Neuroimaging data analysis reveals the underlying interactions in the brain. It is essential, yet controversial, to choose a proper tool to manifest brain functional connectivity. In this regard, researchers have not reached a definitive conclusion between the linear and non-linear approaches, as both have pros and cons. In this study, to evaluate this concern, the functional Magnetic Resonance Imaging (fMRI) data of different stages of Alzheimer’s disease are investigated. In the linear approach, the Pearson Correlation Coefficient (PCC) is employed as a common technique to generate brain functional graphs. On the other hand, for non-linear approaches, two methods including Distance Correlation (DC) and the kernel trick are utilized. By the use of the three mentioned routines and graph theory, functional brain networks of all stages of Alzheimer’s disease (AD) are constructed and then sparsed. Afterwards, graph global measures are calculated over the networks and a non-parametric permutation test is conducted. Results reveal that the non-linear approaches have more potential to discriminate groups in all stages of AD. Moreover, the kernel trick method is more powerful in comparison to the DC technique. Nevertheless, AD degenerates the brain functional graphs more at the beginning stages of the disease. At the first phase, both functional integration and segregation of the brain degrades, and as AD progressed brain functional segregation further declines. The most distinguishable feature in all stages is the clustering coefficient that reflects brain functional segregation.