This paper introduces Multivariate Multiscale Graph-based Dispersion Entropy (mvDEG), a computationally efficient method for analyzing multivariate time series data within graph and complex network frameworks. mvDEG combines temporal dynamics with topological relationships, improving upon traditional nonlinear entropy methods. Its effectiveness is demonstrated through tests on synthetic and real-world datasets (two-phase flow regimes and weather data), showcasing its ability to distinguish different levels of dependency and complexity. The algorithm's linear computational time growth (in contrast to the exponential growth of classical methods) is achieved through optimized matrix power calculations. This efficiency makes mvDEG suitable for large-scale and real-time applications.

John Stewart Fabila-Carrasco, Chao Tan, Javier Escudero