The Ford-Fulkerson method and the Edmonds-Karp algorithm both help us find the maximum flow in a flow network. However, they have different ways of doing this.

1. How They Work:

   • The Ford-Fulkerson method is a general way to solve the problem. It looks for paths in a special type of graph called a residual graph. This method can use different techniques to find these paths, like depth-first search (DFS) or breadth-first search (BFS).
   • The Edmonds-Karp algorithm is a specific version of the Ford-Fulkerson method. It only uses BFS to find the shortest paths that help increase the flow.

2. Speed:

   • The time it takes for the Ford-Fulkerson method to work can vary. It depends on how paths are found. In some cases, it can take a long time if the weights (or values) in the flow network are complicated.
   • The Edmonds-Karp algorithm has a clear time limit. It typically takes $O(VE^2)$ time, where $V$ is the number of points (or vertices) and $E$ is the number of connections (or edges). This makes it easier to predict how long it will take.

3. Choosing Paths:

   • In Ford-Fulkerson, picking different paths can lead to different maximum flows. This means results can change based on the path you choose.
   • The Edmonds-Karp algorithm makes it simpler by always picking the shortest path. This means it often gives more reliable results and avoids slow paths.

In short, both algorithms aim to solve the same problem. However, the Edmonds-Karp algorithm improves on Ford-Fulkerson by following a certain method for finding paths. This helps ensure a more reliable and efficient solution for maximum flow in network flow problems.