Perturbation of Fiedler vector: interest for graph measures and shape analysis
Discrete Mathematics
2023-06-08 v1
Abstract
In this paper we investigate some properties of the Fiedler vector, the so-called first non-trivial eigenvector of the Laplacian matrix of a graph. There are important results about the Fiedler vector to identify spectral cuts in graphs but far less is known about its extreme values and points. We propose a few results and conjectures in this direction. We also bring two concrete contributions, i) by defining a new measure for graphs that can be interpreted in terms of extremality (inverse of centrality), ii) by applying a small perturbation to the Fiedler vector of cerebral shapes such as the corpus callosum to robustify their parameterization.
Keywords
Cite
@article{arxiv.2306.04327,
title = {Perturbation of Fiedler vector: interest for graph measures and shape analysis},
author = {Julien Lefevre and Justine Fraize and David Germanaud},
journal= {arXiv preprint arXiv:2306.04327},
year = {2023}
}