We hypothesized that simple tasks, both resting and visual WM tasks, and features of graph theory are useful tools to differentiate between age-related changes in EEG signals of the human brain. Therefore, this study aimed to investigate the age-related differences in EEG networks in middle-aged and elderly individuals in a resting state and during a visual WM task. We recorded EEG from 20 healthy middle-aged subjects and 20 healthy elderly subjects in eyes-open and eyes-closed states, as well as during a visual WM task. In our work, several network features based on graph theory, including global efficiency, local efficiency, clustering coefficient, characteristic path length, node strength, and assortativity, are extracted from both groups. We additionally applied SVM, KNN, and RF algorithms to classify healthy aging EEG signals using functional network characteristics. The results of this study can pave the way on early cognitive aging detection using EEG signals with simple tasks and features of graph theory.