Algebraic connectivity of an even uniform hypergraph

Authors:
Shenglong Hu;Liqun Qi
Affiliations:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
Venue:
Journal of Combinatorial Optimization
Year:
2012

Citing 4
Cited 1

Matrix analysis

Matrix analysis
Integer and combinatorial optimization

Integer and combinatorial optimization
Foundations of numerical multilinear algebra: decomposition and approximation of tensors

Foundations of numerical multilinear algebra: decomposition and approximation of tensors
Eigenvalues of a real supersymmetric tensor

Journal of Symbolic Computation

On determinants and eigenvalue theory of tensors

Journal of Symbolic Computation

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Abstract

We generalize Laplacian matrices for graphs to Laplacian tensors for even uniform hypergraphs and set some foundations for the spectral hypergraph theory based upon Laplacian tensors. Especially, algebraic connectivity of an even uniform hypergraph based on Z-eigenvalues of the corresponding Laplacian tensor is introduced and its connections with edge connectivity and vertex connectivity are discussed.