构建一种具有较多三角关系且聚类系数可调节的三角生长网络,利用计算机模拟,研究了网络拓扑结构改变对社会平衡动力学演化的影响。结果表明,当网络加边连接概率pa≥0.5,网络为稠密连接时,网络的统计性质与完全连接图类似,社会平衡的演化与初始状态无关,且当转变概率p≥1/2 时, 网络系统发生从非全友好态到全友好态的动力学相变;当连接概率pa<0.5,网络为稀疏连接时,网络的统计性质具有无标度网络的特性,社会平衡的演化呈现初值依赖性和动力学相变消失。
A network with a large number of triangular relations, whose cluster coefficient could be controlled, was constructed in this study. The local dynamics of social balance in the triangle-growing networks was studied through computer simulations. The results show that the statistical features of the networks are approximately the same as the complete graph when the adding-link probability pa≥0.5, and the evolution of the social balance is independent on the initial conditions; moreover, the system undergoes a dynamic phase transition when the transition probability p≥1/2. However, when the network is sparse, i.e. pa<0.5, the final state of the system depends on the initial state and the system does not experience the dynamic phase transition.
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