Eom Y-H, Jeon C, Jeong H, Kahng B
Department of Physics, Korea Advanced Institute of Science and Technology, 305-701 Daejon, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056105. doi: 10.1103/PhysRevE.77.056105. Epub 2008 May 16.
Weighted scale-free networks exhibit two types of degree-strength relationship: linear and nonlinear relationships between them. To understand the mechanism underlying such empirical relationships, theoretical evolution models for weighted scale-free networks have been introduced for each case. However, those models have not yet been tested with empirical data. In this study, we collect temporal records of several online bulletin board systems and a movie actor network. We measure the growth rates of degree and strength of each vertex and weight of each edge within the framework of preferential attachment (PA). We also measure the probability of creating new edges between unconnected pairs of vertices. Then, based on the measured rates, linear and nonlinear growth models are constructed. We find that indeed the dynamics of creating new edges and adding weight to existing edges in a nonlocal manner is essential to reproduce the nonlinear degree-strength relationship. We also find that the degree-driven PA rule is more appropriate to real systems rather than the strength-driven one used for the linear model.
加权无标度网络呈现出两种度-强度关系：它们之间的线性关系和非线性关系。为了理解这种经验关系背后的机制，针对每种情况都引入了加权无标度网络的理论演化模型。然而，这些模型尚未用经验数据进行检验。在本研究中，我们收集了几个在线公告板系统和一个电影演员网络的时间记录。我们在优先连接（PA）框架内测量每个顶点的度和强度的增长率以及每条边的权重。我们还测量了在未连接的顶点对之间创建新边的概率。然后，基于测量的增长率，构建线性和非线性增长模型。我们发现，以非局部方式创建新边并向现有边添加权重的动态过程对于重现非线性度-强度关系至关重要。我们还发现，度驱动的PA规则比线性模型中使用的强度驱动规则更适合实际系统。
