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

TL;DR

This paper introduces a method for partitioning a weighted directed graph into a splitting graph that preserves certain structural information using minimal trees, with potential applications in graph analysis.

Contribution

It proposes a novel approach to split directed graphs based on minimal trees within partitions, preserving key information about the original graph.

Findings

The splitting graph excludes arcs within each partition element.

Arcs between partitions are computed considering minimal trees.

The method preserves specific structural information of the original graph.

Abstract

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.