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Robustness of Regular Ring Lattices Based on Natural Connectivity
WU Jun 1 #,M Barahona 2,DENG Hongzhong 3,TAN Yuejin 3
1.College of Information Systems and Management,National University of Defense Technology, Changsha 410073
2.Department of Bioengineering, Imperial College London, London SW7 2AZ, United Kingdom
3.College of Information Systems and Management, National University of Defense Technology
*Correspondence author
#Submitted by
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Funding: National Science Foundation of China （No.No. 60904065 and 70771111), and Specialized Research Fund for the Doctoral Program of Higher Education）
Opened online: 8 September 2010
Accepted by: none
Citation: WU Jun,M Barahona,DENG Hongzhong.Robustness of Regular Ring Lattices Based on Natural Connectivity[OL]. [ 8 September 2010] http://en.paper.edu.cn/en_releasepaper/content/4384203
 
 
It has been recently proposed that the natural connectivity can be used to characterize efficiently the robustness of complex networks. The natural connectivity quantifies the redundancy of alternative routes in the network by evaluating the weighted number of closed walks of all lengths and can be seen as an average eigenvalue obtained from the graph spectrum. In this paper, we explore both analytically and numerically the natural connectivity of regular ring lattices and regular random graphs obtained through degree-preserving random rewirings from regular ring lattices. We reformulate the natural connectivity of regular ring lattices in terms of generalized Bessel functions and show that the natural connectivity of regular ring lattices is independent of network size and increases with average degree monotonically. We also show that random regular graphs have lower natural connectivity, and are thus less robust, than regular ring lattices.
Keywords:natural connectivity;robustness;regular ring lattices;random regular graphs;generalized Bessel function
 
 
 

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