Scale-free networks emerging from multifractal time series.

Area of Science:

• Complex Systems
• Network Science
• Dynamical Systems Theory

Background:

• Dynamical systems and graph theory integration is growing.
• Multifractal properties are common in time series from chaotic dynamics.

Purpose of the Study:

• Investigate how signal multifractality affects projected network topology.
• Identify conditions for scale-free network emergence.

Main Methods:

• Utilized box-counting formalism to map signal boxes to network nodes.
• Derived analytic expressions linking box measure to graph degree.
• Performed extensive numerical simulations for validation.

Main Results:

• Established connections between fractal dimensions and network topological properties.
• Identified specific conditions leading to scale-free network topologies.
• Analyzed properties of weighted and directed network projections.

Conclusions:

• Signal fractal properties significantly influence network topology.
• The study provides a framework for understanding complex network formation from dynamical systems.
• Findings have implications for analyzing empirical data and chaotic dynamics.