Research on Inverse Reinforcement Learning (IRL) from third-person videos has shown encouraging results on removing the need for manual reward design for robotic tasks. However, most prior works are still limited by training from a relatively restricted domain of videos. In this paper, we argue that the true potential of third-person IRL lies in increasing the diversity of videos for better scaling. To learn a reward function from diverse videos, we propose to perform graph abstraction on the videos followed by temporal matching in the graph space to measure the task progress. Our insight is that a task can be described by entity interactions that form a graph, and this graph abstraction can help remove irrelevant information such as textures, resulting in more robust reward functions. We evaluate our approach, GraphIRL, on cross-embodiment learning in X-MAGICAL and learning from human demonstrations for real-robot manipulation. We show significant improvements in robustness to diverse video demonstrations over previous approaches, and even achieve better results than manual reward design on a real robot pushing task. Videos are available at https://graphirl.github.io/.