How can neural networks evolve themselves without relying on external optimizers? We propose Self-Referential Graph HyperNetworks, systems where the very machinery of variation and inheritance is embedded within the network. By uniting hypernetworks, stochastic parameter generation, and graph-based representations, Self-Referential GHNs mutate and evaluate themselves while adapting mutation rates as selectable traits. Through new reinforcement learning benchmarks with environmental shifts (CartPoleSwitch, LunarLander-Switch), Self-Referential GHNs show swift, reliable adaptation and emergent population dynamics. In the locomotion benchmark Ant-v5, they evolve coherent gaits, showing promising fine-tuning capabilities by autonomously decreasing variation in the population to concentrate around promising solutions. Our findings support the idea that evolvability itself can emerge from neural self-reference. Self-Referential GHNs reflect a step toward synthetic systems that more closely mirror biological evolution, offering tools for autonomous, open-ended learning agents.