Robustness of scale-free networks with various parameters against cascading failures

Abstract Many crucial real-world networks could be modeled as scale-free networks, which play an important role in the human society. Once these functional network systems suffer from cascading failures, they may lead to the malfunction of the rest part of networks. In recent years, the researches on cascading failures of scale-free networks have drawn great attention, and many studies focused on modeling the cascading phenomena and studying how to improve the robustness of networks against failures. However, the scale-free networks used in most existing studies are with fixed network parameters including scaling exponent and assortativity, which is segmentary for depicting the functionality of networked systems comprehensively. Therefore, in this paper, a series of generated scale-free networks with a certain range of parameters is adopted to evaluate the robustness against cascading failures. In addition, to make an accurate description of the ability of scale-free networks against cascading failures, we propose a link-based robustness index. The results show that influenced by the network structure, the enlargement of assortativity makes the networks weaker to resist node-based cascading failures, yet the impact on promoting link-based robustness is not clear enough. With higher scaling exponents, the tolerance of scale-free networks against link-based cascading failures decreases, however, it does not show obvious relation to node-based robustness.

[1]  J. Liu,et al.  Robustness of single and interdependent scale-free interaction networks with various parameters , 2016 .

[2]  An Zeng,et al.  Enhancing network robustness for malicious attacks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Kang Rui,et al.  Spatial correlation analysis of cascading failures: Congestions and Blackouts , 2014, Scientific Reports.

[4]  Xiang Li,et al.  Roles of mixing patterns in cooperation on a scale-free networked game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  S. Redner,et al.  Connectivity of growing random networks. , 2000, Physical review letters.

[6]  Y. Lai,et al.  Self-organized scale-free networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[8]  Jing Liu,et al.  A memetic algorithm for enhancing the robustness of scale-free networks against malicious attacks , 2014 .

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

[10]  Xianglong Tang,et al.  Mitigate Cascading Failures on Networks using a Memetic Algorithm , 2016, Scientific Reports.

[11]  Jianwei Wang,et al.  Edge-based-attack induced cascading failures on scale-free networks , 2009 .

[12]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[13]  Jianwei Wang,et al.  Mitigation strategies on scale-free networks against cascading failures , 2013 .

[14]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[16]  David J. Hill,et al.  Attack Vulnerability of Complex Communication Networks , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Wang Pu,et al.  Enhancement of scale-free network attack tolerance ⁄ , 2010 .

[18]  M. A. Muñoz,et al.  Scale-free networks from varying vertex intrinsic fitness. , 2002, Physical review letters.

[19]  Frances M. T. Brazier,et al.  A robustness metric for cascading failures by targeted attacks in power networks , 2013, 2013 10th IEEE INTERNATIONAL CONFERENCE ON NETWORKING, SENSING AND CONTROL (ICNSC).

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

[21]  Shiyong Zhang,et al.  Robustness of networks against cascading failures , 2010 .

[22]  Margaret J. Eppstein,et al.  Evolutionary Dynamics on Scale-Free Interaction Networks , 2009, IEEE Transactions on Evolutionary Computation.

[23]  Liang Zhang,et al.  Attack vulnerability of scale-free networks due to cascading failures , 2008 .

[24]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[25]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[26]  J. Gómez-Gardeñes,et al.  Robustness of cooperation in the evolutionary prisoner's dilemma on complex networks , 2007, q-bio/0703019.

[27]  V. Jacobson,et al.  Congestion avoidance and control , 1988, CCRV.

[28]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[29]  G. Caldarelli,et al.  Vertex intrinsic fitness: how to produce arbitrary scale-free networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Bo Xu,et al.  Ability paradox of cascading model based on betweenness , 2015, Scientific Reports.

[31]  H E Stanley,et al.  Recovery of Interdependent Networks , 2015, Scientific Reports.

[32]  G. Bimonte.  Johnson noise and the thermal Casimir effect , 2007, 0705.2317.