Hierarchy Structure of Graphs and Weighted Condensations

TL;DR

This paper introduces a hierarchical structure for directed graphs with weighted edges, constructing an algebraic system of subsets and their consolidations, and determining arc weights in the consolidated graphs.

Contribution

It presents a novel hierarchy framework for weighted directed graphs and develops an algebraic system for their consolidations and arc weight calculations.

Findings

Established a hierarchy structure for weighted directed graphs.

Constructed algebraic systems of subsets and consolidations.

Determined arc weights in consolidated graphs.

Abstract

By natural way the hierarchy structure is introduced on directed graphs with weighted adjacencies. Embedded system of algebras of subsets of the set of vertices of such digraph and it's consolidations, which vertices are the elementary sets of corresponding algebra, are constructed. Weights of arcs of consolidated graphs are determined.