Multifractal cross-correlation effects in two-variable time series of complex network vertex observables

Area of Science:

• Complex systems analysis
• Network science
• Statistical physics

Background:

• Understanding complex networks relies on analyzing vertex properties and their temporal dynamics.
• Time series of vertex properties are generated using stationary, unbiased random walks.
• Vertex properties offer insights into topological roles at short, medium, and long ranges.

Purpose of the Study:

• To investigate the scaling of cross-correlations in two-variable time series of vertex properties within complex networks.
• To apply multifractal cross-correlation analysis to uncover nonlinear coupling effects between time series.
• To determine if fractal cross-correlation properties can differentiate between various network models.

Main Methods:

• Generation of time series data from vertex properties using stationary, unbiased random walks.
• Application of multifractal cross-correlation analysis to quantify nonlinear interdependencies.
• Analysis of Erdös-Rényi, Barabási-Albert, and Watts-Strogatz network models.
• Examination of protein contact networks.

Main Results:

• Complex network models exhibit unique multifractal cross-correlation properties.
• Fractal cross-correlation analysis successfully distinguishes between Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks.
• Protein contact networks display characteristics of both scale-free and small-world models.

Conclusions:

• Multifractal cross-correlation analysis is a powerful tool for characterizing complex networks.
• The method provides a quantitative basis for classifying different network topologies.
• Findings on protein contact networks suggest a hybrid structural organization.