Hypothesis: Depending on their composition, hydrated gels can be homogeneous or phase-separated, which, in turn, affects their dynamical and mechanical properties. However, the nature of the structural features, if any, that govern the propensity for a given gel to phase-separate remains largely unknown. Here, we argue that the propensity for hydrated gels to phase-separate is topological in nature. Simulations: We employ reactive molecular dynamics simulations to model the early-age precipitation of calcium-alumino-silicate-hydrate (C-A-S-H) gels with varying compositions, i.e., (CaO)(1.7)(Al2O3)(x)(SiO2)(1-x)(H2O)(3.7 + x), By adopting topological constraint theory, we investigate the struc- tural origin of phase separation in hydrated gels. Findings: We report the existence of a homogeneous-to-phase-separated transition, wherein Si-rich (x <= 0.10) C-A-S-H gels are homogeneous, whereas Al-rich (x > 0.10) C-A-S-H gels tend to phase-separate. Furthermore, we demonstrate that this transition is correlated to a topological flexible-to-rigid transition within the atomic network. We reveal that the propensity for topologically-overconstrained gels to phase-separate arises from the existence of some internal stress within their atomic network, which acts as an energy penalty that drives phase separation. (C) 2021 Elsevier Inc. All rights reserved.