Different subtypes of Alzheimer's disease (AD) with characteristic distributions of neurofibrillary tangles and corresponding brain atrophy patterns have been identified using structural magnetic resonance imaging (MRI). However, the underlying biological mechanisms that determine this differential expression of neurofibrillary tangles are still unknown. Here, we applied graph theoretical analysis to structural MRI data to test the hypothesis that differential network disruption is at the basis of the emergence of these AD subtypes. We studied a total of 175 AD patients and 81 controls. Subtyping was done using the Scheltens' scale for medial temporal lobe atrophy, the Koedam's scale for posterior atrophy, and the Pasquier's global cortical atrophy scale for frontal atrophy. A total of 89 AD patients showed a brain atrophy pattern consistent with typical AD; 30 patients showed a limbic-predominant pattern; 29 patients showed a hippocampal-sparing pattern; and 27 showed minimal atrophy. We built brain structural networks from 68 cortical regions and 14 subcortical gray matter structures for each AD subtype and for the controls, and we compared between-group measures of integration, segregation, and modular organization. At the global level, modularity was increased and differential modular reorganization was detected in the four subtypes. We also found a decrease of transitivity in the typical and hippocampal-sparing subtypes, as well as an increase of average local efficiency in the minimal atrophy and hippocampal-sparing subtypes. We conclude that the AD subtypes have a distinct signature of network disruption associated with their atrophy patterns and further extending to other brain regions, presumably reflecting the differential spread of neurofibrillary tangles. We discuss the hypothetical emergence of these subtypes and possible clinical implications.