Pre-prints

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet

Abstract: 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 to assess the pertinence of the information retrieved, particularly when s⋅he wants to explore other facets of a multi-facetted information space. For instance, in a multimedia dataset different facets such as keyw… ▽ More

Submitted 28 May, 2019; originally announced May 2019.

Comments: Extension of the hypergraph framework shortly presented in arXiv:1809.00164 (possible small overlaps); use the theoretical framework of hb-graphs presented in arXiv:1809.00190

Exchange-Based Diffusion in Hb-Graphs: Highlighting Complex Relationships

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet

Abstract: 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 times in a relationship: this brings the need to deal with multisets instead of sets or simple edges. Diffusion processes are useful to highlight interesting parts of a network: they usually start with a stroke at one verte… ▽ More

Submitted 28 May, 2019; v1 submitted 1 September, 2018; originally announced September 2018.

Comments: arXiv:1809.00190v1: Accepted version of article submitted at CBMI 2018 IEEE This version is an extended version of arXiv:1809.00190v1 currently in submission

Hypergraph Modeling and Visualisation of Complex Co-occurence Networks

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet

Abstract: 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 optimal knowledge discovery by visually rendering co-occurences (i.e. groups of linked data instances attached to a metadata reference) - either inherently present or processed - from a dataset as facets. Hypergraphs are wel… ▽ More

Submitted 1 September, 2018; originally announced September 2018.

Comments: Preprint submitted at ENDM Special Journal 2nd IMA Conference on Theoretical and Computational Discrete Mathematic

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

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet

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 n… ▽ More

Submitted 1 September, 2018; originally announced September 2018.

Comments: Preprint submitted to ENDM special journal 2nd IMA Conference on Theoretical and Computational Discrete Mathematics

Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hb-graphs and Related e-adjacency Tensors

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stephane Marchand-Maillet

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 mu… ▽ More

Submitted 18 September, 2018; v1 submitted 30 May, 2018; originally announced May 2018.

Adjacency and Tensor Representation in General Hypergraphs Part 1: e-adjacency Tensor Uniformisation Using Homogeneous Polynomials

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet

Abstract: 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 n-adic relationship. To keep the n-adic relationship the concepts of k-adjacency and e-adjacency are defined. In graphs 2-adjacency and e-adjacency concepts match, just as k-adjacency and e-adjacency do for k-unifo… ▽ More

Submitted 30 May, 2018; v1 submitted 21 December, 2017; originally announced December 2017.

Authors: Xavier Ouvrard, Jean-Marie Le Goff, Stéphane Marchand-Maillet

Abstract: 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, the transformation is made by clique expansion of the hyperedges resulting in a loss of information for the user and in artificially more complex graphs due to the high number of edges represented. The extra-node repre… ▽ More

Submitted 1 July, 2017; originally announced July 2017.

Comments: 24 pages, 9 figure