Residual Capacity

Given flow network G = (V, E) with flow f and two vertices u, v $\in$ V, define the residual capacity c_f(u,v) as the additional net flow possible from u to v, not exceeding c(u,v). Thus

$$c_f(u,v) \;=\; c(u,v) \;-\; f(u,v).$$

Example

$$c_f(s, v_2) \;=\; c(s, v_2) \;-\; f(s, v_2) \;=\; 4 \;-\; 2 \;=\; 2$$

$$c_f(v_2, t) \;=\; 2 \;-\; 2 \;=\; 0$$

$$c_f(t, v_2) \;=\; 0 \;-\; (-2) \;=\; 2$$