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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 interestarXiv:1801.08724v1 fatcat:hokwnjsykrgexgp7256hatau4q