Graph Theory for Brain Signal Processing

Abstract

This chapter introduces the use of graph-theoretic concepts in analyzing brain signals. For didactic purposes, it has been split into three parts: “theory,” “demonstration,” and “examples.” In the first part, we commence by introducing some basic elements from graph theory and stemming algorithmic tools, which can be employed for data-analytic purposes. Next, we describe how these concepts are adapted for handling evolving connectivity and gaining insights into network reorganization. Finally, the notion of signals residing on a given graph is introduced, and elements from the emerging field of graph signal processing (GSP) are provided. The second part serves as a pragmatic demonstration of the tools and techniques described earlier. It is based on analyzing a multi-trial dataset containing single-trial responses from a visual event-related potential (ERP) paradigm. The third part includes examples from the related literature. This chapter ends with a brief outline of the most recent trends in graph theory that are about to shape brain signal processing in the near future and a more general discussion on the relevance of graph-theoretic methodologies for neural recordings.