Abstract
This paper discusses the connection between inverses of graph Laplacians with the diagonal increased by a positive vector and the covariance matrices of associated Gaussian graphical models.
Afterwards we study the way of modification of a graph Laplacian on the case of daisy graphs.
The author is grateful to Hélène Massam (1949–2020) for her comments and fruitful discussion in scope of this work and he dedicates this work to her. The author owes thanks to the reviewers of the GSI conference and to Bartosz Kołodziejek for their comments and remarks. This research was supported by a French Government Scholarship.
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References
Nakashima, H., Graczyk, P.: Wigner and Wishart Ensembles for graphical models. arXiv:2008.10446 [math.ST] (2020)
Brouwer, A.E., Haemers, W.H.: Spectra of Graphs. Springer, New York (2011). https://doi.org/10.1007/978-1-4614-1939-6
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Skalski, T. (2021). Remarks on Laplacian of Graphical Models in Various Graphs. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_73
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DOI: https://doi.org/10.1007/978-3-030-80209-7_73
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