This paper discusses the application of one of the Discrete Mathematics materials, namely Graph Theory, in determining the fastest route from Subang City, more precisely from Subang Pusakanagara, Subang to Cirebon City. The fastest path is the route taken by considering the minimum travel time from one place to another. There are various ways to determine the minimum travel path, but the goal is the same, namely to find a travel path with the minimum travel time. The research process begins with formulating a problem using Graph Theory with the help of the Google Maps application and the experiences of the researchers. This Google Maps application is very useful when traveling long distances but want to use the path with minimal travel time. After formulating the problem, it is continued with the implementation of the Weighted Average Method and ends with the Floyd Warshall Algorithm. The result of this study is to find the fastest path from the starting point, namely Subang Pusakanagara to the end point, namely Cirebon City.