Dispersion Entropy for Graph Signals

We present a novel method, called Dispersion Entropy for Graph Signals, DEG, as a powerful tool for analysing the irregularity of signals defined on graphs. DEG generalises the classical dispersion entropy concept for univariate time series, enabling its application in diverse domains such as image processing, time series analysis, and network analysis. Furthermore, DEG establishes a theoretical framework that provides insights into the irregularities observed in graph centrality measures and in the spectra of operators acting on graphs. We demonstrate the effectiveness of DEG in detecting changes in the dynamics of signals defined on both synthetic and real-world graphs, by defining a mix process on random geometric graphs or those exhibiting small-world properties. Our results indicate that DEG effectively captures the irregularity of graph signals across various network configurations, successfully differentiating between distinct levels of randomness and connectivity. Consequently, DEG provides a comprehensive framework for entropy analysis of various data types, enabling new applications of dispersion entropy not previously feasible, and uncovering nonlinear relationships between graph signals and their graph topology.