Unstructured environments such as mountains, caves, construction sites, or disaster areas are challenging for autonomous navigation because of terrain irregularities. In particular, it is crucial to plan a path to avoid risky terrain and reach the goal quickly and safely. In this paper, we propose a method for safe and distance-efficient path planning, leveraging Traversal Risk Graph (TRG), a novel graph representation that takes into account geometric traversability of the terrain. TRG nodes represent stability and reachability of the terrain, while edges represent relative traversal risk-weighted path candidates. Additionally, TRG is constructed in a wavefront propagation manner and managed hierarchically, enabling real-time planning even in large-scale environments. Lastly, we formulate a graph optimization problem on TRG that leads the robot to navigate by prioritizing both safe and short paths. Our approach demonstrated superior safety, distance efficiency, and fast processing time compared to the conventional methods. It was also validated in several real-world experiments using a quadrupedal robot. Notably, TRG-planner contributed as the global path planner of an autonomous navigation framework for the DreamSTEP team, which won the Quadruped Robot Challenge at ICRA 2023. The project page is available at https://trg-planner.github.io .