Zheng Dafang, Trimper Steffen, Zheng Bo, Hui P M
Fachbereich Physik, Martin-Luther-Universität, D-06099 Halle, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Apr;67(4 Pt 1):040102. doi: 10.1103/PhysRevE.67.040102. Epub 2003 Apr 25.
We propose a model of weighted scale-free networks incorporating a stochastic scheme for weight assignments to the links, taking into account both the popularity and fitness of a node. As the network grows, the weights of links are driven either by the connectivity with probability p or by the fitness with probability 1-p. Numerical results show that the total weight exhibits a power-law distribution with an exponent sigma that depends on the probability p. The exponent sigma decreases continuously as p increases. For p=0, the scaling behavior is the same as that of the connectivity distribution. An analytical expression for the total weight is derived so as to explain the features observed in the numerical results. Numerical results are also presented for a generalized model with a fitness-dependent link formation mechanism.
我们提出了一种加权无标度网络模型，该模型纳入了一种为链接分配权重的随机方案，同时考虑了节点的受欢迎程度和适应性。随着网络的增长，链接的权重以概率p由连接性驱动，或以概率1 - p由适应性驱动。数值结果表明，总权重呈现幂律分布，其指数σ取决于概率p。随着p的增加，指数σ连续减小。当p = 0时，标度行为与连接性分布的相同。推导出了总权重的解析表达式，以解释数值结果中观察到的特征。还给出了具有依赖适应性的链接形成机制的广义模型的数值结果。
