Consider the following maximum flow problem. The numbers next to each arc represent the capacity of the arc, and our goal is to find the maximum amount of flow that can be sent from the source node $($so$)$ to sink node $($si$).$

$6$

$1$

$3$

$7$

$2$

$1$

$3$

so

$2$

si

$3$

$8$

$2$

$4$

$8$

An IE $342$ student has started implementing the Ford$-$Fulkerson algorithm to find the optimal solution. Currently, she has the following solution as a feasible solution. The number next to an arc represents the amount of flow sent through that arc.

$3$

$1$

$3$

$4$

$2$

so

$13$

$2$

si

$3$

$5$

$2$

$4$

$7$