Estimating the Number of s-t Paths in a Graph

This is the authors' abstract. We don't add key points for this paper.

The problem of counting the number of s-t paths in a graph is #P-complete. We provide an algorithm to estimate the solution stochastically, using sequential importance sampling. We show that the method works effectively for both graphs and digraphs. We also use the method to investigate the expected number of s-t paths in a random graph of size n and density d, and develop a model that shows how this quantity behaves when n and d are varied. Key words. Counting s-t paths, #P-completeness, random graphs, Monte Carlo simulation, sequential importance sampling. 1.