标题： 邻接矩阵系综平均中节点度的渐近行为 显示英文标题

标题： Asymptotic behavior of the node degrees in the ensemble average of adjacency matrix

摘要： 用于表征拓扑网络结构的各种重要且有用的量或度量通常会针对一个网络进行研究，然后在样本上进行平均。 在本文中，我们提出了一种显式表示方法，即通过对增长网络样本的预先平均邻接矩阵，作为研究特征量的新通用框架。 它被应用于一些网络模型，并在渐近意义上显示出对度分布的良好逼近。 特别是，当度的时间过程是一个单调递增函数，如幂律或对数时，我们的方法可以通过数值计算来应用，而不是难以处理的理论分析。 显示英文摘要

摘要： Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by the beforehand averaged adjacency matrix over samples of growing networks as a new general framework for investigating the characteristic quantities. It is applied to some network models, and shows a good approximation of degree distribution asymptotically. In particular, our approach will be applicable through the numerical calculations instead of intractable theoretical analysises, when the time-course of degree is a monotone increasing function like power-law or logarithm.