标题： 基于顶点集的给定划分，按生成树的最小权重分割图 显示英文标题

标题： Splitting a graph by a given partition of the set of vertices based on the minimum weight of the induced trees

摘要： 一种考虑带有顶点集给定划分的加权有向图的方法被提出。 所得的有向图（分裂图）不包含每个划分元素内部的弧，划分原子之间的弧以特殊方式计算，考虑到原始有向图在原子内部的弧。 这种计算基于在原子上定义的最小树。 研究了原始有向图在其分裂中保留了哪些信息。 显示英文摘要

摘要： A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs between the partition atoms are calculated in a special way taking into account the arcs of the original directed graph inside the atoms. This accounting is based on minimal trees defined on atoms. A study was made of what information about the original digraph is preserved in its splitting.