Dementia with Lewy bodies (DLB) and Alzheimer’s disease (AD) require differential management despite presenting with symptomatic overlap. Currently, there is a need of inexpensive DLB biomarkers which can be fulfilled by electroencephalography (EEG). In this regard, an established electrophysiological difference in DLB is a decrease of dominant frequency (DF)—the frequency with the highest signal power between 4 and 15 Hz. Here, we investigated network connectivity in EEG signals acquired from DLB patients, and whether these networks were able to differentiate DLB from healthy controls (HCs) and associated dementias. We analysed EEG recordings from old adults: HCs, AD, DLB and Parkinson’s disease dementia (PDD) patients. Brain networks were assessed with the minimum spanning tree (MST) within six EEG bands: delta, theta, high-theta, alpha, beta and DF. Patients showed lower alpha band connectivity and lower DF than HCs. DLB and PDD showed a randomised MST compared with HCs and AD in high-theta and alpha but not in DF. The MST randomisation in DLB and PDD reflects decreased brain efficiency as well as impaired neural synchronisation. However, the lack of network topology differences at the DF between all dementia groups and HCs may indicate a compensatory response of the brain to the neuropathology.