Spectra of uniform hypergraphs

• Published in: Linear algebra and its applications Vol. 436; no. 9; pp. 3268 - 3292
• Main Authors: Cooper, Joshua, Dutle, Aaron
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.05.2012; Elsevier
• Subjects: Algebra; Characteristic polynomial; Exact sciences and technology; Hypergraph; Linear and multilinear algebra, matrix theory; Mathematics; Resultant; Sciences and techniques of general use; Spectrum; Hypergraph; Primary 05C65; Secondary 15A69; Resultant; Characteristic polynomial; 15A18; Spectrum; Adjacency matrix; Graph theory; Integer; Algebra; Spectral theory; Eigenvalue problem

We present a spectral theory of uniform hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of “symmetric hyperdeterminants” of hypermatrices, a.k.a. multidimensional arrays. Symmetric hyperdeterminant...