§ 1. Introduction

Define a closure of a directed graph $G=(V,E)$ as an induced set of vertexes of $G$, where the out-tended edges in $E$ start at some vertex in the closure of $G$ and end at some vertex in the closure, too. More formally, closure is defined as a set of vertexes $V'\subseteq V$, such that $\forall u\in V',s.t.\forall\left<u,v\right>\in E,v\in V'$.

For the Maximum Weight Closure of a Graph, we define it as, with starting out endowing vertexes in $V'$ costs called $w_u$, the maximum value of $\sum\limits_{u\in V'}w_u$.

§ 2. Construction of Algorithm

Add a source $s$ and a sink $t$ to the original graph, endow the origin edges in $E$ with capacities that $+\infty$, and connect $s$ with points with positive costs with the points' costs as capacities on them while $t$ connects to those with negative costs with the minus points' costs as capacities on them, where $+\infty$ is defined as any number greater or equal to $\sum |w_i|$.

More formally, as explained & illustrated:

Which make it easy to understand the answer would be $\text{min-cut}(G_N=\{V_N,E_N\})$.

[1] Referenced to 最小割模型在信息学竞赛中的应用 by 胡伯涛 Amber.