TL;DR
This paper introduces graphons as limit objects for large graphs, explaining their definition, motivation, and how they connect finite graphs to a continuous framework through key theorems.
Contribution
It provides an accessible exposition on graphons, detailing their role in graph limit theory and establishing foundational theorems linking finite graphs to graphons.
Findings
Graphons serve as limit objects for large graph sequences.
The paper discusses the completion of the space of finite graphs by graphons.
Three theorems connect finite graphs with the continuous graphon framework.
Abstract
Graphons, short for graph functions, are limiting objects for sequences of large, finite graphs with respect to the so-called cut metric. In this expository piece, we define graphons, motivate them, and discuss how they complete the space of finite graphs. We conclude by stating three theorems that connect the finite world of graphs with the continuous world of graphons.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems