Escape games have become widely popular across entertainment, educational, and training domains, yet their underlying mechanics remain largely informal and under-theorized. In this work, we introduce a novel framework that provides a formal representation of both the structural and dynamic aspects of escape games. Our approach relies on the Static Graph, a directed graph that encodes the topological and logical organization of puzzles, clues, rooms, and player roles. Game progression and player interaction are modeled through the Dynamic Graph, capturing the live state of a session, as well as the Game Session Forest, which represents the set of possible traces under alternative player choices. This graph-based design can easily be manipulated by verification algorithms, and as such paves the way for automated reasoning over essential aspects of escape games, ranging from solvability and balance to determining the initial constraints on players and rooms. The framework is operationalized and illustrated in GraphEG, an open-source visualization tool that supports both the design of escape game scenarios and their simulation.