复杂网络测量的灵敏度
Sensitivity of complex networks measurements
摘要：
从现实世界的网络中获取的复杂网络通常具有不完整性和噪声，有限采样的后果以及获取过程中的伪影。由于表征，分析和建模的复杂系统的基础上的复杂网络是严重影响各自的初始结构的质量，它成为必要的设计方法来识别和量化的影响，这样的采样问题的复杂网络的表征。考虑到需要应用几种测量来实现复杂网络的全面表征，重要的是要研究不完整性和噪声对这种量化的影响。在这篇文章中，我们报告了这样一项研究，涉及8种不同的测量方法应用于6种不同的复杂网络模型。我们评估的灵敏度的测量扰动的拓扑结构的网络考虑的相对熵。三个特别重要的类型的渐进扰动的网络被认为是：边缘抑制，除了和重新布线。这些结论具有重要的实际意义，其中包括无标度结构对扰动的鲁棒性更强。还确定了允许稳定性（对扰动的敏感性较小）和可辨别性（不同网络拓扑之间的分离）的最佳平衡的测量。
英文摘要：
Complex networks obtained from the real-world networks are often characterized by incompleteness and noise, consequences of limited sampling as well as artifacts in the acquisition process. Because the characterization, analysis and modeling of complex systems underlain by complex networks are critically affected by the quality of the respective initial structures, it becomes imperative to devise methodologies for identifying and quantifying the effect of such sampling problems on the characterization of complex networks. Given that several measurements need to be applied in order to achieve a comprehensive characterization of complex networks, it is important to investigate the effect of incompleteness and noise on such quantifications. In this article we report such a study, involving 8 different measurements applied on 6 different complex networks models. We evaluate the sensitiveness of the measurements to perturbations in the topology of the network considering the relative entropy. Three particularly important types of progressive perturbations to the network are considered: edge suppression, addition and rewiring. The conclusions have important practical consequences including the fact that scale-free structures are more robust to perturbations. The measurements allowing the best balance of stability (smaller sensitivity to perturbations) and discriminability (separation between different network topologies) were also identified.
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