Reinforcement Learning for Microcanonical Graph Ensemble with Assortativity Constraints

2026-05-22

AI Summary

Existing graph generation methods struggle to precisely control assortativity while strictly preserving the degree sequence, thereby limiting investigations into structure–function relationships. This work proposes the Deep Microcanonical Graph Generator (DMGG), which introduces reinforcement learning to graph generation for the first time. By performing degree-preserving rewiring operations, DMGG directly optimizes the joint degree matrix to accurately achieve a target assortativity, constructing microcanonical ensembles that satisfy hard constraints. In contrast to traditional exponential random graph models—relying on soft constraints and Metropolis–Hastings sampling—DMGG eliminates the need for tedious parameter tuning and accelerates generation by over an order of magnitude. It demonstrates broad generality across graph sizes, sparsity levels, and topologies, while effectively decoupling secondary structural features such as clustering coefficient, thereby providing artifact-free, precise null models for network analysis.

Abstract

How network structure determines function is a fundamental question, and it can be investigated by graph ensembles with precisely controlled structural properties. Canonical approaches, formulated as exponential random graph models (ERGMs), enforce constraints only in expectation, allowing individual realizations to fluctuate around the target. Conversely, microcanonical ensembles impose hard constraints exactly, but practical sampling methods beyond fixing the degree sequence have remained out of reach. Here we introduce the Deep Microcanonical Graph Generator (DMGG), a reinforcement learning (RL) framework that transforms any given graph through degree-preserving rewirings to exactly reach a prescribed assortativity, which characterizes the degree--degree correlation of adjacent nodes. Instead of relying on the entropically dominated Metropolis--Hastings dynamics of the ERGM, DMGG employs a policy-guided search that maximally alters the joint-degree matrix. This eliminates exhaustive parameter tuning and accelerates generation by at least an order of magnitude while preserving configurational diversity. As DMGG generalizes across various graph sizes, sparsities, and topologies, it provides exact null models that allow for the quantitative isolation of secondary observables, such as the clustering coefficient. These results establish RL as a practical and powerful paradigm for generating hard-constrained graphs, opening avenues to investigate structure-function relationships free from ensemble artifacts.

Problem

• microcanonical graph ensemble
• assortativity constraints
• hard constraints
• graph generation
• structure-function relationship

Innovation

• reinforcement learning
• microcanonical graph ensemble
• assortativity constraints
• degree-preserving rewiring
• exact null models