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arXiv · 2303.00373

There is no going back: Properties of the non-backtracking Laplacian

Raffaella Mulas·Dong Zhang·Giulio Zucal
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Abstract

We prove new properties of the non-backtracking graph and the non-backtracking Laplacian for graphs. In particular, among other results, we prove that two simple graphs are isomorphic if and only if their corresponding non-backtracking graphs are isomorphic, and we investigate properties of various classes of non-backtracking Laplacian eigenfunctions, such as symmetric and antisymmetric eigenfunctions. Moreover, we introduce and study circularly partite graphs as a generalization of bipartite graphs, and we use this notion to state a sharp upper bound for the spectral gap from $1$. We also investigate the singular values of the non-backtracking Laplacian in relation to independence numbers, and we use them to bound the moduli of the eigenvalues.

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Raffaella Mulas, Dong Zhang, Giulio Zucal. 2023-03-01. There is no going back: Properties of the non-backtracking Laplacian. https://arxiv.org/abs/2303.00373

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