# Constrained Monte Carlo Markov Chains on Graphs

## TL;DR

This paper introduces a new constrained Monte Carlo Markov chain method on graphs, ensuring convergence to a target distribution while respecting graph connectivity constraints.

## Contribution

It proposes a novel MCMC procedure constrained by graph structure, linking distribution support to graph connectedness for convergence analysis.

## Key findings

- Convergence of the Markov chain to the target distribution under graph constraints
- Analysis of the relationship between distribution support and graph connectedness
- Framework applicable to graph-structured state spaces

## Abstract

This paper presents a novel theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov chain is constrained over an underlying graph, so that states are viewed as vertices and the transition between two states can have positive probability only in presence of an edge connecting them. The analysis is carried out on the basis of the relationship between the support of the target distribution and the connectedness of the graph.