The communicability distance between pairs of regions in human brain is used as a quantitative proxy for studying Alzheimer’s disease. Using this distance, we obtain the shortest communicability path lengths between different regions of brain networks from patients with Alzheimer’s disease (AD) and healthy cohorts (HC). We show that the shortest communicability path length is significantly better than the shortest topological path length in distinguishing AD patients from HC. Based on this approach, we identify 399 pairs of brain regions for which there are very significant changes in the shortest communicability path length after AD appears. We find that 42% of these regions interconnect both brain hemispheres, 28% connect regions inside the left hemisphere only, and 20% affect vermis connection with brain hemispheres. These findings clearly agree with the disconnection syndrome hypothesis of AD. Finally, we show that in 76.9% of damaged brain regions the shortest communicability path length drops in AD in relation to HC. This counterintuitive finding indicates that AD transforms the brain network into a more efficient system from the perspective of the transmission of the disease, because it drops the circulability of the disease factor around the brain regions in relation to its transmissibility to other regions. Author Summary We use a geometric measure for the separation of the different regions in the brain, which accounts for how well such regions communicate to each other. Our approach is based on the consideration of a “susceptible-infected” model of the propagation of a disease factor across the brain network. Our first important result is the finding that the shortest communicability path length is significantly better than the shortest topological path length in differentiating patients with Alzheimer’s disease (AD) from healthy individuals. The second and most important finding is the extraction of structural factors that seems to be responsible for the appearance of AD. In particular, we find brain regions in which communicability distance is significantly affected by AD. Most of them interconnect both brain hemispheres or the vermis with them. Remarkably and counterintuitively, we found that in 76.9% of damaged brain regions there is a drop in the communicability distance, indicating that AD makes the brain network more efficient to the transmission of the disease between brain regions.