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This summary is machine-generated.

This study reveals that the diameter of random graphs with infinite variance degrees is of order when the minimum forward degree is at least 2. The findings apply to configuration and preferential attachment models.

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Area of Science:

  • Graph theory
  • Network science
  • Probability theory

Background:

  • Random graphs with infinite variance degrees are often ultra-small.
  • Typical distances in configuration and preferential attachment models are known.

Purpose of the Study:

  • Investigate the diameter behavior in random graph models.
  • Determine conditions for specific diameter order.
  • Identify the exact constant for the diameter.

Main Methods:

  • Analysis of configuration models.
  • Analysis of preferential attachment models.
  • Asymptotic analysis of graph distances.

Main Results:

  • The diameter is of order when the minimal forward degree (dfwd) is at least 2.
  • The exact constant for the diameter is identified.
  • The proof methodology is consistent across different models.

Conclusions:

  • The diameter of these random graphs is precisely characterized.
  • Minimal forward degree is a critical factor for diameter size.
  • The unified proof approach highlights underlying structural similarities.