有向网络的复制机制及其相关网络分析

鉴于有向网络比无向网络包含了更多的内在信息, 而复杂网络中的基本统计量往往仅适用于无向网络, 使得有向网络的研究相对缺少, 由此提出了一个有向网络的统计量, 并分析该统计量在相关有向网络研究中的有效性. 考虑到复制是有向网络增长的一个主要动力, 定义了有向网络结点复制率和有向网络复制率的概念, 并利用结点入度分布和复制率研究了有向规则网络、复制模型网络及自然数网络. 结果显示, 完全复制模型和自然数网络的入度具有无标度特性, 其入度分布的幂律指数 都为2, 2个有向网络的复制率 , 而部分复制模型的复制率 . 因此, 有向网络的入度分布、复制率都能很好地解释完全复制模型与自然数网络的相关性, 可作为重要统计量广泛应用于有向网络研究中.

Copying Mechanism of Directed Networks and Relevant Networks Analysis

Directed networks contain much more internal information than undirected ones. Many of the basic statistics for complex networks can only be applied to undirected networks, causing relative lack in the research on directed ones. To remedy this shortcoming, the paper proposes the concept of copying rate and analyzes the effectiveness of the statistics for directed networks. Based on statistics of in-degree distribution and copying rate for directed networks, the directed regular networks are selected for study purposes, including both the copying model networks and natural number network. On the rigorous derivation in in-degree distribution and copying rate of directed networks, the result reveals that completely copying model and natural number network have a power-law in-degree distribution with , and copying rate for completely copying model and natural number network is 1, which explains the correlation between completely copying model and natural number network.