Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties

@article{Poignard2018SpectraOL,
  title={Spectra of Laplacian Matrices of Weighted Graphs: Structural Genericity Properties},
  author={Camille Poignard and Tiago Pereira and Jan Philipp Pade},
  journal={SIAM Journal of Applied Mathematics},
  year={2018},
  volume={78},
  pages={372-394}
}
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… CONTINUE READING

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