
for ( each edge e in network ) do { f(e) = 0; } repeat { Clear the label of all nodes; Use DFS to find a path S → T { During DFS traversal: 1. Use only "flow augmenting edges" (1. forward edges that are unsaturated or 2. backward edges with flow > 0) 2. if ( node visited is unlabeled ) label the node x with the predecessor node } if ( T received a label ) { // T was reached by a flow augmenting path !! 1. Use the labels to trace (back) the path; 2. increase flow by the slack of the (flow augmenting) path } } until T not reached during DFS 

(The algorithm uses labels.
The flow augmenting path is highlighted for your convenient.)
Augment flow: by 3
Augment flow: by 1
Augment flow: by 1
Augment flow: by 1
Done
Solution: (max flow = 17)
Flow augmenting paths are "color coded" with the given amount of flow passing through various links.