  Multilayer networks have been the subject of intense research during the last
few years, as they represent better the interdependent nature of many real
world systems. Here, we address the question of describing the three different
structural phases in which a multiplex network might exist. We show that each
phase can be characterized by the presence of gaps in the spectrum of the
supra-Laplacian of the multiplex network. We therefore unveil the existence of
different topological scales in the system, whose relation characterizes each
phase. Moreover, by capitalizing on the coarse-grained representation that is
given in terms of quotient graphs, we explain the mechanisms that produce those
gaps as well as their dynamical consequences.
