Optimal graphons in the edge-2star model
Abstract
In the edge-2star model with hard constraints, we prove the existence of an open set of constraint parameters, bisected by a line segment on which there are nonunique entropy-optimal graphons related by a symmetry. At each point in the open set but off the line segment, there is a unique entropy-optimizer, bipodal and varying analytically with the constraints. We also show that throughout another open set, containing a different portion of the same line of symmetry, there is instead a unique optimal graphon, varying analytically with the parameters. We explore the extent of these open sets, determining the point at which a symmetric graphon ceases to be a local maximizer of the entropy. Finally, we prove some foundational theorems in a general setting, relating optimal graphons to the Boltzmann entropy and the generic structure of large constrained random graphs.
Fields of Study & Subjects
Markov Chains and Monte Carlo Methods
Theoretical and Computational Physics
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions
- Publisher
- European Mathematical Society - EMS - Publishing House GmbH
- Volume
- 13
- Issue
- 2
- Pages
- 217–244
- Publication date
- 7 January 2026
- Language
- EN