Brain connectivity studies have revealed that highly connected 'hub' regions are particularly vulnerable to Alzheimer pathology: they show marked amyloid-β deposition at an early stage. Recently, excessive local neuronal activity has been shown to increase amyloid deposition. In this study we use a computational model to test the hypothesis that hub regions possess the highest level of activity and that hub vulnerability in Alzheimer's disease is due to this feature. Cortical brain regions were modeled as neural masses, each describing the average activity (spike density and spectral power) of a large number of interconnected excitatory and inhibitory neurons. The large-scale network consisted of 78 neural masses, connected according to a human DTI-based cortical topology. Spike density and spectral power were positively correlated with structural and functional node degrees, confirming the high activity of hub regions, also offering a possible explanation for high resting state Default Mode Network activity. 'Activity dependent degeneration' (ADD) was simulated by lowering synaptic strength as a function of the spike density of the main excitatory neurons, and compared to random degeneration. Resulting structural and functional network changes were assessed with graph theoretical analysis. Effects of ADD included oscillatory slowing, loss of spectral power and long-range synchronization, hub vulnerability, and disrupted functional network topology. Observed transient increases in spike density and functional connectivity match reports in Mild Cognitive Impairment (MCI) patients, and may not be compensatory but pathological. In conclusion, the assumption of excessive neuronal activity leading to degeneration provides a possible explanation for hub vulnerability in Alzheimer's disease, supported by the observed relation between connectivity and activity and the reproduction of several neurophysiologic hallmarks. The insight that neuronal activity might play a causal role in Alzheimer's disease can have implications for early detection and interventional strategies.