Define the concept of residual network in maximum flow problems.

A residual network is a graph that represents the remaining capacity of edges in a maximum flow problem.

In a maximum flow problem, the goal is to find the maximum amount of flow that can be sent from a source node to a sink node in a network. The flow is sent through edges, which have a capacity that limits the amount of flow that can pass through them.

A residual network is created by subtracting the current flow from the capacity of each edge in the original network. This residual network shows the remaining capacity of each edge, which can be used to send additional flow.

To find the maximum flow in a network, we use the Ford-Fulkerson algorithm, which repeatedly finds an augmenting path in the residual network and increases the flow along that path. An augmenting path is a path from the source to the sink in the residual network that has positive capacity on all edges.

As we increase the flow along an augmenting path, we update the residual network by subtracting the flow from the forward edges and adding the flow to the backward edges. This creates a new residual network, which is used to find the next augmenting path.

The Ford-Fulkerson algorithm terminates when there are no more augmenting paths in the residual network. At this point, the flow in the network is maximum.