The detection and intervention for early-stage mild cognitive impairment (EMCI) is of vital importance However, the pathology of EMCI remains largely unknown, making it be challenge to the clinical diagnosis. In this paper, the resting-state functional magnetic resonance imaging (rs-fMRI) data derived from EMCI patients and normal controls are analyzed using the complex network theory. We construct the functional connectivity (FC) networks and employ the local false discovery rate approach to successfully detect the abnormal functional connectivities appeared in the EMCI patients. Our results demonstrate the abnormal functional connectivities have appeared in the EMCI patients, and the affected brain regions are mainly distributed in the frontal and temporal lobes In addition, to quantitatively characterize the statistical properties of FCs in the complex network, we herein employ the entropy of the degree distribution () index and some other well-established measures, i.e., clustering coefficient () and the efficiency of graph (). Eventually, we found that the index, better than the widely used and measures, may serve as an assistant and potential marker for the detection of EMCI.