Peng Guan-Sheng, Tan Suo-Yi, Wu Jun, Holme Petter
College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, P. R. China.
Department of Computer Science, University of California, Davis, California 95616, USA.
Sci Rep. 2016 Nov 17;6:37317. doi: 10.1038/srep37317.
Robustness and small-world effect are two crucial structural features of complex networks and have attracted increasing attention. However, little is known about the relation between them. Here we demonstrate that, there is a conflicting relation between robustness and small-world effect for a given degree sequence. We suggest that the robustness-oriented optimization will weaken the small-world effect and vice versa. Then, we propose a multi-objective trade-off optimization model and develop a heuristic algorithm to obtain the optimal trade-off topology for robustness and small-world effect. We show that the optimal network topology exhibits a pronounced core-periphery structure and investigate the structural properties of the optimized networks in detail.
鲁棒性和小世界效应是复杂网络的两个关键结构特征，并且已经引起了越来越多的关注。然而，关于它们之间的关系却知之甚少。在此我们证明，对于给定的度序列，鲁棒性和小世界效应之间存在冲突关系。我们表明，以鲁棒性为导向的优化会削弱小世界效应，反之亦然。然后，我们提出了一个多目标权衡优化模型，并开发了一种启发式算法来获得鲁棒性和小世界效应的最优权衡拓扑结构。我们表明，最优网络拓扑呈现出明显的核心 - 外围结构，并详细研究了优化网络的结构特性。
