You own a power plant and want to transmit electricity to a consumer. To do so, you will use a network of power lines connected through distribution nodes. Each line can carry only a limited current, corresponding to the maximum current it can withstand. Your aim is to transmit as much electricity as possible from the power plant to the customer without exceeding the capacities of the power lines. How can this be done?
A graph model of the power grid
---------------------------------
We can model this problem using graph theory. The arcs represent power lines together with the direction in which the current flows, while the vertices (or nodes) represent the distribution nodes, the power plant and the customer (see the figure below).
