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Nearest-neighbor directed random hyperbolic graphs.

I A Kasyanov1, P van der Hoorn2, D Krioukov3

  • 1Independent researcher, 0105 Tbilisi, Georgia.

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Summary
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We introduce a directed hyperbolic graph model for scale-free networks. This model exhibits a core-periphery structure and tunable reciprocity, offering new insights into complex network analysis.

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Area of Science:

  • Complex Networks
  • Network Science
  • Graph Theory

Background:

  • Undirected hyperbolic graph models are established for scale-free networks with high clustering.
  • Existing models often lack directed properties crucial for many real-world systems.

Purpose of the Study:

  • To propose a novel directed hyperbolic graph model.
  • To analyze the structural properties and emergent behaviors of this new network type.

Main Methods:

  • Nodes are randomly distributed on a hyperbolic disk.
  • Connections are made to a fixed number (m) of nearest spatial neighbors.
  • A canonical version with space-dependent connection radius was also analyzed.

Main Results:

  • The network exhibits a distinct core-periphery structure.
  • In-degree distribution follows a truncated power-law for low node densities.
  • Network reciprocity can be controlled via a temperature-like parameter.

Conclusions:

  • The proposed directed hyperbolic model offers a flexible framework for generating complex networks.
  • The model successfully captures core-periphery organization and tunable reciprocity.
  • This work provides a new tool for modeling directed scale-free networks.