无尺度网络平均路径长度的估计

无尺度网络的拓扑结构研究主要集中于聚类系数和平均路径长度的计算以及度分布分析. 在实际的无尺度网络中，表征网络拓扑结构的三个参数之间是互相联系的，其中一个参数均可近似用另外两个参数表示. 鉴于此，针对大规模无尺度网络的平均路径长度计算问题，基于树形结构模型给出了无尺度网络平均路径长度<l>_SF 的计算公式，并分析了网络规模和节点间连接方式对平均路径长度的影响. 分析结果表明，<l>_SF与无尺度网络的平均度数k、平均聚类系数C以及幂指数γ有关，从而将直接求解平均路径长度的复杂问题转化为间接求解，大大提高了分析无尺度网络拓扑结构的效率. 实验结果表明，提出的无尺度网络平均路径长度计算公式是有效的.

Estimation for the average path length of scale-free networks

Studying the topology of scale-free networks mainly concentrates on computing clustering coefficient and average path length, and analyzing degree distribution. This paper argues that in real world, the three parameters are interrelated. A parameter can be replaced by the other two parameters. According to the viewpoint, this paper gives a formula to compute the average path length <l>_SF of large scale-free networks based on a tree structure model, and analyzes the impact of network scale and junction between nodes on <l>_SF. The results indicate that <l>_SF is related to average degreek, average clustering coefficient C and power exponent γ which are three parameters characterizing the topology of scale-free networks. Therefore, the complexity can be reduced by transferring computing average path length directly to indirectly. The experiments' results show that the formula is valid and the efficiency of studying the topology of large scale-free networks is greatly raised.