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A talk intitulated On Hb-graphs and their application to hypergraph e-adjacency tensor has been accepted: it has been divided in two talks of 20 minutes.
The slides can be found here.
This talk is based on the following pre-print.
arXiv:1805.11952 [pdf, ps, other] cs.DM
Adjacency and Tensor Representation in General Hypergraphs.Part 2: Multisets, Hb-graphs and Related e-adjacency Tensors
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.
Submitted 18 September, 2018; v1 submitted 30 May, 2018; originally announced May 2018.
On the conference itself:
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I presented one talk and one poster.
The talk was intitulated:
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A talk has been presented: Exchange-Based Diffusion in Hb-Graphs: Highlighting Complex Relationships
The slides can be found here:
The accepted article can be found here:
arXiv:1809.00190 [pdf, ps, other] cs.DS
Exchange-Based Diffusion in Hb-Graphs: Highlighting Complex Relationships
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 vertex and diffuse throughout the network to reach a uniform distribution. Several iterations of the process are required prior to reaching a stable solution. We propose an alternative solution to highlighting main components of a network using a diffusion process based on exchanges; it is an iterative two-phase step exchange process. This process allows to evaluate the importance not only at the vertices level but also at the regrouping level. To model the diffusion process, we extend the concept of hypergraphs that are family of sets to family of multisets, that we call hb-graphs.
Submitted 1 September, 2018; originally announced September 2018.
Comments: Accepted version of article submitted at CBMI 2018 IEEE
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A talk intitulated:
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The talk at APMEP was presenting:
Graphs and hypergraphs at CERN
Slides are mixed between English and French and can be found here