Graph-theoretical analyses have been used to investigate changes in the functional connectome in patients with Alzheimer's disease. However, these analyses generally assume static organizational principles, thereby neglecting a fundamental reconfiguration of functional connections in the face of neurodegeneration. Here we focus on differences in the community structure of the functional connectome in young and old individuals and patients with Alzheimer's Disease. Alzheimer's Disease patients, moreover, underwent molecular imaging (PET) using [18F]AV1451 to measure tau burden, a major hallmark of Alzheimer's Disease. Whereas the overall organizational principles of the community structure of the human functional connectome were preserved even in advanced healthy aging, they were considerably changed in Alzheimer's disease. We discovered that the communities in Alzheimer's disease are re-organized with nodes changing their allegiance to communities resulting in an overall less efficient re-organized community structure. We further discovered that nodes with a tendency to leave the communities displayed a relatively higher tau pathology burden. Together, this study suggests that local tau pathology in Alzheimer's disease leads to fundamental changes in basic organizational principles of the human connectome. Our results shed new light on previous findings obtained using graph theory in Alzheimer's disease and imply a general principle of the brain in response to neurodegeneration.