A Tutorial on Graph Theory for Brain Signal Analysis

TL;DR

This tutorial introduces graph theory and graph signal processing concepts for brain signal analysis, demonstrating their application on ERP data and discussing future trends in the field.

Contribution

It provides a comprehensive introduction to graph-theoretic methods and their application to brain signals, including evolving connectivity and graph signal processing techniques.

Findings

Effective analysis of ERP data using graph-based methods

Insights into network reorganization during brain activity

Overview of emerging trends in graph theory for neural data

Abstract

This tutorial paper refers to the use of graph-theoretic concepts for analyzing brain signals. For didactic purposes it splits into two parts: theory and application. 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 ERP paradigm. The paper 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 analyzing continuous-mode neural recordings.