节点吸引度相关联的无标度竞争网络

Dependent attractiveness of nodes for scale-free competition networks

针对WWW网络每时每刻每个网页对人们的吸引程度不同及吸引度相互关联特征,提出了吸引度依赖于时间的Poisson NPA(增长择优网络)竞争网络模型.它不仅是初始吸引度为常数的Dorgovtsev等人的无向网络模型的推广,而且刻画出了增长网络的竞争机制.通过对这个模型进行分析,获得了度分布的解析表达式,并给出了渐近线性吸引系数A与新节点边数m的关系.理论分析与数值模拟表明,这类网络的幂律指数在区间(2,m+1)内,幂律指数为3的条件是渐近线性吸引系数A为0,且|A|/m越小,度分布的理论值与模拟结果的误差越小.

Based on the feature of WWW networks, a Poisson NPA competition model with dependent attractiveness of nodes is proposed. The model is generalized with initial attractiveness. The stationary average degree distribution of the model is calculatedand it is proved that the network is scale-free by using Poisson theory. The relation between the coefficient A of asymptotically linear attractiveness and the number m of edges of a new node is acqaired. Theoretical analysis and simulation show that the power-law exponent of the model is in interval （2, m ＋ 1）, and the smaller the ｜A｜/m the less the error between the theoretical and simulated results.