. 1573, pp. 1721–1725, Aug.
2005.
[27] J.-D. J. Han, D. Dupuy, N. Bertin, M. E. Cusick, and M. Vidal, “Effect of sam-
pling on topology predictions of protein-protein interaction networks,” Nature
Biotechnology, vol. 23, no. 7, pp. 839–844, July 2005.
[28] M. P. Stumpf, C. Wiuf, and R. M. May, “Subnets of scale-free networks are
not scale-free: Sampling properties of networks,” in Proc. PNAS 2005, vol. 102,
no. 12, Feb. 2005, pp. 4221–4224.
[29] “Reactome network dataset – KONECT,” Jan. 2016. [Online]. Available:
http://konect.uni-koblenz.de/networks/reactome
[30] G. Joshi-Tope, M. Gillespie, I. Vastrik, P. D’Eustachio, E. Schmidt, B. de Bono,
B. Jassal, G. Gopinath, G. Wu, L. Matthews, et al., “Reactome: A knowledge-
base of biological pathways,” Nucleic Acids Research, vol. 33, no. suppl 1, pp.
D428–D432, Jan. 2005.
[31] “Route views network dataset – KONECT,” May 2014. [Online]. Available:
http://konect.uni-koblenz.de/networks/as20000102
[32] “Us power grid network dataset – KONECT,” Oct. 2014. [Online]. Available:
http://konect.uni-koblenz.de/networks/opsahl-powergrid