Mathematical graph theory

Mathematical graph theory studies how points, called vertices, are connected by lines, called edges. It helps analyze relationships and patterns in networks such as social connections, transportation systems, or communication networks. Graphs can be used to find the shortest paths, detect clusters, or optimize routes. The discipline provides tools to model complex systems mathematically and assess their structure, connectivity, and efficiency. Essentially, graph theory offers a way to understand and solve problems involving interconnected entities by representing them as a collection of points and links.