Digraphons: connectivity and spectral aspects
Combinatorics
2025-12-16 v2
Abstract
The theory of graphons has proven to be a powerful tool in many areas of graph theory. In this paper, we introduce several foundational aspects of the theory of digraphons -- asymmetric two-variable functions that arise as limits of sequences of directed graphs (digraphs). Our results address their decomposition into strongly connected components, periodicity, spectral properties, and asymptotic behaviour of their large powers.
Cite
@article{arxiv.2510.16839,
title = {Digraphons: connectivity and spectral aspects},
author = {Jan Hladký and Petr Savický},
journal= {arXiv preprint arXiv:2510.16839},
year = {2025}
}
Comments
40 pages, 2 figures; improvements mostly regarding the theorem about asymtotics of powers