Download Speed - Walkthrough

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 $1 \to 2 \to 4$ with bottleneck $3$. Flow becomes $3$. Next BFS finds path $1 \to 3 \to 4$ 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.