Orsini Chiara, Dankulov Marija M, Colomer-de-Simón Pol, Jamakovic Almerima, Mahadevan Priya, Vahdat Amin, Bassler Kevin E, Toroczkai Zoltán, Boguñá Marián, Caldarelli Guido, Fortunato Santo, Krioukov Dmitri
CAIDA, University of California San Diego, San Diego, California 92093, USA.
Information Engineering Department, University of Pisa, Pisa 56122, Italy.
Nat Commun. 2015 Oct 20;6:8627. doi: 10.1038/ncomms9627.
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks--the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain--and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.
真实网络若以图形表示，是有序与无序的复杂组合。将网络模型的某些结构属性固定为在真实网络中观察到的值，许多其他属性便会作为这些固定可观测值的统计结果以及其他方面的随机性而出现。在此，我们采用dk系列（网络结构的一套完整基本特征）来研究不同网络属性之间的统计依赖性。我们考虑了六个真实网络——互联网、美国机场网络、人类蛋白质相互作用网络、技术社会信任网络、英语单词网络以及人类大脑的功能磁共振成像图——并发现这些网络的许多重要局部和全局结构属性都能被dk随机图紧密再现，其度分布、度相关性和聚类情况与相应的真实网络相同。我们讨论了这种对网络随机性评估的重要概念、方法和实际意义，并发布了用于生成dk随机图的软件。
