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X_IN = \textrm{(sum of all edges with X on one end and a node inside the circle on the other end)} 
X_OUT = \textrm{(sum of all edges with X on one end and a node outside the circle on the other end)}





C(v_4,v_5,v_9)
= C(v_1,v_2,v_3,v_6,v_7,v_8)
= C(v_1,v_2,v_3) + C(v_6,v_7,v_8) - 2*c(v_1 v_2 v_3, v_6 v_7 v_8)
\leq  C(v_1,v_2,v_3) + C(v_6,v_7,v_8)
\leq  C(v_1,v_2,v_6) + C(v_6,v_7,v_8)