Black Hole Metric: Overcoming the PageRank Normalization Problem

TL;DR

This paper introduces the Black Hole Metric, a generalization of PageRank, designed to address normalization issues that affect ranking accuracy in network analysis, validated through tests on real and synthetic networks.

Contribution

The paper proposes the Black Hole Metric, a novel ranking method that overcomes PageRank normalization problems, with demonstrated effectiveness on various network types.

Findings

Black Hole Metric reduces normalization side-effects in PageRank.

The new metric improves ranking accuracy in tested networks.

Results show better performance compared to traditional PageRank.

Abstract

In network science, there is often the need to sort the graph nodes. While the sorting strategy may be different, in general sorting is performed by exploiting the network structure. In particular, the metric PageRank has been used in the past decade in different ways to produce a ranking based on how many neighbors point to a specific node. PageRank is simple, easy to compute and effective in many applications, however it comes with a price: as PageRank is an application of the random walker, the arc weights need to be normalized. This normalization, while necessary, introduces a series of unwanted side-effects. In this paper, we propose a generalization of PageRank named Black Hole Metric which mitigates the problem. We devise a scenario in which the side-effects are particularily impactful on the ranking, test the new metric in both real and synthetic networks, and show the results.