大统一的混合网络模型中的相称性系数转变新特点

New Features of Assortativity Characteristic Transition in Large Harmonious Unifying Networks Model

首先建立了大统一的混合网络模型(LUHNM),并在总混合比dr基础上,引入了两个新的混合比:随机性混合比gr和确定性混合比fd,用这3个混合比控制整个网络生长和特性变化。通过调控dr,gr和fd,不仅再现了无权网络中不同类型网络的特性(如BA模型,ER模型,HUHPM模型和BPRA模型等),而且发现在无权的大统一的混合网络模型中出现了若干新现象和新特点:随着3个混合比的变化,相称性系数rc可以在一个(-1,1)较大范围内变化,在dr=1/1附近存在一个阈值fd=0.9/1,随着fd的增加,rc实现从负值到正值大范围的转变;当dr→1/0时,在fd～1/1附近存在一个阈值(相变点),相称性系数rc数值将从零附近迅速增加到较大的正值;特别是随着fd→1/1,rc出现了多峰现象(多极值情形)。

Based on the harmonious unifying hybrid model, the large harmonious unifying network model （LUHNM） is further developed, In this model, two more hybrid ratios, which are gr and fd, are defined besides the previous total hybrid ratio dr. They are introduced as the deterministic hybrid ratio and the random hybrid ratio, respectively. The ratio dr controls the number of deterministic attachment and random attachment. The networks grow through adjusting the three hybrid ratios. In this paper, several new features of assortativity characteristic transition are revealed. The famous un-weighted BA model, ER model and HUHPM model can deduced by asigning different values of the three hybrid ratios. It is found that assortativity coefficient rc can vary in a large range of （-1, 1）, and there exists a threshold value nearby atfd=0.9/1 as dr=1/1, where rc can have a transition from negative to positive values. Also rc can be rapidly increased to a large value from near zero atfd-1/1 as dr→1/0. In addition, the multi-peak phenomena of rc appear asfd→1/1. These results can provide a better understanding about the evolution characteristics and the difference in growing complex networks between social networks and technological and biological networks.