The hybrid SDN environment exhibits highly dynamic and rapidly fluctuating traffic patterns, posing significant challenges to achieving efficient routing. While deep reinforcement learning (DRL) has shown promise in addressing traffic engineering tasks, existing models often overlook node-level routing behaviors and struggle to adapt to changing network topologies. This study introduces GGKM, a novel routing framework that combines a dual-adaptive graph neural architecture with Proximal Policy Optimization (PPO) to enhance route optimization. Unlike traditional methods, GGKM leverages a node-adaptive graph convolution operation to capture personalized routing preferences and incorporates a time-adaptive adjacency matrix to model the evolving dependencies between traffic flows. Extensive evaluations on real-world network scenarios demonstrate that GGKM outperforms existing approaches, achieving superior routing decisions in dynamic and fluctuating traffic conditions.