Neighbor-Neighbor Correlations Explain Measurement Bias in Networks

TL;DR

This paper investigates how neighbor-neighbor correlations influence measurement bias in networks, particularly explaining the strong friendship paradox through a predictive model that accounts for degree correlations beyond immediate neighbors.

Contribution

It introduces a model incorporating neighbor-neighbor correlations to accurately predict the strong friendship paradox in real-world networks.

Findings

Negative degree correlations amplify the friendship paradox.

Including neighbor-neighbor correlations improves prediction accuracy.

Understanding these biases aids in better network measurements.

Abstract

In numerous physical models on networks, dynamics are based on interactions that exclusively involve properties of a node's nearest neighbors. However, a node's local view of its neighbors may systematically bias perceptions of network connectivity or the prevalence of certain traits. We investigate the strong friendship paradox, which occurs when the majority of a node's neighbors have more neighbors than does the node itself. We develop a model to predict the magnitude of the paradox, showing that it is enhanced by negative correlations between degrees of neighboring nodes. We then show that by including neighbor-neighbor correlations, which are degree correlations one step beyond those of neighboring nodes, we accurately predict the impact of the strong friendship paradox in real-world networks. Understanding how the paradox biases local observations can inform better measurements of network structure and our understanding of collective phenomena.