曼陀罗网络：超鲁棒、超小世界和高度稀疏图
Mandala Networks: ultra-robust, ultra-small-world and highly sparse graphs
摘要：
基础设施对安全性和可靠性的要求越来越高，这就要求对其嵌入式复杂网络拓扑结构进行优化设计。接下来的问题出现了：什么是最佳布局，以满足最好的所有需求？在这里，我们提出了一个通用的解决方案，这个问题与无标度网络，如互联网和航空公司网络。准确地说，我们公开了一种系统地构建网络的方法，该网络对随机故障以及恶意攻击具有100个$\%$鲁棒性。此外，随着这些网络规模的增加，它们的最短路径变得渐近不变，链接密度变为零，分别使它们成为超小世界和高度稀疏。第一个属性是理想的通信和导航目的，而第二个是有趣的经济。
英文摘要：
The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands? Here we present a general solution for this problem with scale-free networks, like the Internet and airline networks. Precisely, we disclose a way to systematically construct networks which are 100$\%$ robust against random failures as well as to malicious attacks. Furthermore, as the sizes of these networks increase, their shortest paths become asymptotically invariant and densities of links go to zero, making them ultra-small worlds and highly sparse, respectively. The first property is ideal for communication and navigation purposes, while the second is interesting economically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
