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Universal spectral properties of multiplex networks allow us to assess thenature of the transition between disease-free and endemic phases in the SISepidemic spreading model. In a multiplex network, depending on a couplingparameter, $p$, the inverse participation ratio ($IPR$) of the leadingeigenvector of the adjacency matrix can be in two different structural regimes:(i) layer-localized and (ii) delocalized. Here we formalize the structuraltransition point, $p^*$, between these two regimes, showing that there areuniversal properties regarding both the layer size $n$ and the layerconfigurations. Namely, we show that $IPR \sim n^{-\delta}$, with$\delta\approx 1$, and revealed an approximately linear relationship between$p^*$ and the difference between the layers' average degrees. Furthermore, weshowed that this multiplex structural transition is intrinsically connectedwith the nature of the SIS phase transition, allowing us to both understand andquantify the phenomenon. As these results are related to the universalproperties of the leading eigenvector, we expect that our findings might berelevant to other dynamical processes in complex networks.

Universality of eigenvector delocalization and the nature of the SIS phase transition in multiplex networks