Learning Random Regular Graphs

The family of random regular graphs is a classic topic in the realms of graph theory, combinatorics and computer science. In this paper we study the problem of learning random regular graphs from random paths. A random regular graph is generated uniformly at random and in a standard label-guided graph exploration setting, the edges incident from a node in the graph have distinct local labels. The input data to the statistical query oracle are path-vertex pairs (x, v) where x is a random uniform path (a random sequence of edge labels) and v is the vertex of the graph reached on the path x starting from a particular start vertex v0. We present a comprehensive study and prove positive results on the convergence of random walks on many types of random regular graphs. In addition to the theoretical results, we generalize Angluin and Chen’s learning algorithm to learning random regular graphs from uniform paths in the statistical query model. Extensive experiments demonstrate the efficiency and accuracy of the algorithm.