Digraphons: connectivity and spectral aspects

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.

💡 Research Summary

The paper extends the dense graph limit theory from symmetric graphons to asymmetric digraphons, which are measurable functions Γ : Ω² →