Reciprocal characterization from multivariate time series to multilayer complex networks.

Area of Science:

• Complex systems analysis
• Network science
• Time series analysis

Background:

• Transformations from time series to complex networks offer new insights into system dynamics.
• Investigating complex systems often requires novel analytical perspectives.

Purpose of the Study:

• To present a novel transformation from multivariate time series to multilayer networks for reciprocal characterization.
• To ensure the preservation of underlying geometrical features of time series in their network representations.
• To introduce and validate a new metric, interlayer entropy, for quantifying information flow and coupling strength in multilayer networks.

Main Methods:

• Developed a transformation method mapping multivariate time series to multilayer networks.
• Utilized network structure statistics to identify dynamical transitions in time series.
• Defined and applied interlayer entropy to measure coupling strength between network layers.
• Proved the equivalence of interlayer entropy and transfer entropy under specific conditions.

Main Results:

• The proposed transformation preserves essential geometrical features of time series in the resulting multilayer networks.
• Dynamical transitions within time series can be effectively identified through the analysis of network structural statistics.
• Interlayer entropy is demonstrated to be a robust measure of coupling strength between network layers.
• The study establishes the equivalence between interlayer entropy and transfer entropy for information flow measurement.

Conclusions:

• The transformation from time series to multilayer networks provides a powerful tool for complex systems analysis.
• Interlayer entropy offers a novel and effective method for quantifying information flow and interlayer coupling in multilayer networks.
• This work bridges network science and time series analysis, offering complementary perspectives for understanding complex system dynamics.