Construction and Random Generation of Hypergraphs with Prescribed Degree and Dimension Sequences

by   Naheed Anjum Arafat, et al.

We propose algorithms for construction and random generation of hypergraphs without loops and with prescribed degree and dimension sequences. The objective is to provide a starting point for as well as an alternative to Markov chain Monte Carlo approaches. Our algorithms leverage the transposition of properties and algorithms devised for matrices constituted of zeros and ones with prescribed row- and column-sums to hypergraphs. The construction algorithm extends the applicability of Markov chain Monte Carlo approaches when the initial hypergraph is not provided. The random generation algorithm allows the development of a self-normalised importance sampling estimator for hypergraph properties such as the average clustering coefficient.We prove the correctness of the proposed algorithms. We also prove that the random generation algorithm generates any hypergraph following the prescribed degree and dimension sequences with a non-zero probability. We empirically and comparatively evaluate the effectiveness and efficiency of the random generation algorithm. Experiments show that the random generation algorithm provides stable and accurate estimates of average clustering coefficient, and also demonstrates a better effective sample size in comparison with the Markov chain Monte Carlo approaches.


page 1

page 2

page 3

page 4


Towards derandomising Markov chain Monte Carlo

We present a new framework to derandomise certain Markov chain Monte Car...

Dimension-independent Markov chain Monte Carlo on the sphere

We consider Bayesian analysis on high-dimensional spheres with angular c...

Structured Prediction of Sequences and Trees using Infinite Contexts

Linguistic structures exhibit a rich array of global phenomena, however ...

Linear-time uniform generation of random sparse contingency tables with specified marginals

We give an algorithm that generates a uniformly random contingency table...

A fast Metropolis-Hastings method for generating random correlation matrices

We propose a novel Metropolis-Hastings algorithm to sample uniformly fro...

Fast Lane-Level Intersection Estimation using Markov Chain Monte Carlo Sampling and B-Spline Refinement

Estimating the current scene and understanding the potential maneuvers a...

Convergence criteria for sampling random graphs with specified degree sequences

The configuration model is a standard tool for generating random graphs ...

Please sign up or login with your details

Forgot password? Click here to reset