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The early diagnosis of Alzheimer’s disease (AD) is particularly challenging. Mild Cognitive Impairment (MCI) has been linked to AD and electroencephalogram (EEG) recordings are able to measure brain activity directly with high temporal resolution. In this context, with appropriate processing, the EEG recordings can be used to construct a graph representative of brain functional connectivity. Here, we study a functional network created from a non-linear measure of coupling of beta-filtered EEG recordings during a short-term memory binding task. We show that the values of the small world characteristic and eccentricity are, respectively, lower and higher in MCI patients than in controls. The results show how MCI leads to EEG functional connectivity changes. We expect that the network differences between MCIs and control subjects could be used to gain insight into the early stages of AD.