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Related Experiment Video

Updated: Jun 9, 2026

A Tactile Automated Passive-Finger Stimulator (TAPS)
19:44

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Published on: June 3, 2009

Threshold Graph Limits and Random Threshold Graphs.

Persi Diaconis1, Susan Holmes, Svante Janson

  • 1Department of Mathematics, Stanford University, Stanford, CA 94305.

Internet Mathematics
|September 3, 2010
PubMed
Summary
This summary is machine-generated.

We explore the limit theory for large threshold graphs, applying it to random graph models. This research provides key examples for the developing field of graph limits.

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Area of Science:

  • Graph theory
  • Probability theory
  • Statistical modeling

Background:

  • Threshold graphs are a significant class of graphs with applications in various fields.
  • Understanding the asymptotic behavior of large graphs is crucial for developing robust statistical models.
  • The theory of graph limits provides a framework for analyzing the properties of large, complex networks.

Purpose of the Study:

  • To investigate the limit theory of large threshold graphs.
  • To apply these theoretical findings to diverse models of random threshold graphs.
  • To illustrate the utility of graph limit theory with concrete examples.

Main Methods:

  • Developing and applying limit theorems specific to threshold graphs.
  • Analyzing various probabilistic models for constructing random threshold graphs.
  • Utilizing tools from extremal graph theory and random graph theory.

Main Results:

  • Established convergence results for sequences of large threshold graphs.
  • Demonstrated the application of graph limit theory to specific random threshold graph models.
  • Provided a set of illustrative examples showcasing the power of graph limits.

Conclusions:

  • The study successfully extends graph limit theory to the domain of threshold graphs.
  • The findings offer valuable insights into the structure and properties of random threshold graphs.
  • This work contributes to the growing body of research on graph limits and their applications.