Here we tested the hypothesis of a relationship between the cortical default mode network (DMN) structural integrity and the resting-state electroencephalographic (rsEEG) rhythms in patients with Alzheimer’s disease with dementia (ADD). Clinical and instrumental datasets in 45 ADD patients and 40 normal elderly (Nold) persons originated from the PDWAVES Consortium (www.pdwaves.eu). Individual rsEEG delta, theta, alpha, and fixed beta and gamma bands were considered. Freeware platforms served to derive (1) the (gray matter) volume of the DMN, dorsal attention (DAN), and sensorimotor (SMN) cortical networks and (2) the rsEEG cortical eLORETA source activities. We found a significant positive association between the DMN gray matter volume, the rsEEG alpha source activity estimated in the posterior DMN nodes (parietal and posterior cingulate cortex), and the global cognitive status in the Nold and ADD participants. Compared with the Nold, the ADD group showed lower DMN gray matter, lower rsEEG alpha source activity in those nodes, and lower global cognitive status. This effect was not observed in the DAN and SMN. These results suggest that the DMN structural integrity and the rsEEG alpha source activities in the DMN posterior hubs may be related and predict the global cognitive status in ADD and Nold persons.