Title: Skill Graph for Real-world Quadrupedal Robot Reinforcement Learning. Abstract: Deep Reinforcement Learning (DRL) is one of the promising methods for general learning policies from the environment. However, DRL has two basic problems: sample inefficiency and weak generalization. Real-world robotic DRL, for example, often requires time-consuming data collection and frequent human intervention to reset the environment. If faced with a new environment or task, the robot can master basic skills in advance instead of learning from scratch, then its learning efficiency and adaptability will be greatly improved. Therefore, in this paper, we propose a novel structured skill graph (SG) for accelerating the learning of robotic DRL policies and rapid adaptation to unseen real-world tasks. Similar to the knowledge graph (KG), SG adopts the tri-element structure to store information. But different from KG storing static knowledge, SG can store dynamic policies and adopt different tri-elements. To construct the SG, we utilize the various real-world quadrupedal locomotion skills in different realistic environments. When faced with new real-world tasks, the relevant skills in SK will be extracted and used to help the robotic DRL learning and rapid adaptation. Extensive experimental results on the real-world quadruped robot locomotion tasks demonstrate the effectiveness of SG for facilitating DRL-based robot learning. Real-world quadrupedal robots can adapt to new environments or tasks in minutes with the help of our SG.