The relationship between analyzed objects, signal processing, and sensing points is incredibly beneficial for data processing. An entirely new domain of data comes from the structure of the graph, which concisely and naturally considers the relations of irregular data in the definition of the problem along with the corresponding data connectivity. Due to the introduction of new relations among time-series samples based on graphs, the idea of signal analysis and rendering augmented data processing has been initiated.

Graph theory is a well-established research field, however, not until recently, it has become a popular research topic due to its ability to investigate underlying data instead of data and signals on graphs. In addition, with the help of entropy-like measures, entropy measures and complexity measures were updated recently. This emphasized multi-dimensional extension of the idea with an immense inclination towards similarity quantification and coupling between time series and its system components. Current research aims to elaborate complexity measures, their relationships, and the appropriate selection of parameters for practical applications.

The aim of this Special Issue is to bring together original research review articles on discussing graph and complexity-based data analysis and processing. Submissions can include graph theory and graph-based data classification and clustering, graph neural networks, graph topology, learning from data, and graph theory in fuzzy systems. We also welcome research about dynamic graph structure, vertex–frequency, and wavelet analysis of signals on graphs. Moreover, submissions should include graph complexity and the complexity of signals on graphs, entropy, and entropy-like measures.

Potential topics include but are not limited to the following:

• Graph and graph-based data classification and clustering
• Graph neural network
• Graph topology learning from data
• Dynamic fuzzy graph structure
• Vertex–frequency and wavelet analysis of signals on graphs
• Graph complexity and the complexity of signals on graphs
• Entropy and entropy-like measures
• Complexity measures
• Classical signal and image processing assisted by graph theory
• Graph filtering and adaptive processing
• Interpolation, subsampling, and downscaling of graph signals and graphs
• Applications of graph data processing
• Fuzzy set and graph applications
• Complexity measures and fuzzy logics
• Applications of fuzzy graph data processing