TY - GEN A1 - Pade, Jan Philipp A1 - Poignard, Camille A1 - Pereira, Tiago T1 - Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Propoerties N2 - This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity) and its associated eigenvector, the so-called Fiedler vector. Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only non-zero entries. These structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems. KW - Spectra of Graphs, Laplacians, Perturbations of Eigenvalues Y1 - 2017 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1404 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-14045 ER -