Graph theory provides a promising technique to investigate Alzheimer's disease (AD)-related alterations in brain connectivity. However, discrepancies exist in the reported disruptions that occur to network topology across the AD continuum, which may be attributed to differences in the denoising approach used in fMRI processing to remove the effect of non-neuronal sources from signal. The current study aimed to determine if diagnostic differences in graph metrics were dependent on nuisance regression strategy. Sixty cognitively normal (CN), 60 MCI, and 40 AD matched for age, sex, and motion, were selected from the ADNI database for analysis. Resting state images were preprocessed using AFNI (v21.2.04) and 16 nuisance regression approaches were employed, which included the unique combination of four nuisance regressors (derivatives of the realignment parameters, motion censoring [euclidean norm > 0.3mm], outlier censoring [outlier fraction > .10], bandpass filtering [0.01 - 0.1 Hz]). Graph metrics representing network segregation (clustering coefficient, local efficiency, modularity), network integration (largest connected component, path length, local efficiency), and small-worldness (clustering coefficient/path length) were calculated. The results showed a significant interaction between diagnosis and nuisance approach on path length, such that diagnostic differences were only evident when motion derivatives and censoring of both motion and outlier volumes were applied. Further, regardless of the denoising approach, AD patients exhibited less segregated networks and lower small-worldness than CN and MCI. Finally, independent of diagnosis, denoising strategy significantly affected the magnitude of nearly all metrics (except local efficiency), such that models including bandpass filtering had higher graph metrics than those without. These findings suggest the relative robustness of network segregation and small-worldness properties to denoising strategy. However, caution should be taken when interpreting path length findings across studies, as subtle variations in regression approach may account for discrepancies. Continued efforts should be taken towards harmonizing preprocessing pipelines across studies to aid replication efforts and build consensus towards understanding the mechanisms underlying pathological aging.