Development of Parkinson's disease causes functional impairment in the brain network of Parkinson's patients. The aim of this study is to analyze brain networks of people with Parkinson's disease based on higher resolution parcellations and newer graphical features. The topological features of brain networks were investigated in Parkinson's patients (19 individuals) compared to healthy individuals (17 individuals) using graph theory. In addition, four different methods were used in graph formation to detect linear and nonlinear relationships between functional magnetic resonance imaging (fMRI) signals. The functional connectivity between the left precuneus and the left amygdala, as well as between the vermis 1-2 and the left temporal lobe was evaluated for the healthy and the patient groups. The difference between the healthy and patient groups was evaluated by parametric t-test and nonparametric U-test. Based on the results, Parkinson's patients exhibited a noteworthy reduction in centrality criterion compared to healthy subjects. Moreover, alterations in the regional features of the brain network were evident. Applying centrality criteria and correlation coefficients revealed significant distinctions between healthy subjects and Parkinson's patients across various brain areas. The results obtained for topological features indicate changes in the functional brain network of Parkinson's patients. Finally, similar areas obtained by all three methods of graph formation in the evaluation of connectivity between paired regions in the brain network of Parkinson's patients increased the reliability of the results.