MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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

Raffaella Mulas, Dong Zhang and Giulio Zucal


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.


Related publications

2024 Journal Open Access
Raffaella Mulas, Dong Zhang and Giulio Zucal

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

In: Linear algebra and its applications, 680 (2024), pp. 341-370