How can graphs represent transportation networks?

In graph theory, transportation networks are represented by modeling locations as vertices (points or nodes) and the routes connecting them as edges (lines).12

To accurately reflect real-world logistics, these models often utilize directed graphs, where edges have a specific direction to account for one-way streets or specific travel paths. Furthermore, mathematicians assign a non-negative weight to each edge, which typically represents the distance, travel time, or cost associated with that specific route.12

By structuring a network this way, researchers can apply optimization techniques to solve complex logistical challenges, such as the traveling-salesman problem. This classic problem seeks the most efficient path that visits every city in a network exactly once while minimizing the total weight of the edges traversed. These mathematical representations are essential for modern operations research, allowing for the efficient routing of people, products, and data.12