Ability paradox of cascading model based on betweenness

Must Investing more resources to protect every node in a network improve the robustness of the whole network subject to target attacks? To answer this question, we investigate the cascading dynamics in some typical networks. In real networks, the load on a node is generally correlated with the betweenness. Considering the weight of a node, we give a new method to define the initial load on a node by the revised betweenness. Then we present a simple cascading model. We investigate the cascading dynamics by disabling a single key node with the highest load. We find that in BA scale-free networks, the bigger the capacity of every node, the stronger the robustness of the whole network. However, in WS networks and some random networks, when we increase the capacity of every node, instead, the robustness of the whole network is weaker. In US power grid and the China power grid, we also observe this counterintuitive phenomenon. We give a reasonable explanation by a simple illusion. By the analysis, we think that resurrections of some nodes in a ring network structure after removing a node may be the reason of this phenomenon.

[1]  Guanrong Chen,et al.  Universal robustness characteristic of weighted networks against cascading failure. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Haipeng Peng,et al.  Robustness of Interrelated Traffic Networks to Cascading Failures , 2014, Scientific Reports.

[3]  Jian-Wei Wang,et al.  Robustness of the western United States power grid under edge attack strategies due to cascading failures , 2011 .

[4]  Jianwei Wang,et al.  Attack robustness of cascading model with node weight , 2014 .

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

[6]  Tao Zhou,et al.  Perturbation: the Catastrophe Causer in Scale-Free Networks , 2004 .

[7]  D S Callaway,et al.  Network robustness and fragility: percolation on random graphs. , 2000, Physical review letters.

[8]  Jian Xu,et al.  Cascading failures in coupled map lattices. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Jianwei Wang,et al.  OPTIMIZED SCALE-FREE NETWORKS AGAINST CASCADING FAILURES , 2012 .

[10]  Dirk Helbing,et al.  Transient dynamics increasing network vulnerability to cascading failures. , 2007, Physical review letters.

[11]  R Pastor-Satorras,et al.  Dynamical and correlation properties of the internet. , 2001, Physical review letters.

[12]  S. Buldyrev,et al.  Interdependent networks with identical degrees of mutually dependent nodes. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Leonardo Dueñas-Osorio,et al.  Cascading failures in complex infrastructure systems , 2009 .

[14]  Chen Hong,et al.  Improving the network robustness against cascading failures by adding links , 2013 .

[15]  H. Herrmann,et al.  How to Make a Fragile Network Robust and Vice Versa , 2009, Physical review letters.

[16]  Baharan Mirzasoleiman,et al.  Cascaded failures in weighted networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[18]  Sakshi Pahwa,et al.  Optimal intentional islanding to enhance the robustness of power grid networks , 2013 .

[19]  Massimo Marchiori,et al.  Model for cascading failures in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Zhiming Zheng,et al.  Searching for superspreaders of information in real-world social media , 2014, Scientific Reports.

[21]  Sakshi Pahwa,et al.  Abruptness of Cascade Failures in Power Grids , 2014, Scientific Reports.

[22]  Alessandro Vespignani,et al.  Complex networks: The fragility of interdependency , 2010, Nature.

[23]  Dirk Helbing,et al.  Efficient response to cascading disaster spreading. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Jianwei Wang,et al.  Mitigation of cascading failures on complex networks , 2012, Nonlinear Dynamics.

[25]  D. Newth,et al.  Optimizing complex networks for resilience against cascading failure , 2007 .

[26]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[27]  Harry Eugene Stanley,et al.  Assortativity Decreases the Robustness of Interdependent Networks , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Hernán A. Makse,et al.  A review of fractality and self-similarity in complex networks , 2007 .

[29]  Adilson E Motter.  Cascade control and defense in complex networks. , 2004, Physical review letters.

[30]  Wolfgang A. Halang,et al.  Understanding the cascading failures in Indian power grids with complex networks theory , 2013 .

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

[32]  Doyle,et al.  Highly optimized tolerance: robustness and design in complex systems , 2000, Physical review letters.

[33]  Lixiang Li,et al.  Revealing the process of edge-based-attack cascading failures , 2012 .

[34]  Martin Greiner,et al.  Proactive robustness control of heterogeneously loaded networks. , 2006, Physical review letters.

[35]  Chen Jiang,et al.  Robustness of interdependent networks with different link patterns against cascading failures , 2014 .

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

[37]  S. Havlin,et al.  Interdependent networks: reducing the coupling strength leads to a change from a first to second order percolation transition. , 2010, Physical review letters.

[38]  Zhou Tao,et al.  Catastrophes in Scale-Free Networks , 2005 .

[39]  Liang Chang,et al.  Performance and reliability of electrical power grids under cascading failures , 2011 .

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

[41]  M. Perc.  Evolution of cooperation on scale-free networks subject to error and attack , 2009, 0902.4661.

[42]  Kaiquan Cai,et al.  Effective usage of shortest paths promotes transportation efficiency on scale-free networks , 2013 .

[43]  Zhejing Bao,et al.  Dynamics of load entropy during cascading failure propagation in scale-free networks , 2008 .

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

[45]  Wen-Bo Du,et al.  Particle Swarm Optimization with Scale-Free Interactions , 2014, PloS one.

[46]  Réka Albert,et al.  Structural vulnerability of the North American power grid. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  M. L. Sachtjen,et al.  Disturbances in a power transmission system , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  J. S. Andrade,et al.  Avoiding catastrophic failure in correlated networks of networks , 2014, Nature Physics.

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

[50]  Martí Rosas-Casals,et al.  Robustness of the European power grids under intentional attack. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Ying-Cheng Lai,et al.  Attack vulnerability of scale-free networks due to cascading breakdown. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Guanrong Chen,et al.  Optimal weighting scheme for suppressing cascades and traffic congestion in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Wei Li,et al.  Cascading Failures in Interdependent Lattice Networks: The Critical Role of the Length of Dependency Links , 2012, Physical review letters.

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

[55]  Jian-Wei Wang,et al.  Cascade-based attack vulnerability on the US power grid. , 2009 .

[56]  K-I Goh,et al.  Fluctuation-driven dynamics of the internet topology. , 2002, Physical review letters.

[57]  Ying-Cheng Lai,et al.  Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks. , 2011, Chaos.

[58]  Reuven Cohen,et al.  Percolation in Interdependent and Interconnected Networks: Abrupt Change from Second to First Order Transition , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[60]  Harry Eugene Stanley,et al.  Robustness of a Network of Networks , 2010, Physical review letters.

[61]  Bing Wang,et al.  A high-robustness and low-cost model for cascading failures , 2007, 0704.0345.

[62]  Zhi-Xi Wu,et al.  Cascading failure spreading on weighted heterogeneous networks , 2008 .

[63]  E A Leicht,et al.  Suppressing cascades of load in interdependent networks , 2011, Proceedings of the National Academy of Sciences.

[64]  Nong Ye,et al.  Tolerance of scale-free networks against attack-induced cascades. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.