  In this paper, we propose a multilayer inhomogeneous random graph model
(MIRG), whose layers may consist of both single-edge and multi-edge graphs. In
the single layer case, it has been shown that the regular variation of the
weight distribution underlying the inhomogeneous random graph implies the
regular variation of the typical degree distribution. We extend this
correspondence to the multilayer case by showing that the multivariate regular
variation of the weight distribution implies the multivariate regular variation
of the asymptotic degree distribution. Furthermore, in certain circumstances,
the extremal dependence structure present in the weight distribution will be
adopted by the asymptotic degree distribution. By considering the asymptotic
degree distribution, a wider class of Chung-Lu and Norros-Reittu graphs may be
incorporated into the MIRG layers. Additionally, we prove consistency of the
Hill estimator when applied to degrees of the MIRG that have a tail index
greater than 1. Simulation results indicate that, in practice, hidden regular
variation may be consistently detected from an observed MIRG.
