Background: Identification of stage-specific changes in brain network of patients with Alzheimer’s disease (AD) is critical for rationally designed therapeutics that delays the progression of the disease. However, pathological neural processes and their resulting changes in brain network topology with disease progression are not clearly known. Methods: The current study was designed to investigate the alterations in network topology of resting state fMRI among patients in three different clinical dementia rating (CDR) groups (i.e., CDR = 0.5, 1, 2) and amnestic mild cognitive impairment (aMCI) and age-matched healthy subject groups. We constructed cost networks from these 5 groups and analyzed their network properties using graph theoretical measures.Results: The topological properties of AD brain networks differed in a non-monotonic, stage-specific manner. Interestingly, local and global efficiency and betweenness of the network were rather higher in the aMCI and AD (CDR 1) groups than those of prior stage groups. The number, location, and structure of rich-clubs changed dynamically as the disease progressed.Conclusions: The alterations in network topology of the brain are quite dynamic with AD progression, and these dynamic changes in network patterns should be considered meticulously for efficient therapeutic interventions of AD.