Counting and Uniform Sampling from Markov Equivalent DAGs

We propose an exact solution for the problem of finding the size of a Markov equivalence class (MEC). For the bounded degree graphs, the proposed solution is capable of computing the size of the MEC in polynomial time. Our proposed approach is based on a recursive method for counting the number of the elements of the MEC when a specific vertex is set as the source variable. We will further use the idea to design a sampler, which is capable of sampling from an MEC uniformly in polynomial time.