The exact Laplacian spectrum for the Dyson hierarchical network

@article{Agliari2017TheEL,
  title={The exact Laplacian spectrum for the Dyson hierarchical network},
  author={Elena Agliari and Flavia Tavani},
  journal={Scientific Reports},
  year={2017},
  volume={7}
}
  • Elena Agliari, Flavia Tavani
  • Published 2017
  • Mathematics, Physics, Medicine
  • Scientific Reports
  • We consider the Dyson hierarchical graph , that is a weighted fully-connected graph, where the pattern of weights is ruled by the parameter σ ∈ (1/2, 1]. Exploiting the deterministic recursivity through which is built, we are able to derive explicitly the whole set of the eigenvalues and the eigenvectors for its Laplacian matrix. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes (e.g., random walks) occurring on the graph, as well as in the… CONTINUE READING

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