平衡无标度网络的热力学极限
Approaching the thermodynamic limit in equilibrated scale-free networks
摘要：
我们讨论了各种模型的无标度复杂网络接近其极限性质时，网络的大小N的增长。我们主要关注平衡网络及其有限大小的度分布。我们的研究结果表明，即使对于10^9阶节点的网络，对截止点位置标度的次引导修正也很强。当度分布服从幂律k^（-3）时，我们还观察到退化图的标度的对数修正。我们还研究了最大程度的分布，并表明，它可能有一个不同的缩放比截止，而且，它接近热力学极限快得多。我们还提出了一些结果的截止函数和最大程度的分布在平衡网络。
英文摘要：
We discuss how various models of scale-free complex networks approach their limiting properties when the size N of the network grows. We focus mainly on equilibrated networks and their finite-size degree distributions. Our results show that subleading corrections to the scaling of the position of the cutoff are strong even for networks of order 10^9 nodes. We observe also a logarithmic correction to the scaling for degenerated graphs when the degree distribution follows a power law k^(-3). We study also the distribution of the maximal degree and show that it may have a different scaling than the cutoff and, moreover, it approaches the thermodynamic limit much faster. We present also some results on the cutoff function and the distribution of the maximal degree in equilibrated networks.
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