Developing robotic intelligent systems that can adapt quickly to unseen wild situations is one of the critical challenges in pursuing autonomous robotics. Although some impressive progress has been made in walking stability and skill learning in the field of legged robots, their ability for fast adaptation is still inferior to that of animals in nature. Animals are born with a massive set of skills needed to survive, and can quickly acquire new ones, by composing fundamental skills with limited experience. Inspired by this, we propose a novel framework, named Robot Skill Graph (RSG) for organizing a massive set of fundamental skills of robots and dexterously reusing them for fast adaptation. Bearing a structure similar to the Knowledge Graph (KG), RSG is composed of massive dynamic behavioral skills instead of static knowledge in KG and enables discovering implicit relations that exist in between the learning context and acquired skills of robots, serving as a starting point for understanding subtle patterns existing in robots' skill learning. Extensive experimental results demonstrate that RSG can provide reliable skill inference upon new tasks and environments, and enable quadruped robots to adapt to new scenarios and quickly learn new skills.