Mapping flows on sparse networks with missing links

TL;DR

This paper introduces a Bayesian-enhanced map equation method to detect meaningful flow-based communities in sparse, incomplete networks, reducing overfitting and uncovering significant structures.

Contribution

It extends the map equation framework by integrating Bayesian network uncertainty estimates, enabling reliable community detection in undersampled networks.

Findings

Bayesian map equation outperforms traditional methods on synthetic data.

Effective in revealing true communities in real-world sparse networks.

Reduces overfitting caused by missing links in network analysis.

Abstract

Unreliable network data can cause community-detection methods to overfit and highlight spurious structures with misleading information about the organization and function of complex systems. Here we show how to detect significant flow-based communities in sparse networks with missing links using the map equation. Since the map equation builds on Shannon entropy estimation, it assumes complete data such that analyzing undersampled networks can lead to overfitting. To overcome this problem, we incorporate a Bayesian approach with assumptions about network uncertainties into the map equation framework. Results in both synthetic and real-world networks show that the Bayesian estimate of the map equation provides a principled approach to revealing significant structures in undersampled networks.