Network Theoretical Approach to Describe Epileptic Processes

Epilepsy is characterized by recurrent unprovoked seizures. Recent studies suggest that seizure generation may be caused by the abnormal activity of the entire network. This new paradigm requires new tools and methods for its study. In this sense, synchronization by linear as well as nonlinear measures are used to determine network structure and functional connectivity of neurophysiological data. Electroencephalography (EEG) data can be analyzed using each electrode’s activity as a node of the underlying cortical network. The information provided by the synchronization matrix is the basic brick upon which several lines of analysis can be performed thereafter. Detection of community structures, identification of centrality nodes, transformation of the underlying network into a simpler one, and the identification of the basic network architecture are only some of the many lines of basic works that can be done in order to characterize the epilepsy as a network disease. This chapter describes new approaches in network epilepsy, provides mathematical concepts in order to understand the complex network analyses, and reviews the advances in network analyses and its application to epilepsy research