从几何增长网络谈起

Starting with Geometrically Growing Networks

如何判断实际网络和模型网络(如层次网络、伪分形图、阿波罗网等)的度分布为幂律和确定其度指数?这将涉及测量网络度分布的方法。文献上有3种方法:度频率、对数盒子、度秩次或补分布,指出正确的方法是采用秩次或补分布画图。因为模型网络是实际网络的抽象,仅仅度分布相同不能说明就是恰当的模型。实际网络通常只能得到部分数据,数据(子)网络与实际网络两者度分布的关系也需要探讨。

How to judge whether the degree distribution of a real network or model network （ e. g. , hier- archical networks, pseudofractal graphs, Apollonian networks, etc. ） is power-law, and to determine its degree exponent, this problem deals with the measurement of degree distributions. There are three methods： size-frequency; logarithmic binning; size-rank or complementary CDF in the literature on complex networks. It is pointed out that correct method is plotting size-rank or complementary CDF on doubly-logarithmic scale. Since model network is an abstract of real network, only both degree distributions match case, we can not say it is just a correct model. For a real network, obtained data only is a subnetwork of real network, are their degree distributions the same？ This still need to be explored.