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Scientific Programming
Volume 2016, Article ID 5659687, 7 pages
http://dx.doi.org/10.1155/2016/5659687
Research Article

Optimal Design on Robustness of Scale-Free Networks Based on Degree Distribution

1School of Electrical Engineering and Automation, Jiangsu Normal University, Xuzhou 221116, China
2School of Government, Beijing Normal University, Beijing 100875, China
3People’s Government of Wuduan Town, Peixian, Xuzhou 221638, China

Received 3 April 2016; Revised 7 June 2016; Accepted 5 July 2016

Academic Editor: Meng Guo

Copyright © 2016 Jianhua Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper uses 2-norm degree and coefficient of variation on degree to analyze the basic characteristics and to discuss the robustness of scale-free networks. And we design two optimal nonlinear mixed integer programming schemes to investigate the optimal robustness and analyze the characteristic parameters of different schemes. In this paper, we can obtain the optimal values of the corresponding parameters of optimal designs, and we find that coefficient of variation is a better measure than 2-norm degree and two-step degree to study the robustness of scale-free networks. Meanwhile, we discover that there is a tradeoff among the robustness, the degree, and the cost of scale-free networks, and we find that when average degree equals 6, this point is a tradeoff point between the robustness and cost of scale-free networks.