The present book illustrates the theoretical aspects of several methodologies related to the
possibility of i) enhancing the poor spatial information of the electroencephalographic (EEG)
activity on the scalp and giving a measure of the electrical activity on the cortical surface.
ii) estimating the directional influences between any given pair of channels in a multivariate
dataset. iii) modeling the brain networks as graphs. The possible applications are discussed in
three different experimental designs regarding i) the study of pathological conditions during a
motor task ii) the study of memory processes during a cognitive task iii) the study of the
instantaneous dynamics throughout the evolution of a motor task in physiological conditions.
The main outcome from all those studies indicates clearly that the performance of cognitive and
motor tasks as well as the presence of neural diseases can affect the brain network topology.
This evidence gives the power of reflecting cerebral states or traits to the mathematical
indexes derived from the graph theory. In particular the observed structural changes could
critically depend on patterns of synchronization and desynchronization - i.e. the dynamic
binding of neural assemblies - as also suggested by a wide range of previous
electrophysiological studies. Moreover the fact that these patterns occur at multiple
frequencies support the evidence that brain functional networks contain multiple frequency
channels along which information is transmitted. The graph theoretical approach represents an
effective means to evaluate the functional connectivity patterns obtained from scalp EEG
signals. The possibility to describe the complex brain networks sub-serving different functions
in humans by means of numbers is a promising tool toward the generation of a better
understanding of the brain functions. Table of Contents: Introduction Brain Functional
Connectivity Graph Theory High-Resolution EEG Cortical Networks in Spinal Cord Injured
Patients Cortical Networks During a Lifelike Memory Task Application to Time-varying
Cortical Networks Conclusions
