MaxEnt frameworks for weighted, temporal, multiplex, and higher‑order networks

Develop maximum-entropy ensembles for weighted and signed networks, temporal networks, multiplex (multilayer) networks, and higher-order interaction structures (hypergraphs and simplicial complexes) that remain analytically tractable, scalable, and compatible with geometric embeddings and renormalization, extending the existing fermionic MaxEnt framework for binary pairwise graphs and, where appropriate, formulating bosonic analogues for multi-edge or weighted descriptions.

Background

The paper frames simple, unweighted links as indistinguishable fermions in a grand-canonical MaxEnt ensemble, yielding tractable models with strong explanatory power for many structural features. However, real systems often involve weights, signs, temporal dynamics, multiplex couplings, and higher-order interactions, for which analogous MaxEnt formulations are not yet established.

The authors explicitly identify extending MaxEnt to these richer settings as a largely open frontier, noting that weighted/multi-edge cases may require bosonic analogues and that higher-order interactions demand ensembles defined on hyperedges or simplices rather than just links.

References

Increasing realism in the description of real networks brings additional layers of information---weights and signs on links, temporal evolution, multiplex structure, and higher-order interactions---which demand new generative models and inference tools that retain interpretability while balancing accuracy against computational and conceptual complexity. Extending maximum-entropy approaches to these settings is a largely open frontier: while binary, pairwise ensembles admit a clean fermionic interpretation, weighted or multi-edge descriptions naturally suggest bosonic analogues, and higher-order interactions call for ensembles defined on hyperedges or simplices rather than on links.

— Statistical Mechanics of Random Hyperbolic Graphs within the Fermionic Maximum-Entropy Framework  (2603.18170 - Serrano, 18 Mar 2026) in Section 5: Discussion and open problems