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Bianka Kovács1, Sámuel G Balogh2, Gergely Palla1,3,4

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We introduce the dPSO model, a generalization of the popularity-similarity optimization (PSO) model for hyperbolic random graphs. This model

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Area of Science:

  • Network science
  • Complex systems
  • Graph theory

Background:

  • Hyperbolic network models explain real-world network features.
  • The popularity-similarity optimization (PSO) model generates networks with small-world properties, scale-free degree distribution, high clustering, and strong community structure.
  • Existing models are limited to two-dimensional hyperbolic space.

Purpose of the Study:

  • To generalize the popularity-similarity optimization (PSO) model to arbitrary integer dimensions.
  • To investigate how the dimension of hyperbolic space influences network properties.
  • To provide a foundation for generalizing existing hyperbolic embedding techniques.

Main Methods:

  • Introduction of the dPSO model, a generalization of the PSO model.
  • Analysis of the structural properties of networks generated by the dPSO model.
  • Mathematical formulation for arbitrary integer dimensions.

Main Results:

  • The dPSO model generates hyperbolic random graphs in any integer dimension.
  • Network properties are non-trivially affected by the dimension of the hyperbolic space.
  • The model successfully reproduces key features like small-world property and scale-free degree distribution.

Conclusions:

  • The dPSO model offers a generalized framework for studying hyperbolic random graphs.
  • Network structure is sensitive to the dimensionality of the underlying hyperbolic space.
  • This work extends the applicability of hyperbolic network models and embedding techniques.