Fast approximation of average shortest path length of directed BA networks

The average shortest path length is an important feature for complex networks. However, for large networks, it is very difficult to compute it due to the limitation of computing power. By analyzing the node reachability from several real BA networks as the example, we brought forward the concept of Global Reachable Nodes and Local Reachable Nodes. We found that the average shortest path length of a BA network is determined by the Global Reachable Nodes. From the mechanism of the BA network we illustrated this feature and hereby presented a randomized approximation algorithm for computing the average shortest path length. We verified the accuracy of this algorithm using 8 different networks. For large-scale BA network with millions of nodes, the experiments indicate that our method can estimate its ASPL with high accuracy using only several hundreds of Global Reachable Nodes.