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- W2140994015 abstract "We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of hyperdeterminants of hypermatrices, a.k.a. multidimensional arrays. Hyperdeterminants share many properties with determinants, but the context of multilinear algebra is substantially more complicated than the linear algebra required to address Spectral Graph Theory (i.e., ordinary matrices). Nonetheless, it is possible to define eigenvalues of a via its characteristic polynomial as well as variationally. We apply this notion to the adjacency hypermatrix of a uniform hypergraph, and prove a number of natural analogues of basic results in Spectral Graph Theory. Open problems abound, and we present a number of directions for further study." @default.
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- W2140994015 date "2011-06-23" @default.
- W2140994015 modified "2023-09-27" @default.
- W2140994015 title "Spectra of Uniform Hypergraphs" @default.
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