Local-to-global mechanisms in multiscale networks

Investigate how local interaction mechanisms in multiscale complex networks generate global behavior and ascertain how global constraints feed back to shape local connectivity patterns within the maximum-entropy hyperbolic geometric framework.

Background

The review situates random hyperbolic graph models within a maximum-entropy (MaxEnt) statistical-mechanics framework and discusses their renormalizability and multiscale implications. Despite progress, the authors emphasize that connecting micro-level rules to macro-level structure and understanding feedback from global constraints to local organization is not yet resolved.

This open direction is motivated by the demonstrated scale-consistent properties of the S1/ℍ2 MaxEnt ensemble under geometric renormalization, suggesting that a principled explanation of how local and global scales interact should be possible but remains incomplete.

References

Real networks are inherently multiscale, with structure and function intertwined across spatial, temporal, and organizational levels, so understanding how local mechanisms generate global behavior, and how global constraints feed back locally, remains an open pursuit.

— 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