Studies have shown that sporadic AD is related to perturbation of the synchronization of the EEG signal. In Colombia has been reported the largest known group with familial AD characterized by the presence of the PS-1 E280A (Glu280Ala) mutation. Previous works with EEG in this kindred showed differences of the electrical sources patterns. 30 healthy asymptomatic subjects (15 carriers and 15 non carriers of PS-1 E280A mutation) were enrolled. We recorded EEG signals in resting condition. To analyze the functional interactions between the different EEG channels the coherence was calculated over the principal rhythms of the EEG (delta, theta, alfa-1, alfa-2 and beta) giving five 64x64 association matrixes for each group. Once the synchronization was measured, graphs were built to obtain differences in the brain network measures between the groups. To build the graphs different thresholds were used trying to maintain the same connectivity density between groups. A total of eleven densities were evaluated in the range between [0.25, 0.5]. To obtain statistical confidence interval for the measures 1000 random networks were obtained and used as surrogates. We found significant differences (p < 0.001) in all the EEG bands for different densities in the clustering coefficient, the path length and the Lambda coefficient. For the alfa-2 and beta bands the differences existed for almost all (8 of the 11) of the densities evaluated. In both bands the clustering coefficient, the characteristic path length and Lambda, were bigger in the control than the carriers group. To avoid the possibility that the differences in the characteristic path length were given by nodes without any connection we also used the global efficiency which was bigger also in the carriers group. In this study carriers were characterized by differences in the network topology, evidenced in the path length and clustering coefficients. These findings constitute new evidences of neurophysiological changes in the brain dynamics in preclinical forms of familial Alzheimer disease.