  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.
