Normalized Sombor indices as complexity measures of random graphs
Combinatorics
2021-08-11 v1
Abstract
We perform a detailed computational study of the recently introduced Sombor indices on random graphs. Specifically, we apply Sombor indices on three models of random graphs: Erd\"os-R\'enyi graphs, random geometric graphs, and bipartite random graphs. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the graph, scale with the graph average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random graphs and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the graph adjacency matrix.
Keywords
Cite
@article{arxiv.2106.03190,
title = {Normalized Sombor indices as complexity measures of random graphs},
author = {R. Aguilar-Sanchez and J. A. Mendez-Bermudez and Jose M. Rodriguez and Jose M. Sigarreta},
journal= {arXiv preprint arXiv:2106.03190},
year = {2021}
}
Comments
21 pages, 8 figures