Generalized Erdos Numbers

TL;DR

This paper introduces a real-valued, asymmetric generalization of Erdos numbers to better capture node 'closeness' in weighted graphs, demonstrating its utility in network analysis and improving ratings prediction.

Contribution

It presents a novel real-valued, asymmetric Erdos number generalization and applies it to network analysis and ratings prediction, outperforming baseline methods.

Findings

The generalized Erdos number distinguishes network topologies better than standard metrics.

Application to Netflix data improved ratings prediction accuracy.

The measure is effective on analytically tractable networks.

Abstract

We propose a simple real-valued generalization of the well known integer-valued Erdos number as a topological, non-metric measure of the `closeness' felt between two nodes in an undirected, weighted graph. These real-valued Erdos numbers are asymmetric and are able to distinguish between network topologies that standard distance metrics view as identical. We use this measure to study some simple analytically tractable networks, and show the utility of our measure to devise a ratings scheme based on the generalized Erdos number that we deploy on the data from the NetFlix prize, and find a significant improvement in our ratings prediction over a baseline.