Alzheimer's disease (AD) is a neurodegenerative disorder marked by memory loss and cognitive decline, making early detection vital for timely intervention. However, early diagnosis is challenging due to the heterogeneous presentation of symptoms. Resting-state functional magnetic resonance imaging (rs-fMRI) captures spontaneous brain activity and functional connectivity, which are known to be disrupted in AD and mild cognitive impairment (MCI). Traditional methods, such as Pearson's correlation, have been used to calculate association matrices, but these approaches often overlook the dynamic and non-stationary nature of brain activity. In this study, we introduce a novel method that integrates discrete wavelet transform (DWT) and graph theory to model the dynamic behavior of brain networks. Our approach captures the time-frequency representation of brain activity, allowing for a more nuanced analysis of the underlying network dynamics. Machine learning was employed to automate the discrimination of different stages of AD based on learned patterns from brain network at different frequency bands. We applied our method to a dataset of rs-fMRI images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, demonstrating its potential as an early diagnostic tool for AD and for monitoring disease progression. Our statistical analysis identifies specific brain regions and connections that are affected in AD and MCI, at different frequency bands, offering deeper insights into the disease's impact on brain function.