平均最短路径长度是复杂网络的一个重要特性,但是对于大规模网络的平均最短路径长度的计算是困难的。在最近的一次对中国教育网的研究中,建立了一个有2354934个网页和26816209个链接的网络。要想计算该网络的平均最短路径长度,无论是传统的Floyd、Dijkstra算法,还是基于MPI的并行算法,在现有的计算机资源下都难以实现。提出了二级网络的概念,并基于此给出了一种针对中国教育网的新算法,使得在可以接受的时间内完成平均最短路径的近似计算,经试算效果令人满意,说明这种方法对于计算大规模网络的平均最短路径是有效的。
The average shortest path length is one of characteristics of complex networks. However, it is hard to calculate the average shortest path length of vary large networks. In the recent research of China Education and Research Network, we construct a network that contains 2 354 934 pages and 26 816 209 links. It is hard to calculate its average shortest path length either using the classic Floyd or Dijkstra algorithm or the message passing interface (MPI) according to the available computer resources. In this pa- per, we give a concept of 2-layer network, based on which, we propose a new algorithm which can help us to get an approximate result of the average shortest path length of CERNET. The experimental result is satisfaction, which proves that this algorithm is useful to calculate the average shortest path of large complex networks.