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

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.