Maximum entropy temporal networks

Researcher Paolo Barucca has published a significant paper titled 'Maximum entropy temporal networks' on arXiv, introducing a novel framework for modeling continuous-time network interactions. The work addresses a key gap in network science—few studies have directly tackled continuous-time modeling of networks where interactions appear as timestamped events. Barucca's approach applies maximum-entropy principles to create temporal network ensembles with basic constraints, resulting in a modular representation that factors into global time processes and static maximum-entropy edge probabilities.

This factorization yields several practical benefits: closed-form log-likelihood calculations, expectations for network properties like degree distributions and clustering coefficients, and a whole class of effective generative models. The paper demonstrates how the maximum-entropy derivation connects non-homogeneous Poisson process (NHPP) intensities—which govern the probability of directed edges in temporal networks—to maximum-entropy network ensembles through functional optimization over path entropy. The NHPP approach consistently improves log-likelihood over generic Poisson processes while recovering strength constraints and reproducing expected unique-degree curves.

The framework also discusses integration points with existing methodologies, including multivariate Hawkes calibration procedures, renewal theory, and neural kernel estimation in graph neural networks. While acknowledging limitations, the paper provides a mathematically rigorous foundation that could significantly advance how researchers model dynamic networks where timing and sequence of interactions matter, from social networks to financial transaction networks.