  We present a renormalization group analysis of the problem of Anderson
localization on a Random Regular Graph (RRG) which generalizes the
renormalization group of Abrahams, Anderson, Licciardello, and Ramakrishnan to
infinite-dimensional graphs. The renormalization group equations necessarily
involve two parameters (one being the changing connectivity of sub-trees), but
we show that the one-parameter scaling hypothesis is recovered for sufficiently
large system sizes for both eigenstates and spectrum observables. We also
explain the non-monotonic behavior of dynamical and spectral quantities as a
function of the system size for values of disorder close to the transition, by
identifying two terms in the beta function of the running fractal dimension of
different signs and functional dependence. Our theory provides a simple and
coherent explanation for the unusual scaling behavior observed in numerical
data of the Anderson model on RRG and of Many-Body Localization.
