  Understanding the local structure of a graph provides valuable insights about
the underlying phenomena from which the graph has originated. Sampling and
examining k-subgraphs is a widely used approach to understand the local
structure of a graph. In this paper, we study the problem of sampling uniformly
k-subgraphs from a given graph. We analyze a few different Markov chain Monte
Carlo (MCMC) approaches, and obtain analytical results on their mixing times,
which improve significantly the state of the art. In particular, we improve the
bound on the mixing times of the standard MCMC approach, and the
state-of-the-art MCMC sampling method PSRW, using the canonical-paths argument.
In addition, we propose a novel sampling method, which we call recursive
subgraph sampling, RSS, and its optimized variant RSS+. The proposed methods,
RSS and RSS+, are significantly faster than existing approaches.
