Spectrum of Laplacians for Graphs with Self-Loops
Optimization and Control
2015-06-09 v2
Abstract
This note introduces a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of undirected graphs with self-loops. We extend on the known results for the spectrum of undirected graphs without self-loops or multiple edges. For this purpose, we introduce a new concept of pseudo-connected graphs and apply a lifting of the graph with self-loops to a graph without self-loops, which is then used to quantify the spectrum of the Laplacian for the graph with self-loops.
Cite
@article{arxiv.1505.08133,
title = {Spectrum of Laplacians for Graphs with Self-Loops},
author = {Behcet Acikmese},
journal= {arXiv preprint arXiv:1505.08133},
year = {2015}
}