Alzheimer’s disease is a neurological disorder characterized by functional and structural atrophy, leading to symptoms like memory loss and cognitive decline. This study seeks to analyze the disruptions of functional connectivity pathways within the brain caused by Alzheimer’s disease from the maximum flow perspective. More specifically, we computed the maximum flow pathways within the functional brain networks, and compared it between healthy controls and Alzheimer’s patients. Our results suggest that the Alzheimer’s patients utilize pathways related to the default mode network (DMN) more frequently and display significant alterations in the usage of paths connected to the striate cortex (SC). The increased usage of DMN pathways might point to a compensation mechanism that facilitates interregional communications in Alzheimer’s patients. Understanding the nature of such a compensation mechanism could help develop new treatment options for Alzheimer’s patients.