  The largest eigenvalue of a network provides understanding to various
dynamical as well as stability properties of the underlying system. We
investigate an interplay of inhibition and multiplexing on the largest
eigenvalue statistics of networks. Using numerical experiments, we demonstrate
that presence of the inhibitory coupling may lead to a very different behaviour
of the largest eigenvalue statistics of multiplex networks than those of the
isolated networks depending upon network architecture of the individual layer.
We demonstrate that there is a transition from the Weibull to the Gumbel or to
the Frechet distribution as networks are multiplexed. Furthermore, for denser
networks, there is a convergence to the Gumbel distribution as network size
increases indicating higher stability of larger systems.
