Geometric multiplicity of unitary non-backtracking eigenvalues
Combinatorics
2026-01-05 v2
Abstract
We completely characterize the conditions under which a complex unitary number is an eigenvalue of the non-backtracking matrix of an undirected graph. Further, we provide a closed formula to compute its geometric multiplicity and describe an algorithm to compute this multiplicity without making a single matrix computation. The algorithm has time complexity that is linear in the size of the graph.
Cite
@article{arxiv.2205.02004,
title = {Geometric multiplicity of unitary non-backtracking eigenvalues},
author = {Leo Torres},
journal= {arXiv preprint arXiv:2205.02004},
year = {2026}
}