Cascade defense via navigation in scale free networks

Abstract.In this paper, we investigate cascade defense and control in scale free networks via navigation strategy. It is found that with an appropriate parameter a, which is tunable in controlling the effect of degree in the navigation strategy, one can reduce the risk of cascade break down. By checking the distribution of efficient betweenness centrality (EBC) and the average EBC of vertices with degree k, the validity can be guaranteed. Despite the advantage of cascade defense, the degree based navigation strategy may also lead to lower network efficiency. To avoid this disadvantage, we propose a new navigation strategy. Importantly and interestingly, the new strategy can defend cascade break down effectively even without reducing the network efficiency. Distribution of the EBC and EBC-degree correlation of the new strategy are also investigated to explain the effectiveness in cascade defense.

[1]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[2]  Tao Zhou,et al.  Traffic dynamics based on local routing protocol on a scale-free network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  V. Latora,et al.  Efficiency of scale-free networks: error and attack tolerance , 2002, cond-mat/0205601.

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

[5]  Nong Ye,et al.  Onset of traffic congestion in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  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.

[8]  G. J. Rodgers,et al.  Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  H. Stanley,et al.  Optimal paths in disordered complex networks. , 2003, Physical review letters.

[10]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

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

[12]  Alexandre Arenas,et al.  Optimal network topologies for local search with congestion , 2002, Physical review letters.

[13]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[14]  Petter Holme.  Edge overload breakdown in evolving networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

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

[17]  Hawoong Jeong,et al.  Classification of scale-free networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Tao Zhou,et al.  Efficient routing on scale-free networks based on local information , 2006 .

[19]  Alessandro Vespignani,et al.  Evolution and Structure of the Internet: A Statistical Physics Approach , 2004 .

[20]  K. Goh,et al.  Robustness of the avalanche dynamics in data-packet transport on scale-free networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  K Sneppen,et al.  Networks and cities: an information perspective. , 2005, Physical review letters.

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

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

[24]  A Díaz-Guilera,et al.  Communication in networks with hierarchical branching. , 2001, Physical review letters.

[25]  Xiao Fan Wang,et al.  Effects of network structure and routing strategy on network capacity. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Bo Hu,et al.  Efficient routing on complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  B. Tadić.  Dynamics of directed graphs: the world-wide Web , 2000, cond-mat/0011442.

[28]  Wen-Xu Wang,et al.  Traffic dynamics based on an efficient routing strategy on scale free networks , 2006 .

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

[30]  A. Clauset,et al.  Scale invariance in road networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Wen-Xu Wang,et al.  Integrating local static and dynamic information for routing traffic. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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