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arXiv · 2306.04327

Perturbation of Fiedler vector: interest for graph measures and shape analysis

Julien Lefevre·Justine Fraize·David Germanaud
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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.

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Julien Lefevre, Justine Fraize, David Germanaud. 2023-06-07. Perturbation of Fiedler vector: interest for graph measures and shape analysis. https://arxiv.org/abs/2306.04327

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