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We study the transition in the functional networks that characterize the human brains’ conscious-state to an unconscious subliminal state of perception by using k-core percolation. We find that the most inner core (i.e., the most connected kernel) of the conscious-state functional network corresponds to areas which remain functionally active when the brain transitions from the conscious-state to the subliminal-state. That is, the inner core of the conscious network coincides with the subliminal-state. Mathematical modeling allows to interpret the conscious to subliminal transition as driven by k-core percolation, through which the conscious state is lost by the inactivation of the peripheral k-shells of the conscious functional network. Thus, the inner core and most robust component of the conscious brain corresponds to the unconscious subliminal state. This finding imposes constraints to theoretical models of consciousness, in that the location of the core of the functional brain network is in the unconscious part of the brain rather than in the conscious state as previously thought. Fil: Arese Lucini, Francesca. City University of New York. The City College of New York; Estados Unidos Fil: Del Ferraro, Gino. City University of New York. The City College of New York; Estados Unidos. Memorial Sloan-kettering Cancer Center.; Estados Unidos Fil: Sigman, Mariano. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nebrija; Fil: Makse, Hernán Alejandro. City University of New York. The City College of New York; Estados Unidos

$k$-core percolation is an extension of the concept of classical percolation and is particularly relevant to understanding the resilience of complex networks under random damage. A new analytical formalism has been recently proposed to deal with heterogeneous $k$-cores, where each vertex is assigned a local threshold ${k}_{i}$. In this Letter we identify a binary mixture of heterogeneous $k$-cores which exhibits a tricritical point. We investigate the new scaling scenario and calculate the relevant critical exponents, by analytical and computational methods, for Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi networks and 2D square lattices.