This paper explores Pursuit-Evasion scenarios within game theory, focusing on environments with finite spaces, a limited number of pursuers, and evaders. It introduces a novel approach employing Petri nets to model Pursuit-Evasion in a bidirectional graph. Each area of the environment is represented by a set of places in the Petri net, capturing its specific behavior. Petri nets, known for their efficacy in modeling finite state spaces, are utilized to combine sub-nets representing individual areas. The detailed modeling provides a structured and formal representation of Pursuit-Evasion dynamics, offering a powerful tool to validate search strategies in graph-based pursuit-evasion models and contributing to the broader understanding of game theory and system modeling.