- An active network is a prototype modeling of a system where the `particles' have a self-propulsion mechanism. We highlight the emergent aspect of topological stochastic disorder (TSD), and discuss its consequences. We illuminate 3 different routes to under-damped relaxation: (a) delocalization of a relaxation mode due to drift; (b) topological symmetry breaking of a relaxation mode; (c) TSD-induced mixing of different relaxation modes. The localization of the relaxation modes due to TSD plays a major role in the analysis. This type of novel non-Hermitian localization is very different from the conservative Anderson-type localization.