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1	Graph Laplacians, Nodal Domains, and Hyperplane Arrangements Biyikoglu, Türker, Hordijk, Wim, Leydold, Josef, Pisanski, Tomaz, Stadler, Peter F. 08 November 2018 (has links) Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e. the connected components of the maximal induced subgraphs of G on which an eigenvector ψ does not change sign. An analogue of Courant's nodal domain theorem provides upper bounds on the number of nodal domains depending on the location of ψ in the spectrum. This bound, however, is not sharp in general. In this contribution we consider the problem of computing minimal and maximal numbers of nodal domains for a particular graph. The class of Boolean Hypercubes is discussed in detail. We find that, despite the simplicity of this graph class, for which complete spectral information is available, the computations are still non-trivial. Nevertheless, we obtained some new results and a number of conjectures. info:eu-repo/classification/ddc/510.72 ddc:510.72
2	Hypernode graphs for learning from binary relations between sets of objects / Un modèle d'hypergraphes pour apprendre des relations binaires entre des ensembles d'objets Ricatte, Thomas 23 January 2015 (has links) Cette étude a pour sujet les hypergraphes. / This study has for subject the hypergraphs. Hypergraphes Laplaciens de graphe Noyaux de graphe Apprentissage spectral Apprentissage semi-supervisé Algorithmes de skill rating Hypergraphs Graph laplacians Graph kernels Spectral learning Semi-supervised learning Skill rating algorithms

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Graph Laplacians, Nodal Domains, and Hyperplane Arrangements

Hypernode graphs for learning from binary relations between sets of objects / Un modèle d'hypergraphes pour apprendre des relations binaires entre des ensembles d'objets