In recent years, brain signal complexity has gained attention as an indicator of brain well-being and a predictor of disease and dysfunction. Brain entropy quantifies this complexity. Assessment of functional network centrality and connectivity reveals that information communication induces neural signal oscillations in certain brain regions. However, their relationship is uncertain. This work studied brain signal complexity, network centrality, and connectivity in both healthy and depressed individuals. The current work comprised a sample of 124 first-episode drug-naïve patients with major depressive disorder (MDD) and 105 healthy controls (HC). Six functional networks were created for each person using resting-state functional magnetic resonance imaging. For each network, entropy, centrality, and connectivity were computed. Using structural equation modeling, this study examined the associations between brain network entropy, centrality, and connectivity. The findings demonstrated substantial correlations of entropy with both centrality and connectivity in HC and these correlation patterns were disrupted in MDD. Compared to HC, MDD exhibited higher entropy in four networks and demonstrated changes in centralities across all networks. The structural equation modeling showed that network centralities, connectivity, and depression severity had impacts on brain entropy. Nevertheless, no impacts were observed in the opposite directions. This study indicated that the complexity of brain signals was influenced not only by the interactions among different areas of the brain but also by the severity level of depression. These findings enhanced our comprehension of the associations of brain entropy with its influential factors.