A Measure of the Connection Strengths between Graph Vertices with Applications

TL;DR

This paper introduces a simple, efficient iterative method to measure connection strengths between graph vertices, demonstrating its effectiveness in combinatorial optimization problems and offering a parallelizable solution.

Contribution

It proposes a novel, linear-complexity, parallelizable iterative strategy for assessing vertex connection strengths, supported by a convergence analysis and practical applications.

Findings

Effective in combinatorial optimization problems

Linear complexity and easily parallelizable

Converges reliably based on analysis

Abstract

We present a simple iterative strategy for measuring the connection strength between a pair of vertices in a graph. The method is attractive in that it has a linear complexity and can be easily parallelized. Based on an analysis of the convergence property, we propose a mutually reinforcing model to explain the intuition behind the strategy. The practical effectiveness of this measure is demonstrated through several combinatorial optimization problems on graphs and hypergraphs.