Over the past few years, there has been an increased interest in studying the underlying neural mechanism of cognitive brain activity as well as in diagnosing certain pathologies. Noninvasive imaging modalities such as functional magnetic resonance imaging (fMRI), positron emission tomography (PET), and dynamic signal acquisition techniques such as quantitative electroencephalography (EEG) have been vastly used to estimate cortical connectivity and identify functional interdependencies among synchronized brain lobes. In this area, graph-theoretic concepts and tools are used to describe large scale brain networks while performing cognitive tasks or to characterize certain neuropathologies. Such tools can be of particular value in basic neuroscience and can be potential candidates for future inclusion in a clinical setting. This paper discusses the application of the high time resolution EEG to resolve interdependence patterns using both linear and nonlinear techniques. The network formed by the statistical dependencies between the activations of distinct and often well separated neuronal populations is further analyzed using a number of graph theoretic measures capable of capturing and quantifying its structure and summarizing the information that it contains. Finally, graph visualization reveals the hidden structure of the networks and amplifies human understanding. A number of possible applications of the graph theoretic approach are also listed. A freely available standalone brain visualization tool to benefit the healthcare engineering community is also provided (http://www.ics.forth.gr/bmi/tools.html).