Mapping memory-biased dynamics with compact models reveals overlapping communities in large networks

TL;DR

This paper introduces a method to identify overlapping communities in large networks by modeling higher-order flows with compact, memory-biased models, improving robustness and interpretability over traditional approaches.

Contribution

It presents a novel approach using compact models and the map equation framework to detect overlapping communities based on higher-order flow dynamics.

Findings

Robust detection of overlapping communities in synthetic benchmarks.

Reveals interpretable communities in empirical networks.

Scales efficiently to large networks.

Abstract

Many real-world systems, from social networks to protein-protein interactions and species distributions, exhibit overlapping flow-based communities that reflect their functional organisation. However, reliably identifying such overlapping flow-based communities requires higher-order relational data, which are often unavailable. To address this challenge, we capitalise on the flow model underpinning the representation-learning algorithm node2vec and model higher-order flows through memory-biased random walks on first-order networks. Instead of simulating these walks, we model their higher-order dynamic constraints with compact models and control model complexity with an information-theoretic approach. Using the map equation framework, we identify overlapping modules in the resulting higher-order networks. Our compact-model approach proves robust across synthetic benchmark networks, reveals interpretable overlapping communities in empirical networks, and scales to large networks.