Mathematical modeling The shortest path model in graph theory has important application value in urban planning. First of all, it can help urban planners to determine the optimal layout of urban transportation network. By constructing the road network map of the city, the shortest path from one place to another can be calculated by using the shortest path algorithm, thus providing a basis for the planning of urban roads, public transportation and other infrastructure.

Secondly, the shortest path model can help urban planners optimize the urban logistics distribution system. In modern cities, logistics distribution is an important link, and how to transport goods from one place to another quickly and efficiently is of great significance to improve the efficiency of urban operation. By establishing the city logistics distribution network diagram and using the shortest path algorithm, we can provide the best distribution route for logistics companies, reduce transportation costs and improve distribution efficiency.

In addition, the shortest path model can also be applied to the planning of urban public service facilities. For example, when planning public service facilities such as medical care and education, the shortest path model can be used to analyze the distance and time between residents and these facilities, so as to rationally arrange public service facilities and improve the quality of life of residents.

In a word, mathematical modeling and graph theory shortest path model have a wide application prospect in urban planning. Through the optimization of urban transportation, logistics and public services, it is helpful to improve the operational efficiency of the city and the quality of life of residents. In the future urban development, the shortest path model will play an increasingly important role.