Distance Distribution and Average Shortest Path Length Estimation in Real-World Networks

The average shortest path length is one of the most important and frequent-invoked characteristics of real-world complex networks. However, the high time complexity of the algorithms prevents us to apply them to calculate the average shortest path lengths in real-world massive networks. In this paper, we present an empirical study of the vertex-vertex distance distributions in more than 30 artificial and real-world networks. To best of our knowledge, we are the first to find out the vertex-vertex distance distributions in these networks conform well to the normal distributions with different means and variations. We also investigate how to use the sampling algorithms to estimate the average shortest path lengths in these networks. Comparing our average shortest path estimating algorithm with other three different sampling strategies, the results show that we can estimate the average shortest path length quickly by just sampling a small number of vertices in both of real-world and artificial networks.