  In this paper, we explore the role of network topology on maintaining the
extensive property of entropy. We study analytically and numerically how the
topology contributes to maintaining extensivity of entropy in multiplex
networks, i.e. networks of subnetworks (layers), by means of the sum of the
positive Lyapunov exponents, $H_{KS}$, a quantity related to entropy. We show
that extensivity relies not only on the interplay between the coupling
strengths of the dynamics associated to the intra (short-range) and inter
(long-range) interactions, but also on the sum of the intra-degrees of the
nodes of the layers. For the analytically treated networks of size $N$, among
several other results, we show that if the sum of the intra-degrees (and the
sum of inter-degrees) scales as $N^{\theta+1},\;\theta>0$, extensivity can be
maintained if the intra-coupling (and the inter-coupling) strength scales as
$N^{-\theta}$, when evolution is driven by the maximisation of $H_{KS}$. We
then verify our analytical results by performing numerical simulations in
multiplex networks formed by electrically and chemically coupled neurons.
