Community detection is a classical problem in the field of graph mining. While most algorithms work on the entire graph, it is often interesting in practice to recover only the community containing some given set of seed nodes. In this paper, we propose a novel approach to this problem, using some low-dimensional embedding of the graph based on random walks starting from the seed nodes. From this embedding, we propose some simple yet efficient versions of the PageRank algorithm as well as a novel algorithm, called WalkSCAN, that is able to detect multiple communities, possibly overlapping. We provide insights into the performance of these algorithms through the theoretical analysis of a toy network and show that WalkSCAN outperforms existing algorithms on real networks.