Convergence of spectra of digraph limits

Titelangaben

Grebík, Jan ; Král’, Daniel ; Liu, Xizhi ; Pikhurko, Oleg ; Slipantschuk, Julia:
Convergence of spectra of digraph limits.
In: European Journal of Combinatorics. Bd. 134 (2026) . - 104349.
ISSN 0195-6698
DOI: https://doi.org/10.1016/j.ejc.2026.104349

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Abstract

The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness of the linear operator associated with a graphon. In this short paper, we consider the setting of digraphons, which are limits of directed graphs, and prove that the spectra of convergent digraphons converge. Using this result, we establish the relation between densities of directed cycles and the spectrum of a digraphon.