Define the concept of feasible flow in networks.

Feasible flow in networks refers to the maximum amount of flow that can be sent through a network without violating any capacity constraints.

In a network, each edge has a capacity limit that restricts the amount of flow that can pass through it. Feasible flow is the maximum amount of flow that can be sent through the network without exceeding any of these capacity limits. This concept is important in network optimization problems, where the goal is to find the maximum flow that can be sent through the network.

To determine the feasible flow in a network, we can use the Ford-Fulkerson algorithm. This algorithm starts with an initial feasible flow and iteratively increases the flow until it reaches the maximum feasible flow. At each iteration, the algorithm finds an augmenting path, which is a path from the source to the sink that has available capacity. The algorithm then increases the flow along this path by the maximum amount possible, which is the minimum capacity of all the edges in the path. This process is repeated until no more augmenting paths can be found.

The maximum feasible flow is also known as the maximum flow, and it can be found using the max-flow min-cut theorem. This theorem states that the maximum flow in a network is equal to the minimum capacity of all the cuts in the network. A cut is a partition of the nodes into two disjoint sets, such that the source is in one set and the sink is in the other set. The capacity of a cut is the sum of the capacities of all the edges that cross the cut. The minimum cut is the cut with the smallest capacity, and its capacity is equal to the maximum flow.