  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.
