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

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