On Adjacency and e-Adjacency in General Hypergraphs: Towards a New e-Adjacency Tensor

Ouvrard, Xavier Eric; Le Goff, Jean-Marie; Marchand-Maillet, Stéphane

doi:10.1016/j.endm.2018.11.012

Scientific article

English

On Adjacency and e-Adjacency in General Hypergraphs: Towards a New e-Adjacency Tensor

Contributors

Ouvrard, Xavier Eric; Le Goff, Jean-Marie; Marchand-Maillet, Stéphane

Published in

Electronic Notes in Discrete Mathematics, vol. 70, p. 71-76

Publication date

2018

Abstract

In graphs, the concept of adjacency is clearly defined: it is a pairwise relationship between vertices. Adjacency in hypergraphs has to integrate hyperedge multi-adicity: the concept of adjacency needs to be defined properly by introducing two new concepts: k-adjacency – k vertices are in the same hyperedge – and e-adjacency – vertices of a given hyperedge are e-adjacent. In order to build a new e-adjacency tensor that is interpretable in terms of hypergraph uniformisation, we designed two processes: the first is a hypergraph uniformisation process (HUP) and the second is a polynomial homogeneisation process (PHP). The PHP allows the construction of the e-adjacency tensor while the HUP ensures that the PHP keeps interpretability. This tensor is symmetric and can be fully described by the number of hyperedges; its order is the range of the hypergraph, while extra dimensions allow to capture additional hypergraph structural information including the maximum level of k-adjacency of each hyperedge. Some results on spectral analysis are discussed.

Keywords

Hypergraph
E-adjacency tensor
Uniformisation
Homogeneisation

UNIGE affiliation entities

UNIGE research groups

Citation (ISO format)

OUVRARD, Xavier Eric, LE GOFF, Jean-Marie, MARCHAND-MAILLET, Stéphane. On Adjacency and e-Adjacency in General Hypergraphs: Towards a New e-Adjacency Tensor. In: Electronic Notes in Discrete Mathematics, 2018, vol. 70, p. 71–76. doi: 10.1016/j.endm.2018.11.012

Article (Published version)

Identifiers

PID : unige:129063
DOI : 10.1016/j.endm.2018.11.012

Additional URL for this publication

https://linkinghub.elsevier.com/retrieve/pii/S1571065318302075

Journal ISSN

1571-0653

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15/01/2020 16:05:00

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08/05/2025 11:24:46

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03/12/2025 07:40:08

On Adjacency and e-Adjacency in General Hypergraphs: Towards a New e-Adjacency Tensor

Contributors

Published in

Publication date

Abstract

Keywords

UNIGE affiliation entities

UNIGE research groups

Citation (ISO format)

Main files (1)

Identifiers

Additional URL for this publication

Journal ISSN

Technical informations

Creation

First validation

Update

Status update

Last indexation