Abstract: BA model is a classic scale-free network model, which has some small world characteristics, but the clustering coefficient approaches zero with increasing number of points. In order to further optimize the average path length and clustering coefficient of BA network model, an improved scale-free network model based on adaptive algorithm is designed. The improved model optimizes the correlation degree of network nodes and the system. By calculating the optimal value of the correlation degree and the value of each parameter in the network Thus, the ideal network model is obtained. Through the mathematical analysis of the adaptive algorithm, the average path length of the system is the convergence state with conditions. The simulation results show that the improved network model is further optimized in terms of average path length and clustering coefficient. Unlike the BA scale-free network, the improved model has obvious clustering characteristics and is more accord with small world network characteristics.

Key words: Scale-free network, BA model, correlation degree, adaptive algorithm

摘要： BA模型是经典的无标度网络模型，具有一定小世界特性，但聚类系数随着点数增多趋近于零。为进一步优化BA网络模型的平均路径长度和聚类系数的特性，设计了一种基于自适应算法的无标度网络改进模型。改进模型优化了系统与网络节点的关联度，通过计算得到关联度的最优值及此时网络各参数的值，从而获得理想的网络模型。通过对自适应算法中关联度的数学分析，可知系统平均路径长度呈带有条件的收敛状态。仿真结果表明，改进后网络模型在平均路径长度和聚类系数方面，有进一步优化。不同于BA无标度网络的是，改进模型优化后具有较明显的聚类特性，更符合小世界网络特性。

关键词: 无标度网络, BA模型, 关联度, 自适应算法