标题： 洋葱结构和网络鲁棒性 显示英文标题

标题： Onion structure and network robustness

摘要： 在最近的工作[Proc. Natl. Acad. Sci. USA 108, 3838 (2011)]中，Schneider等人提出了一种新的网络鲁棒性度量，并研究了与此量相关的最优网络。对于具有幂律度分布的网络，优化后的网络具有洋葱结构——高度顶点形成一个核心，其度数呈径向递减，并且同一径向层内的边过度集中。在本文中，我们将洋葱结构与具有良好扩展器特性的图相关联（另一种鲁棒网络的表征），并认为具有偏度度分布和大谱间隙（因此具有良好的扩展器特性）的网络通常具有洋葱结构。此外，我们提出了一种生成算法，可以生成具有洋葱结构的合成无标度网络，从而绕过了Schneider等人的优化过程。我们验证了所生成网络对恶意攻击和随机移除的鲁棒性。 显示英文摘要

摘要： In a recent work [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], Schneider et al. proposed a new measure for network robustness and investigated optimal networks with respect to this quantity. For networks with a power-law degree distribution, the optimized networks have an onion structure-high-degree vertices forming a core with radially decreasing degrees and an over-representation of edges within the same radial layer. In this paper we relate the onion structure to graphs with good expander properties (another characterization of robust network) and argue that networks of skewed degree distributions with large spectral gaps (and thus good expander properties) are typically onion structured. Furthermore, we propose a generative algorithm producing synthetic scale-free networks with onion structure, circumventing the optimization procedure of Schneider et al. We validate the robustness of our generated networks against malicious attacks and random removals.