Spectral theory of the non-backtracking Laplacian for graphs

TL;DR

This paper introduces a non-backtracking Laplace operator for graphs, demonstrating through theory and computation that its spectrum more accurately reflects graph structure than traditional operators.

Contribution

It presents a novel non-backtracking Laplacian and analyzes its spectral properties, offering improved insights into graph structure over existing methods.

Findings

Spectrum captures detailed graph structural properties

Outperforms classical operators in structural analysis

Combines theoretical and computational approaches

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.