21 citations · 63 across the 9 of their papers we have counts for
9 papers
Hypergraphs: an introduction and review
Xavier Ouvrard
Hypergraphs were introduced in 1973 by Bergé. This review aims at giving some hints on the main results that we can find in the literature, both on the mathematical side and on the…
Tuning Ranking in Co-occurrence Networks with General Biased Exchange-based Diffusion on Hyper-bag-graphs
Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet
Co-occurence networks can be adequately modeled by hyper-bag-graphs (hb-graphs for short). A hb-graph is a family of multisets having same universe, called the vertex set. An effic…
The HyperBagGraph DataEdron: An Enriched Browsing Experience of Multimedia Datasets
Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet
Traditional verbatim browsers give back information in a linear way according to a ranking performed by a search engine that may not be optimal for the surfer. The latter may need…
Exchange-Based Diffusion in Hb-Graphs: Highlighting Complex Relationships
Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet
Most networks tend to show complex and multiple relationships between entities. Networks are usually modeled by graphs or hypergraphs; nonetheless a given entity can occur many tim…
Hypergraph Modeling and Visualisation of Complex Co-occurence Networks
Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet
Finding inherent or processed links within a dataset allows to discover potential knowledge. The main contribution of this article is to define a global framework that enables opti…
On Adjacency and e-Adjacency in General Hypergraphs: Towards a New e-Adjacency Tensor
Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet
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 conce…
Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hb-graphs and Related e-adjacency Tensors
Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet
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 multiplici…
Adjacency and Tensor Representation in General Hypergraphs Part 1: e-adjacency Tensor Uniformisation Using Homogeneous Polynomials
Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet
Adjacency between two vertices in graphs or hypergraphs is a pairwise relationship. It is redefined in this article as 2-adjacency. In general hypergraphs, hyperedges hold for -…
Networks of Collaborations: Hypergraph Modeling and Visualisation
Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet
The acknowledged model for networks of collaborations is the hypergraph model. Nonetheless when it comes to be visualized hypergraphs are transformed into simple graphs. Very often…