Spectral theory of weighted hypergraphs via tensors
Francesco Galuppi, Raffaella Mulas, Lorenzo Venturello
Abstract
One way to study a hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper, we study how properties of weighted hypergraphs are reflected on eigenvalues and eigenvectors of their associated tensors. We also show how to efficiently compute eigenvalues with some techniques from numerical algebraic geometry.
Topics & Concepts
HypergraphEigenvalues and eigenvectorsGeneralizationTensor (intrinsic definition)MathematicsAlgebraic numberENCODEAlgebraic propertiesPure mathematicsAlgebra over a fieldCombinatoricsMathematical analysisPhysicsBiochemistryQuantum mechanicsChemistryGeneTensor decomposition and applicationsMatrix Theory and AlgorithmsAdvanced Optimization Algorithms Research