Several researchers have analyzed brain activities by investigating brain networks. However, there is a lack of the research on the temporal characteristics of the brain network during a stroke by EEG and the comparative studies between motor execution and imagery, which became known to have similar motor functions and pathways. In this study, we proposed the possibility of temporal characteristics on the brain networks of a stroke. We analyzed the temporal properties of the brain networks for nine chronic stroke patients by the active and motor imagery tasks by EEG. High beta band has a specific role in the brain network during motor tasks. In the high beta band, for the active task, there were significant characteristics of centrality and small-worldness on bilateral primary motor cortices at the initial motor execution. The degree centrality significantly increased on the contralateral primary motor cortex, and local efficiency increased on the ipsilateral primary motor cortex. These results indicate that the ipsilateral primary motor cortex constructed a powerful subnetwork by influencing the linked channels as compensatory effect, although the contralateral primary motor cortex organized an inefficient network by using the connected channels due to lesions. For the MI task, degree centrality and local efficiency significantly decreased on the somatosensory area at the initial motor imagery. Then, there were significant correlations between the properties of brain networks and motor function on the contralateral primary motor cortex and somatosensory area for each motor execution/imagery task. Our results represented that the active and MI tasks have different mechanisms of motor acts. Based on these results, we indicated the possibility of customized rehabilitation according to different motor tasks. We expect these results to help in the construction of the customized rehabilitation system depending on motor tasks by understanding temporal functional characteristics on brain network for a stroke.