# An Efficient Monte Carlo Method to Make a Geometric Graph with a Fixed Connectivity

@article{Sasaki2020AnEM,
title={An Efficient Monte Carlo Method to Make a Geometric Graph with a Fixed Connectivity},
author={Munetaka Sasaki},
journal={arXiv: Statistical Mechanics},
year={2020}
}
• M. Sasaki
• Published 2 April 2020
• Mathematics, Computer Science
• arXiv: Statistical Mechanics
We present a Markov chain Monte-Carlo (MCMC) method to make a geometric graph which satisfies the following two conditions: (i) The degree of each vertex is fixed to a positive integer $k$. (ii) The probability that two vertices located on a $d$-dimensional hypercubic lattice are connected by an edge is proportional to $d_{ij}^{-\alpha}$, where $d_{ij}$ is the distance between the two vertices and $\alpha$ is a positive exponent. We introduce a reverse update method and a list-based update…

## References

The graph becomes a d-dimensional hypercubic lattice when k = 2d and α = ∞