Mapping flows on weighted and directed networks with incomplete observations

TL;DR

This paper extends Bayesian community detection methods to weighted and directed networks with incomplete data, improving robustness and reliability in identifying significant community structures despite missing observations.

Contribution

It introduces a new Bayesian approach for community detection in weighted and directed networks with incomplete data, incorporating metadata and enhancing robustness.

Findings

More reliable community detection with missing data

Effective incorporation of metadata information

Improved robustness over previous methods

Abstract

Detecting significant community structure in networks with incomplete observations is challenging because the evidence for specific solutions fades away with missing data. For example, recent research shows that flow-based community detection methods can highlight spurious communities in sparse undirected and unweighted networks with missing links. Current Bayesian approaches developed to overcome this problem do not work for incomplete observations in weighted and directed networks that describe network flows. To address this gap, we extend the idea behind the Bayesian estimate of the map equation for unweighted and undirected networks to enable more robust community detection in weighted and directed networks. We derive a weighted and directed prior network that can incorporate metadata information and show how an efficient implementation in the community-detection method Infomap provides more reliable communities even with a significant fraction of data missing.