Whether the balance between integration and segregation of information in the brain is damaged in Mild Cognitive Impairment (MCI) subjects is still a matter of debate. Here we characterize the functional network architecture of MCI subjects by means of complex networks analysis. Magnetoencephalograms (MEG) time series obtained during a memory task were evaluated by synchronization likelihood (SL), to quantify the statistical dependence between MEG signals and to obtain the functional networks. Graphs from MCI subjects show an enhancement of the strength of connections, together with an increase in the outreach parameter, suggesting that memory processing in MCI subjects is associated with higher energy expenditure and a tendency toward random structure, which breaks the balance between integration and segregation. All features are reproduced by an evolutionary network model that simulates the degenerative process of a healthy functional network to that associated with MCI. Due to the high rate of conversion from MCI to Alzheimer Disease (AD), these results show that the analysis of functional networks could be an appropriate tool for the early detection of both MCI and AD.