Construction and random generation of hypergraphs with prescribed degree and dimension sequences
Paper in proceedings, 2020

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.

Author

Naheed Anjum Arafat

National University of Singapore (NUS)

Debabrota Basu

Chalmers, Computer Science and Engineering (Chalmers), Data Science

Laurent Decreusefond

Institut Polytechnique de Paris

Stéphane Bressan

National University of Singapore (NUS)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

03029743 (ISSN) 16113349 (eISSN)

Vol. 12392 LNCS 130-145

31st International Conference on Database and Expert Systems Applications, DEXA 2020
Bratislava, Slovakia,

Subject Categories

Probability Theory and Statistics

Discrete Mathematics

Computer Vision and Robotics (Autonomous Systems)

DOI

10.1007/978-3-030-59051-2_9

More information

Latest update

10/12/2020