Spectral theory of the non-backtracking Laplacian for graphs

Jürgen Jost; Raffaella Mulas; Leo Torres

doi:10.1016/j.disc.2023.113536

Spectral theory of the non-backtracking Laplacian for graphs

Jürgen Jost, Raffaella Mulas^*, Leo Torres

^*Corresponding author for this work

Mathematics

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Abstract

We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural properties of the graph in a more precise way than the classical operators that have been studied so far in the literature, including the non-backtracking matrix.

Original language	English
Article number	113536
Pages (from-to)	1-19
Number of pages	19
Journal	Discrete Mathematics
Volume	346
Issue number	10
Early online date	7 Jun 2023
DOIs	https://doi.org/10.1016/j.disc.2023.113536
Publication status	Published - Oct 2023

Bibliographical note

Funding Information:
Raffaella Mulas was supported by the Max Planck Society 's Minerva Grant.

Publisher Copyright:
© 2023 Elsevier B.V.

Keywords

Laplacian eigenvalues
Non-backtracking matrix
Non-backtracking random walks
Spectral graph theory

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Spectral theory of the non-backtracking Laplacian for graphsFinal published version, 617 KBLicence: CC BY

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N2 - We introduce a non-backtracking Laplace operator for graphs and we investigate its spectral properties. With the use of both theoretical and computational techniques, we show that the spectrum of this operator captures several structural properties of the graph in a more precise way than the classical operators that have been studied so far in the literature, including the non-backtracking matrix.

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KW - Spectral graph theory

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Spectral theory of the non-backtracking Laplacian for graphs

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