Brain Hyperscanning, i.e. the simultaneous recording of the cerebral activity of different human subjects involved in interaction tasks, is a very recent field of Neuroscience aiming at understanding the cerebral processes generating and generated by social interactions. This approach allows the observation and modeling of the neural signature specifically dependent on the interaction between subjects, and, even more interestingly, of the functional links existing between the activities in the brains of the subjects interacting together. In this EEG hyperscanning study we explored the functional hyperconnectivity between the activity in different scalp sites of couples of Civil Aviation Pilots during different phases of a flight reproduced in a flight simulator. Results shown a dense network of connections between the two brains in the takeoff and landing phases, when the cooperation between them is maximal, in contrast with phases during which the activity of the two pilots was independent, when no or quite few links were shown. These results confirms that the study of the brain connectivity between the activity simultaneously acquired in human brains during interaction tasks can provide important information about the neural basis of the "spirit of the group".