The significance of the existing analysis methods in complex networks and easy access to the ever-increasing volume of information present the emergence of proposing new methods in various fields based on complex system ideas. However, these systems are usually faced with various random failures and intelligent attacks. Due to the nature of the components’ behaviors, the occurrence of the failures and faults in their operations and the alteration of their topologies are the most important problems. Since the complex systems are usually used as the infrastructures of other networks, their robustness against failures and the adoption of suitable precautions are necessary. Moreover, the small-world effect in most complex systems is one of the crucial structural features. The authors found that the relation between these two is not well-known and may even be in conflict in some networks. The main goal in this paper is to achieve an optimal topology by utilizing a robustness-oriented multi-objective trade-off optimization model (edge rewiring) to establish a peaceful relationship between the two requirements. By offering a proposed rewiring method with the small-world effect, which is called core-periphery Windmill property, the authors demonstrated that the generated networks are able to exhibit appropriate robustness even during intelligent attacks. The results obtained in terms of Windmill graphs are presented very good approximations to demonstrate the small-world effect. These graphs are used as the initial core in the construction of the optimized networks’ topologies.

中文翻译：

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风车图骨干网的最优连接混合复杂网络

复杂网络中现有分析方法的重要性以及易于获取不断增长的信息量，提出了基于复杂系统思想在各个领域提出新方法的提议。但是，这些系统通常面临各种随机故障和智能攻击。由于组件行为的性质，最重要的问题是组件操作中出现故障和错误以及拓扑更改。由于复杂的系统通常用作其他网络的基础结构，因此它们对于故障的鲁棒性和采取适当的预防措施是必要的。此外，在大多数复杂系统中的小世界效应是关键的结构特征之一。作者发现这两者之间的关系不是众所周知的，甚至在某些网络中可能存在冲突。本文的主要目标是通过利用面向健壮性的多目标权衡优化模型（边缘重新布线）来建立两个需求之间的和平关系，从而获得最佳拓扑。通过提供一种提议的具有小世界效应的重新布线方法，即核心外围风车属性，作者证明了生成的网络即使在智能攻击期间也能够表现出适当的鲁棒性。根据风车图获得的结果呈现出非常好的近似值，以证明小世界效应。这些图被用作构建优化网络拓扑的初始核心。本文的主要目标是通过利用面向健壮性的多目标权衡优化模型（边缘重新布线）来建立两个需求之间的和平关系，从而获得最佳拓扑。通过提供一种提议的具有小世界效应的重新布线方法，即核心外围风车属性，作者证明了生成的网络即使在智能攻击期间也能够表现出适当的鲁棒性。根据风车图获得的结果呈现出非常好的近似值，以证明小世界效应。这些图被用作构建优化网络拓扑的初始核心。本文的主要目标是通过利用面向健壮性的多目标权衡优化模型（边缘重新布线）来建立两个需求之间的和平关系，从而获得最佳拓扑。通过提供一种提议的具有小世界效应的重新布线方法，即核心外围风车属性，作者证明了生成的网络即使在智能攻击期间也能够表现出适当的鲁棒性。根据风车图获得的结果呈现出非常好的近似值，以证明小世界效应。这些图被用作构建优化网络拓扑的初始核心。