Hierarchical deposition and scale-free networks: A visibility algorithm approach.

Area of Science:

• Complex systems
• Network science
• Statistical physics

Background:

• Interface growth phenomena are crucial in various scientific fields.
• Understanding hierarchical deposition processes is key to material science and physics.
• Dynamical networks offer a novel framework for studying complex growth patterns.

Purpose of the Study:

• To investigate the network properties arising from hierarchical particle deposition.
• To analyze the impact of deterministic and random deposition models on network characteristics.
• To explore the scale-invariance and modularity of the generated networks.

Main Methods:

• Utilizing a dynamical network model based on the horizontal visibility algorithm.
• Applying deterministic and random deposition models for particle placement.
• Conducting exact calculations for network diameter and clustering coefficient.
• Analyzing the degree-dependent clustering coefficient C(k).

Main Results:

• Deterministic model yields a scale-free network with specific exponents (γe=ln3/ln2, γo=1).
• Networks exhibit scale invariance and inherit modular hierarchy from the deposition process.
• Random model results in a scale-free network with a degree exponent (γ=3) linked to fractional Gaussian noise.
• Modularity is confirmed to persist in the system through C(k).

Conclusions:

• The study demonstrates that hierarchical deposition processes generate scale-free and modular networks.
• The findings connect network properties to fractional Gaussian noise, providing a deeper understanding of growth dynamics.
• The research highlights the utility of dynamical network analysis for complex systems.