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Modeling the Functional Network for Spatial Navigation in the Human Brain
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Binary Apollonian networks.

Eduardo M K Souza1, Guilherme M A Almeida2

  • 1Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristóvão, Sergipe, Brazil.

Physical Review. E
|March 18, 2023
PubMed
Summary
This summary is machine-generated.

Researchers explored binary Apollonian networks, inspired by the Sierpinski triangle. These networks exhibit dendritic growth and inherit small-world, scale-free properties without clustering, suggesting broader applications in modeling real-world systems.

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Area of Science:

  • Network Science
  • Graph Theory
  • Fractal Geometry

Background:

  • The Sierpinski triangle is derived from Pascal's triangle using modulo 2 additions.
  • Understanding network structures is crucial for modeling complex systems.

Purpose of the Study:

  • To define and analyze binary Apollonian networks.
  • To investigate their structural and topological properties.
  • To explore their potential for modeling real-world systems.

Main Methods:

  • Definition of binary Apollonian networks based on fractal concepts.
  • Analysis of network properties including small-world, scale-free, and clustering coefficients.
  • Comparison with known fractal networks like the Sierpinski triangle.

Main Results:

  • The binary Apollonian network exhibits dendritic growth patterns.
  • These networks possess small-world and scale-free characteristics.
  • Notably, they lack the clustering property typically found in other complex networks.

Conclusions:

  • Binary Apollonian networks offer a novel structure with unique properties.
  • Their inherited characteristics suggest applicability in diverse real-world modeling scenarios.
  • The absence of clustering provides a distinct feature for specific system representations.