Refinement of Metrics: Erd\H{o}s Number, a Case Study

TL;DR

This paper introduces the concept of refinement to improve metrics, specifically refining the Erdős number by applying new methods to the collaboration graph's shortest-path distance.

Contribution

It proposes two novel methods for refining metrics and applies them to generate new versions of the Erdős number based on the collaboration graph.

Findings

Developed two methods for metric refinement.

Produced several refined Erdős numbers.

Enhanced understanding of collaboration distances.

Abstract

We introduce a concept called refinement and develop two different ways of refining metrics. By applying these methods we produce several refinements of the shortest-path distance on the collaboration graph and hence a couple new versions of the Erd\H{o}s number.