Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hb-graphs and Related e-adjacency Tensors
Discrete Mathematics
2018-09-19 v3 Combinatorics
Abstract
HyperBagGraphs (hb-graphs as short) extend hypergraphs by allowing the hyperedges to be multisets. Multisets are composed of elements that have a multiplicity. When this multiplicity has positive integer values, it corresponds to non ordered lists of potentially duplicated elements. We define hb-graphs as family of multisets over a vertex set; natural hb-graphs correspond to hb-graphs that have multiplicity function with positive integer values. Extending the definition of e-adjacency to natural hb-graphs, we define different way of building an e-adjacency tensor, that we compare before having a final choice of the tensor. This hb-graph e-adjacency tensor is used with hypergraphs.
Keywords
Cite
@article{arxiv.1805.11952,
title = {Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hb-graphs and Related e-adjacency Tensors},
author = {Xavier Ouvrard and Jean-Marie Le Goff and Stephane Marchand-Maillet},
journal= {arXiv preprint arXiv:1805.11952},
year = {2018}
}