  Researchers use networks to model relational data from complex systems, and
tools from network science to map them and understand their function. Flow
communities capture the organization of various real-world systems such as
social networks, protein-protein interactions, and species distributions, and
are often overlapping. However, mapping overlapping flow-based communities
requires higher-order data, which is not always available. To address this
issue, we take inspiration from the representation-learning algorithm node2vec,
and apply higher-order biased random walks on first-order networks to obtain
higher-order data. But instead of explicitly simulating the walks, we model
them with sparse memory networks and control the complexity of the higher-order
model with an information-theoretic approach through a tunable information-loss
parameter. Using the map equation framework, we partition the resulting
higher-order networks into overlapping modules. We find that our method
recovers planted overlapping partitions in synthetic benchmarks and identifies
overlapping communities in real-world networks.
