Example: 4 nodes, 5 edges. Edges: (1,2,3), (1,3,5), (2,3,2), (2,4,4), (3,4,6). First BFS finds path 1→2→4 with bottleneck 3. Flow becomes 3. Next BFS finds path 1→3→4 with bottleneck 5. Flow becomes 8. No more paths exist from 1 to 4 in the residual graph.
Maximum flow is 8. The algorithm systematically finds all paths and uses them efficiently. Each augmentation increases the total flow until no improvement is possible.