Both deepening sleep and evolving epileptic seizures are associated with increasing slow-wave activity. Larger-scale functional networks derived from electroencephalogram indicate that in both transitions dramatic changes of communication between brain areas occur. During seizures these changes seem to be 'condensed', because they evolve more rapidly than during deepening sleep. Here we set out to assess quantitatively functional network dynamics derived from electroencephalogram signals during seizures and normal sleep. Functional networks were derived from electroencephalogram signals from wakefulness, light and deep sleep of 12 volunteers, and from pre-seizure, seizure and post-seizure time periods of 10 patients suffering from focal onset pharmaco-resistant epilepsy. Nodes of the functional network represented electrical signals recorded by single electrodes and were linked if there was non-random cross-correlation between the two corresponding electroencephalogram signals. Network dynamics were then characterized by the evolution of global efficiency, which measures ease of information transmission. Global efficiency was compared with relative delta power. Global efficiency significantly decreased both between light and deep sleep, and between pre-seizure, seizure and post-seizure time periods. The decrease of global efficiency was due to a loss of functional links. While global efficiency decreased significantly, relative delta power increased except between the time periods wakefulness and light sleep, and pre-seizure and seizure. Our results demonstrate that both epileptic seizures and deepening sleep are characterized by dramatic fragmentation of larger-scale functional networks, and further support the similarities between sleep and seizures.