Research Paper#Graph Theory, Network Analysis, Machine Learning (potentially)🔬 ResearchAnalyzed: Jan 3, 2026 19:10
Graph Limits via Random Quotients
Published:Dec 29, 2025 02:26
•1 min read
•ArXiv
Analysis
This paper introduces a novel approach to graph limits, called "grapheurs," using random quotients. It addresses the limitations of existing methods (like graphons) in modeling global structures like hubs in large graphs. The paper's significance lies in its ability to capture these global features and provide a new framework for analyzing large, complex graphs, particularly those with hub-like structures. The edge-based sampling approach and the Szemerédi regularity lemma analog are key contributions.
Key Takeaways
- •Introduces "grapheurs" as a new graph limit based on random quotients.
- •Addresses limitations of existing graph limit methods in modeling global structures like hubs.
- •Provides an edge-based sampling approach for analyzing large graphs.
- •Presents an edge-based analog of the Szemerédi regularity lemma.
Reference
“Grapheurs are well-suited to modeling hubs and connections between them in large graphs; previous notions of graph limits based on subgraph densities fail to adequately model such global structures as subgraphs are inherently local.”