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Related Experiment Video

Updated: Mar 17, 2026

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
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Groupies in multitype random graphs.

Yilun Shang1

  • 1Department of Mathematics, Tongji University, Shanghai, 200092 China.

Springerplus
|July 22, 2016
PubMed
Summary
This summary is machine-generated.

In random graphs, a "groupie" vertex has a degree greater than or equal to its neighbors' average degree. Our study shows groupies constitute nearly half of all vertices in complex random graph models.

Keywords:
DegreeGroupieMultitypeRandom graph

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Area of Science:

  • Graph theory
  • Network analysis
  • Probability theory

Background:

  • Graph theory defines vertices and edges, with vertex degree being a key metric.
  • Understanding vertex properties in random graphs is crucial for network analysis.
  • Groupies are vertices with degrees exceeding their neighbors' average degree.

Purpose of the Study:

  • To investigate the prevalence of groupies in multitype random graphs.
  • To analyze the proportion of groupies in various complex network models.
  • To provide theoretical and numerical insights into groupie distribution.

Main Methods:

  • Defining groupies based on vertex degree and neighbor average degree.
  • Analyzing multitype random graph models, including stochastic block models.
  • Applying theoretical conditions to derive the proportion of groupies.

Main Results:

  • The proportion of groupies in multitype random graphs approaches 1/2.
  • This finding holds under mild conditions for various graph types.
  • Numerical examples validate the theoretical predictions.

Conclusions:

  • Groupies are a significant and predictable feature in complex random graphs.
  • The 1/2 proportion suggests a balanced distribution of groupie vertices.
  • The results offer a new perspective on vertex centrality in random networks.