Flow problems

Another really interesting field of graph theory applications is flow problems, also known as maximum flow problems. In essence, this field is part of a larger field of optimization problems, which is trying to establish the best possible path across a flow network. Flow networks types of graphs in which the nodes/vertices of the graphs are connected by relationships/edges that specify the capacity of that particular relationship. Examples can be found in fields such as the telecom networks, gas networks, airline networks, package delivery networks, and many others, where graph-based models are then used in combination with complex algorithms. The following diagram is an example of such a network, as you can find it on http://enipedia.tudelft.nl/:

These algorithms are then used to identify the calculated optimal path, find bottlenecks, plan maintenance activities, conduct long-term capacity planning, and many other operations.