Mapping compact memory-biased dynamics reveals overlapping communities

Abstract:

Researchers use networks to model relational data from complex systems and apply tools from network science to reveal their organisation and function. 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, identifying such overlapping flow-based communities typically requires higher-order relational data, which is often unavailable. To address this challenge, we draw inspiration from the representation-learning algorithm \textsl{node2vec} and model higher-order flows through memory-biased random walks on first-order networks. Instead of simulating these walks, we model their constraints with sparse memory networks 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 method proves robust across synthetic benchmark networks and reveals interpretable overlapping communities in empirical networks.