The brain structure is a complex network of interconnected regions with specific topological characteristics. Since the disruption of this infrastructure has been linked to brain diseases, a key element to the quest for understanding how such diseases start and spread is to outline the degenerative pattern. In this paper, we explored this aspect using network attack simulation on the structural connectomes of 60 patients among Alzheimer's disease (AD) and mild cognitive impairment (MCI) and 30 healthy subjects. We considered different attack strategies and different metrics to evaluate and compare the induced changes between the different groups. We found out that patients and controls share common attack tolerance patterns in the peripheral connections compared to each other, and that hubs played analogous role in the tolerance impact. These results suggest that the spreading pattern of Alzheimer's disease does not target specific class of regions.