  Random matrix theory has played an important role in recent work on
statistical network analysis. In this paper, we review recent results on
regimes of concentration of random graphs around their expectation, showing
that dense graphs concentrate and sparse graphs concentrate after
regularization. We also review relevant network models that may be of interest
to probabilists considering directions for new random matrix theory
developments, and random matrix theory tools that may be of interest to
statisticians looking to prove properties of network algorithms. Applications
of concentration results to the problem of community detection in networks are
discussed in detail.
