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The human brain is increasingly seen as a dynamic neural system, the function of which relies on a diverse set of connections between brain regions. To assess these complex dynamical interactions, formalism of complex networks was suggested as one of the most promising tools to offer new insight into the brain's structural and functional organization, with a potential also for clinical implications. Irrespective of the brain mapping technique, modern network approaches have revealed fundamental aspects of normal brain-network organization, such as small-world and scale-free patterns, hierarchical modularity, and the presence of hubs. Moreover, the utility of these approaches, to gain a better understanding of neurological diseases, is of great interest. In the present contribution, we first describe the basic network measures and how the brain networks are constructed on the basis of brain activity data in order to introduce clinical neurologists to this new theoretical paradigm. We then demonstrate how network formalism can be used to detect changes in EEG-based functional connectivity patterns in six paediatric patients with childhood absence epilepsy. Notably, our results do not only indicate enhanced synchronicity during epileptic episodes but also reveal specific spatial changes in the electrical activity of the brain. We argue that the network-based evaluation of functional brain networks can provide clinicians with more detailed insight into the activity of a pathological brain and can also be regarded as a support for objective diagnosis and treatment for various neurological diseases.