Analysis of Robustness of Complex Networks based on Optimization Theory

The analysis of robustness of complex networks tries to find out the relation between the structure of a complex network and its robustness performance, which will be beneficial to some work such as network design. The robustness measurement of a complex network is defined at first to evaluate its robustness performance. Then a framework is put forward for robustness analysis of complex networks. The framework analyzes the impacts of structural parameters of a complex network on its robustness by comparing the network structures and its robustness performance before and after optimization. These network structural parameters include the degree distribution, the average clustering coefficient, the network efficiency and so on. An optimization method based on the variable neighborhood search method is developed to solve the network optimization problem appearing in the framework. Finally, through the application of this analytical framework, it is found that if the degree of nodes in a complex network tends to be consistent, then the upper bound of the robustness measurement of the network will increase. In addition, the regression relationships between the robustness measurement and some structural parameters of the network, such as the average clustering coefficient, the network efficiency and so on, will become evident.

[1]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[2]  M. Weigt,et al.  On the properties of small-world network models , 1999, cond-mat/9903411.

[3]  Michele Bellingeri,et al.  Efficiency of attack strategies on complex model and real-world networks , 2013, ArXiv.

[4]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[5]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[6]  S. Havlin,et al.  Optimization of network robustness to waves of targeted and random attacks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Tom Fleischer.  Handbook Of Optimization In Complex Networks Theory And Applications , 2016 .

[8]  Mauricio Barahona,et al.  Spectral Measure of Structural Robustness in Complex Networks , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[9]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[10]  Minas Gjoka,et al.  2.5K-graphs: From sampling to generation , 2012, 2013 Proceedings IEEE INFOCOM.

[11]  K. Sneppen,et al.  Detection of topological patterns in complex networks: correlation profile of the internet , 2002, cond-mat/0205379.

[12]  Beom Jun Kim,et al.  Attack vulnerability of complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Jiang Yu,et al.  Analysis of attack and defense strategies on complex networks , 2013, PROCEEDINGS OF 2013 International Conference on Sensor Network Security Technology and Privacy Communication System.

[14]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[15]  Damien Fay,et al.  Propagation Phenomena in Real World Networks , 2015, Propagation Phenomena in Real World Networks.

[16]  Yong Li,et al.  ATTACK VULNERABILITY OF COMPLEX NETWORKS BASED ON LOCAL INFORMATION , 2007 .

[17]  Adilson E Motter,et al.  Introduction: optimization in networks. , 2007, Chaos.

[18]  Pramode K. Verma,et al.  Topological resilience of complex networks against failure and attack , 2011, 2011 Fifth IEEE International Conference on Advanced Telecommunication Systems and Networks (ANTS).

[19]  H. Stanley,et al.  Optimization of network robustness to random breakdowns , 2005, cond-mat/0507249.

[20]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[21]  Albert-László Barabási,et al.  Scale-Free Networks: A Decade and Beyond , 2009, Science.

[22]  Kon Shing Kenneth Chung,et al.  Quantifying topological robustness of networks under sustained targeted attacks , 2013, Social Network Analysis and Mining.

[23]  T. Tanizawa,et al.  Optimization of robustness of complex networks , 2005 .

[24]  Marco Tomassini,et al.  Smart Rewiring for Network Robustness , 2013, J. Complex Networks.

[25]  Abhijit Sarkar,et al.  Two-peak and three-peak optimal complex networks. , 2004, Physical review letters.

[26]  Hans J. Herrmann,et al.  Mitigation of malicious attacks on networks , 2011, Proceedings of the National Academy of Sciences.

[27]  Wu Jun,et al.  Natural Connectivity of Complex Networks , 2010 .

[28]  Piraveenan Mahendra,et al.  On the Influence of Topological Characteristics on Robustness of Complex Networks , 2013, J. Artif. Intell. Soft Comput. Res..