Geometric Characterization of the $H$-property for Step-graphons
Mohamed Ali Belabbas, Xudong Chen
TL;DR
This paper establishes that the previously identified necessary conditions for the $H$-property in step-graphons are also sufficient, providing a complete geometric characterization.
Contribution
It proves that the necessary conditions for the $H$-property in step-graphons are also sufficient, completing the characterization.
Findings
Necessary conditions are also sufficient for the $H$-property.
Provides a geometric characterization of the $H$-property.
Completes the theoretical understanding of step-graphons.
Abstract
In a recent paper arXiv:2109.08340, we have exhibited a set of conditions that are necessary for the -property to hold for the class of step-graphons. In this paper, we prove that these conditions are essentially sufficient.
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Taxonomy
TopicsAdvanced Graph Theory Research · Topological and Geometric Data Analysis · Graph theory and applications