Gallos Lazaros K, Song Chaoming, Makse Hernán A
Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Phys Rev Lett. 2008 Jun 20;100(24):248701. doi: 10.1103/PhysRevLett.100.248701. Epub 2008 Jun 19.
Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here, we use scaling theory to quantify the degree of correlations in the particular case of networks with a power-law degree distribution. These networks are classified in terms of their correlation properties, revealing additional information on their structure. For instance, the studied social networks and the Internet at the router level are clustered around the line of random networks, implying a strongly connected core of hubs. On the contrary, some biological networks and the WWW exhibit strong anticorrelations. The present approach can be used to study robustness or diffusion, where we find that anticorrelations tend to accelerate the diffusion process.
连通性关联在无标度网络结构中起着重要作用。虽然存在一些实证研究，但尚无能够解释真实网络中广泛变化行为的一般性理论分析。在此，我们运用标度理论来量化具有幂律度分布的网络这一特定情形下的关联程度。这些网络依据其关联特性进行分类，揭示了有关其结构的更多信息。例如，所研究的社交网络以及路由器层面的互联网聚集在随机网络线附近，这意味着存在一个由枢纽构成的强连接核心。相反，一些生物网络和万维网呈现出强反关联。当前方法可用于研究鲁棒性或扩散，我们发现反关联往往会加速扩散过程。
