Abstract Objective. Brain connectivity networks are usually characterized in terms of properties coming from the complex network theory. Using new measures to summarize the attributes of functional connectivity networks can be an important step for their better understanding and characterization, as well as to comprehend the alterations associated with neuropsychiatric and neurodegenerative disorders. In this context, the main objective of this study was to introduce a novel methodology to evaluate network robustness, which was subsequently applied to characterize the brain activity in the Alzheimer’s disease (AD) continuum. Approach. Functional connectivity networks were built using 478 electroencephalographic and magnetoencephalographic resting-state recordings from three different databases. These functional connectivity networks computed in the conventional frequency bands were modified simulating an iterative attack procedure using six different strategies. The network changes caused by these attacks were evaluated by means of Spearman’s correlation. The obtained results at the conventional frequency bands were aggregated in a correlation surface, which was characterized in terms of four gradient distribution properties: mean, variance, skewness, and kurtosis. Main results. The new proposed methodology was able to consistently quantify network robustness. Our results showed statistically significant differences in the inherent ability of the network to deal with attacks (i.e. differences in network robustness) between controls, mild cognitive impairment subjects, and AD patients for the three different databases. In addition, we found a significant correlation between mini-mental state examination scores and the changes in network robustness. Significance. To the best of our knowledge, this is the first study which assesses the robustness of the functional connectivity network in the AD continuum. Our findings consistently evidence the loss of network robustness as the AD progresses for the three databases. Furthermore, the changes in this complex network property may be related with the progressive deterioration in brain functioning due to AD.