  A very important problem in combinatorial optimization is partitioning a
network into communities of densely connected nodes; where the connectivity
between nodes inside a particular community is large compared to the
connectivity between nodes belonging to different ones. This problem is known
as community detection, and has become very important in various fields of
science including chemistry, biology and social sciences. The problem of
community detection is a twofold problem that consists of determining the
number of communities and, at the same time, finding those communities. This
drastically increases the solution space for heuristics to work on, compared to
traditional graph partitioning problems. In many of the scientific domains in
which graphs are used, there is the need to have the ability to partition a
graph into communities with the ``highest quality'' possible since the presence
of even small isolated communities can become crucial to explain a particular
phenomenon. We have explored community detection using the power of quantum
annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out
that the problem of detecting at most two communities naturally fits into the
architecture of a quantum annealer with almost no need of reformulation. This
paper addresses a systematic study of detecting two or more communities in a
network using a quantum annealer.
