基于标准的无标度网络模型，建立了一般的网络动力系统所符合的偏微分方程，不仅给出无标度网络的一个拓扑性质，而且讨论了其中每个功能函数的实际意义.接着本文扩展了BA网络模型增长的"度优先连接机制"原则，从更一般的情形出发，建立了一类具有2种不同优先连接概率共存的网络模型，通过理论分析，得知该模型具有无标度特性.最后对无标度网络的幂律指数γ的取值范围与多种择优概率并存现象之间的相互关系做了探索，并依据节点在整个网络中的"贡献度"，提出了一类优先连接概率.
Based on the classic scale-free network model, we set up the partial differential equation satisfied a more general network dynamic system, and then we not only find another important topological property of scale-free network, but also discuss the real background meaning of every function. Meanwhile, we extend the BA-network-model growth principle, degree-preferential attachment mechanism. Starting from a more general situation, we establish a network model containing degree-preferential attachment probability and special-graph-preferential attachment probability. By analysis, this model is scale-free. Finally, we distinguish the connect between the scope of the power law parameter γ of scale-free network and the phenomena all kinds of preferential attachment probabilities co-existing. According to the contribution level from the vertex to the whole network, we come up with a preferential attachment probability.
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中国综合性科技类核心期刊(北大核心)