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Proceedings/Recueil Des Communications Année : 2023

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

Résumé

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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Dates et versions

hal-04200187 , version 1 (08-09-2023)

Identifiants

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Julien Lefèvre, Justine Fraize, David Germanaud. Perturbation of Fiedler vector: interest for graph measures and shape analysis. 14072, Springer Nature Switzerland, pp.593-601, 2023, Lecture Notes in Computer Science, ⟨10.1007/978-3-031-38299-4_61⟩. ⟨hal-04200187⟩
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