On the eigenvalues of weighted directed graphs

Marwa Balti (1, 2)

1 Faculté des Sciences de Bizerte [Université de Carthage]
2 LMJL - Laboratoire de Mathématiques Jean Leray

This paper deals with spectral graph theory issues related to questions of monotonicity and comparison of eigenvalues. We consider finite directed graphs with non symmetric edge weights and we introduce a special self-adjoint operator as the sum of two non self-adjoint Laplacians. We investigate how the perturbation of the graph can affect the eigenvalues. Our approach is to take well known techniques from finite dimensional matrix analysis and show how they can be generalized for graph Laplacians.

Mots clés: Domain monotonicity; Bounds of eigenvalues; Graph Laplacian; Com- parison of eigenvalues.

Domaines: Théorie spectrale [math.SP]

Marwa Balti. On the eigenvalues of weighted directed graphs. Complex Analysis and Operator Theory, 2016, ⟨10.1007/s11785-016-0615-7⟩. ⟨hal-01532967v1⟩