基于优化理论的社区无标度网络模型

A Model of Community-Structure and Scale-Free Network Based on Optimization Theory

当前建模社区无标度网络的研究多基于组合法,即先构造无标度特征再构造社区特征,或者先构造社区特征再构造无标度特征.基于组合法的模型能生成令人满意的社区无标度网络,但是该方法需要满足社区大小相等、社区特征和无标度特征间的顺序依赖等特定条件,而这些特定条件在真实网络的演化中往往并不存在.值得注意的是,多数学者同意社区网络起源于网络节点之间的类别距离,如地理距离、兴趣距离、偏好距离等,但现有研究尚未确证社区结构与类别距离之间的因果关系.针对组合法的缺点和社区特征起源的问题,该文建立了一个优化模型,该模型以无标度属性为优化目标,以类别距离为约束条件.仿真结果表明该模型揭示了类别距离与社区特征间的因果关系,能生成多种参数下的社区无标度网络,更好地拟合了现实世界中的社区无标度网络.

Most of current researches generate the community-structure and scale-free networks （CSSF networks） by the composition method, i. e. , constructing CSSF networks by generating scale-free property firstly and then community-structure property or vice versa. Models based on the composition method can generate satisfactory CSSF networks, but the composition method has many constraints, such as all communities with the same size and the sequential dependencies between community-structure and scale-free property, so that these constraints hardly exist in the evolution process of real-world networks. Moreover, it is noticeable that most scholars agree on a viewpoint that communities originate from the similarity distance, such as geographical distance, interests and preferences, but current researches have not confirmed the causality between community property and similarity distance. To eliminate the shortcomings of the composition method and clarify the origin of community property, this paper proposes an optimization model by modeling the scale-free property as an objective and similarity distance as a constraint. The simulation results show that. （1） the causality between community-structure property and the similarity distance is revealed by the optimization model; （2） the proposed optimization model can generate CSSF networks under various parameters; （3） the optimization model simulates the real networks well.