【摘 要】
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We present a spectral theory of hypergraphs that closely parallels graph spectral theory.Classic work by Gelfand-Kapranov-Zelevinsky and Canny,as well as mo
【机 构】
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UniversityofSouthCarolina
【出 处】
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International Conference on the spectral theory of the tenso
论文部分内容阅读
We present a spectral theory of hypergraphs that closely parallels graph spectral theory.Classic work by Gelfand-Kapranov-Zelevinsky and Canny,as well as more recent developments by Chang,Lim,Pearson,Qi,Zhang,and others 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 understand spectral graph theory (i.e.,ordinary matrices).Nonetheless,it is possible to define eigenvalues of a tensor via its characteristic polynomial and variationally.We apply this notion to the “adjacency hypermatrix” of a uniform hypergraph,and prove a number of natural analogues of graph theoretic results.Computations are particularly cumbersome with hyperdeterminants,so we discuss software developed in Sage which can perform basic calculations on small hypergraphs.Open problems abound,and we present a few directions for further research.
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