84 citations · 354 across the 25 of their papers we have counts for
8 papers · 1 filter
The contractivity of cone-preserving multilinear mappings
Antoine Gautier, Francesco Tudisco
With the notion of mode- Birkhoff contraction ratio, we prove a multilinear version of the Birkhoff-Hopf and the Perron-Fronenius theorems, which provide conditions on the exist…
The Perron-Frobenius theorem for multi-homogeneous mappings
Antoine Gautier, Francesco Tudisco, Matthias Hein
The Perron-Frobenius theory for nonnegative matrices has been generalized to order-preserving homogeneous mappings on a cone and more recently to nonnegative multilinear forms. We…
A unifying Perron-Frobenius theorem for nonnegative tensors via multi-homogeneous maps
Antoine Gautier, Francesco Tudisco, Matthias Hein
We introduce the concept of shape partition of a tensor and formulate a general tensor eigenvalue problem that includes all previously studied eigenvalue problems as special cases.…
The Perron-Frobenius Theorem for Multi-homogeneous Maps
Antoine Gautier, Francesco Tudisco, Matthias Hein
We introduce the notion of order-preserving multi-homogeneous mapping which allows to study Perron-Frobenius type theorems and nonnegative tensors in unified fashion. We prove a we…
A nodal domain theorem and a higher-order Cheeger inequality for the graph -Laplacian
Francesco Tudisco, Matthias Hein
We consider the nonlinear graph -Laplacian and its set of eigenvalues and associated eigenfunctions of this operator defined by a variational principle. We prove a nodal domain…
Localization of dominant eigenpairs and planted communities by means of Frobenius inner products
Dario Fasino, Francesco Tudisco
We propose a new localization result for the leading eigenvalue and eigenvector of a symmetric matrix . The result exploits the Frobenius inner product between and a given r…
Modularity bounds for clusters located by leading eigenvectors of the normalized modularity matrix
Dario Fasino, Francesco Tudisco
Nodal theorems for generalized modularity matrices ensure that the cluster located by the positive entries of the leading eigenvector of various modularity matrices induces a conne…
Generalized modularity matrices
Dario Fasino, Francesco Tudisco
Various modularity matrices appeared in the recent literature on network analysis and algebraic graph theory. Their purpose is to allow writing as quadratic forms certain combinato…