The large-scale organization of the brain has features of complex networks that can be quantified using network measures from graph theory. However, many network measures were designed to be calculated on binary graphs, whereas functional brain organization is typically inferred from a continuous measure of correlations in temporal signal between brain regions. Thresholding is a necessary step to use binary graphs derived from functional connectivity data. However, there is no current consensus on what threshold to use, and network measures and group contrasts may be unstable across thresholds. Nevertheless, whole-brain network analyses are being applied widely with findings typically reported at an arbitrary threshold or range of thresholds. This study sought to evaluate the stability of network measures across thresholds in a large resting state functional connectivity dataset. Network measures were evaluated across absolute (correlation-based) and proportional (sparsity-based) thresholds, and compared between sex and age groups. Overall, network measures were found to be unstable across absolute thresholds. For example, the direction of group differences in a given network measure may change depending on the threshold. Network measures were found to be more stable across proportional thresholds. These results demonstrate that caution should be used when applying thresholds to functional connectivity data and when interpreting results from binary graph models.