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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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Random hyperbolic graphs in d+1 dimensions.

Gabriel Budel1, Maksim Kitsak1, Rodrigo Aldecoa2,3

  • 1Faculty of Electrical Engineering, Mathematics and Computer Science, <a href="https://ror.org/02e2c7k09">Delft University of Technology</a>, 2628 CD, Delft, the Netherlands.

Physical Review. E
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Summary
This summary is machine-generated.

We unified random hyperbolic graph models across dimensions using parameter rescaling. This preserves degree distribution but shows clustering decreases with higher dimensions.

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Area of Science:

  • Graph Theory
  • Hyperbolic Geometry
  • Network Science

Background:

  • Random hyperbolic graphs are a significant model in network science.
  • Understanding their properties across different dimensions is crucial for theoretical and applied research.

Purpose of the Study:

  • To develop a unified framework for random hyperbolic graphs in any dimension.
  • To analyze the impact of dimensionality on graph properties like degree distribution and clustering.
  • To provide a computational tool for generating and analyzing these graphs.

Main Methods:

  • Introduced a rescaling of model parameters for a unified mathematical framework.
  • Analyzed the degree distribution and clustering coefficients.
  • Investigated other limiting regimes of the random hyperbolic graph model.
  • Developed and released a software package.

Main Results:

  • The degree distribution of random hyperbolic graphs is invariant to the dimension of the hyperbolic space.
  • Clustering in these graphs is dimension-dependent, tending to zero as dimension increases (d→∞).
  • All limiting regimes of the model were analyzed.

Conclusions:

  • A dimension-independent framework for random hyperbolic graphs is established.
  • Dimensionality significantly influences graph clustering but not degree distribution.
  • The released software facilitates further research in this area.