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000597028 1001_ $$0P:(DE-H253)PIP1106484$$aFazeny, Ariane$$b0$$eCorresponding author
000597028 245__ $$aHypergraph p-Laplacians and Scale Spaces
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000597028 520__ $$aThe aim of this paper is to revisit the definition of differential operators on hypergraphs, which are a natural extension of graphs in systems based on interactions beyond pairs. {In particular, we focus on the definition of Laplacian and $p$-Laplace operators for oriented and unoriented hypergraphs} their basic properties, variational structure, and their scale spaces.        We illustrate that diffusion equations on hypergraphs are possible models for different applications such as information flow on social networks or image processing. Moreover, the spectral analysis and scale spaces induced by these operators provide a potential method to further analyze complex {data} and their multiscale structure.     The quest for spectral analysis and suitable scale spaces on hypergraphs motivates in particular a definition of differential operators with trivial first eigenfunction and thus more interpretable second eigenfunctions. This property is not automatically satisfied in existing definitions of hypergraph $p$-Laplacians and we hence provide a novel axiomatic approach that extends previous definitions and can be specialized to satisfy such (or other) desired properties.
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000597028 7001_ $$0P:(DE-HGF)0$$aLukin, Kseniaa$$b2
000597028 7001_ $$0P:(DE-H253)PIP1103953$$aBurger, Martin$$b3
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