Optimization of network structure to random failures

Network's resilience to the malfunction of its components has been of great concern. The goal of this work is to determine the network design guidelines, which maximizes the network efficiency while keeping the cost of the network (that is the average connectivity) constant. With a global optimization method, memory tabu search (MTS), we get the optimal network structure with the approximately best efficiency. We analyze the statistical characters of the network and find that a network with a small quantity of hub nodes, high degree of clustering may be much more resilient to perturbations than a random network and the optimal network is one kind of highly heterogeneous networks. The results strongly suggest that networks with higher efficiency are more robust to random failures. In addition, we propose a simple model to describe the statistical properties of the optimal network and investigate the synchronizability of this model.

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

[2]  Damien Magoni,et al.  Tearing down the Internet , 2003, IEEE J. Sel. Areas Commun..

[3]  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.

[4]  Elmer S. West.  From the U. S. A. , 1965 .

[5]  Beom Jun Kim,et al.  Factors that predict better synchronizability on complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  M. A. Muñoz,et al.  Entangled networks, synchronization, and optimal network topology. , 2005, Physical review letters.

[7]  Reuven Cohen,et al.  Tolerance of scale-free networks: from friendly to intentional attack strategies , 2004 .

[8]  Jian-Guo Liu,et al.  Optimization of Robustness of Scale-Free Network to Random and Targeted Attacks , 2005 .

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

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

[11]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[12]  S. Strogatz.  Exploring complex networks , 2001, Nature.

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

[14]  Mark Newman,et al.  Detecting community structure in networks , 2004 .

[15]  Huanwen Tang,et al.  Global optimizations and tabu search based on memory , 2004, Appl. Math. Comput..

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

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

[18]  Michael Menzinger,et al.  Clustering and the synchronization of oscillator networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Wenxu Wang,et al.  Enhanced synchronizability by structural perturbations. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[22]  S. Havlin,et al.  Optimization of robustness of complex networks , 2004, cond-mat/0404331.

[24]  S. Havlin,et al.  Breakdown of the internet under intentional attack. , 2000, Physical review letters.

[25]  Chonghui Guo,et al.  Entropy optimization of scale-free networks’ robustness to random failures , 2005, cond-mat/0506725.

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

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

[28]  Adilson E Motter,et al.  Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? , 2003, Physical review letters.

[29]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[30]  Tao Zhou,et al.  Maximal planar networks with large clustering coefficient and power-law degree distribution. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

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