Eigenvariety of nonnegative symmetric weakly irreducible tensors associated with spectral radius and its application to hypergraphs

摘要

For a nonnegative symmetric weakly irreducible tensor, its spectral radius is an eigenvalue of the tensor corresponding to a unique positive eigenvector called the Perron vector. But including the Perron vector, it may have more than one eigenvector corresponding to the spectral radius. The projective eigenvariety of the tensor associated with the spectral radius is the set of the eigenvectors of the tensor corresponding to the spectral radius considered in the complex projective space.