On the spectra of large sparse graphs with cycles
Disordered Systems and Neural Networks
2023-01-12 v3 Statistical Mechanics
Mathematical Physics
math.MP
Probability
Abstract
We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high accuracy. In particular, for (un)directed regular graphs with cycles of arbitrary length we derive exact and simple equations for the resolvent of the associated adjacency matrix. Solving these equations we obtain analytical formulas for the spectra and the boundaries of their support.
Keywords
Cite
@article{arxiv.1206.1512,
title = {On the spectra of large sparse graphs with cycles},
author = {D. Bollé and F. L. Metz and I. Neri},
journal= {arXiv preprint arXiv:1206.1512},
year = {2023}
}
Comments
23 pages, 8 figures, a few typos have been corrected in the latest version