Elucidation of the neural correlates of time perception constitutes an important research topic in cognitive neuroscience. The focus to date has been on durations in the millisecond to seconds range, but here we used electroencephalography (EEG) to examine brain functional connectivity during much longer durations (i.e., 15 min). For this purpose, we conducted an initial exploratory experiment followed by a confirmatory experiment. Our results showed that those participants who overestimated time exhibited lower activity of beta (18-30 Hz) at several electrode sites. Furthermore, graph theoretical analysis indicated significant differences in the beta range (15-30 Hz) between those that overestimated and underestimated time. Participants who underestimated time showed higher clustering coefficient compared to those that overestimated time. We discuss our results in terms of two aspects. FFT results, as a linear approach, are discussed within localized/dedicated models (i.e., scalar timing model). Second, non-localized properties of psychological interval timing (as emphasized by intrinsic models) are addressed and discussed based on results derived from graph theory. Results suggested that although beta amplitude in central regions (related to activity of BG-thalamocortical pathway as a dedicated module) is important in relation to timing mechanisms, the properties of functional activity of brain networks; such as the segregation of beta network, are also crucial for time perception. These results may suggest subjective time may be created by vector units instead of scalar ticks.