Following a stroke, the functional brain connections are impaired, and there is some evidence that the brain tries to reorganize them to compensate the disruption, establishing novel neural connections. Electroencephalography (EEG) can be used to study the effects of stroke on the brain network organization, indirectly, through the study of brain-electrical connectivity. The main objective of this work is to study the asymmetry in the brain network organization of the two hemispheres in case of a lesion due to stroke (ischemic or hemorrhagic), starting from high-density EEG (HD-EEG) signals. The secondary objective is to show how HD-EEG can detect such asymmetry better than standard low-density EEG. A group of seven stroke patients was recruited and underwent HD-EEG recording in an eye-closed resting state condition. The permutation disalignment index (PDI) was used to quantify the coupling strength between pairs of EEG channels, and a complex network model was constructed for both the right and left hemispheres. The complex network analysis allowed to compare the small-worldness (SW) of the two hemispheres. The impaired hemisphere exhibited a larger SW (p < 0.05). The analysis conducted using traditional EEG did not allow to observe such differences. In the future, SW could be used as a biomarker to quantify longitudinal patient improvement.