Abstract
Network methods capture the interplay between structure and dynamics of complex systems across scales by modeling indirect interactions as random walks. However, path data from real-world systems frequently exhibit memory effects that this first-order Markov model fails to capture. Although higher-order Markov models can capture these effects, they grow rapidly in size and require large amounts of data, making them prone to overfitting some parts and underfitting others in systems with uneven coverage. To address this challenge, we construct concise networks from path data by interpolating between first-order and second-order Markov models. We prioritize simplicity and interpretability by creating state nodes that capture prominent second-order effects and by proposing a transparent measure that balances model size and quality. Our concise networks reveal large-scale memory patterns in both synthetic and real-world systems while remaining far simpler than full second-order models.