  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.
