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arXiv · 2506.04426

Convergence of spectra of digraph limits

Jan Grebík·Daniel Král'·Xizhi Liu·Oleg Pikhurko·Julia Slipantschuk
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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.

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Jan Grebík, Daniel Král', Xizhi Liu, Oleg Pikhurko, Julia Slipantschuk. 2026-01-19. Convergence of spectra of digraph limits. https://arxiv.org/abs/2506.04426

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