The Edmonds-Karp algorithm is an efficient method for solving the maximum flow problem in a flow network. It builds on the Ford-Fulkerson method by using BFS (Breadth-First Search) to find the shortest augmenting paths. This ensures that the algorithm runs in polynomial time, specifically O(VE²), where V is the number of vertices and E is the number of edges in the network. In the Edmonds-Karp algorithm, the flow is increased iteratively by finding paths from the source to the sink. Each path found allows for additional flow to be pushed through the network until no more augmenting paths can be identified, resulting in the maximum flow from the source to the sink.