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Updated: Jun 23, 2025

Modeling the Functional Network for Spatial Navigation in the Human Brain
Published on: October 13, 2023
Random Apollonian networks with tailored clustering coefficient
Eduardo M K Souza1, Guilherme M A Almeida2
1Departamento de Física, <a href="https://ror.org/028ka0n85">Universidade Federal de Sergipe</a>, 49100-000 São Cristóvão, Sergipe, Brazil.
Abstract:
We introduce a family of complex networks that interpolates between the Apollonian network and its binary version, recently introduced in E. M. K. Souza et al. [Phys. Rev. E 107, 024305 (2023)2470-004510.1103/PhysRevE.107.024305], via random removal of nodes. The dilution process allows the clustering coefficient to vary from C=0.828 to C=0 while maintaining the behavior of average path length and other relevant quantities as in the deterministic Apollonian network. Robustness against the random deletion of nodes is also reported on spectral quantities such as the ground-state localization degree and its energy gap to the first excited state. The loss of the 2π/3 rotation symmetry as a treelike network emerges is investigated in the light of the hub wavefunction amplitude. Our findings expose the interplay between the small-world property and other distinctive traits exhibited by Apollonian networks, as well as their resilience against random attacks.
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