This program finds the maximum capacity in a directed graph with capacity at every edge. This is known as the Ford-Fulkerson algorithm.

It traverses from a start node named source to the final node named sink by finding a valid path through the graph. As it finds a valid path it allocates the maximum flow through that path to the entire graph. According to the Max-flow min-cut theorem any allocation of capacity which has exausted all available flows is a maximum flow.

When all paths are exausted the maximum flow is added up by summing all capacity allocated from the start node.

This program is written, and debugged with Go 1.10