  Multilayer networks are widespread in natural and manmade systems. Key
properties of these networks are their spectral and eigenfunction
characteristics, as they determine the critical properties of many dynamics
occurring on top of them. In this paper, we numerically demonstrate that the
normalized localization length $\beta$ of the eigenfunctions of multilayer
random networks follows a simple scaling law given by $\beta=x^*/(1+x^*)$, with
$x^*=\gamma(b_{\text{eff}}^2/L)^\delta$, $\gamma,\delta\sim 1$ and
$b_{\text{eff}}$ being the effective bandwidth of the adjacency matrix of the
network, whose size is $L=M\times N$. The reported scaling law for $\beta$
might help to better understand criticality in multilayer networks as well as
to predict the eigenfunction localization properties of them.
