Significance: Functional near-infrared spectroscopy (fNIRS) has been widely used to assess brain functional networks due to its superior ecological validity. Generally, fNIRS signals are sensitive to motion artifacts (MA), which can be removed by various MA correction algorithms. Yet, fNIRS signals may also undergo varying degrees of distortion due to MA correction, leading to notable alternation in functional connectivity (FC) analysis results. Aim: We aimed to investigate the effect of different MA correction algorithms on the performance of brain FC and topology analyses. Approach: We evaluated various MA correction algorithms on simulated and experimental datasets, including principal component analysis, spline interpolation, correlation-based signal improvement, Kalman filtering, wavelet filtering, and temporal derivative distribution repair (TDDR). The mean FC of each pre-defined network, receiver operating characteristic (ROC), and graph theory metrics were investigated to assess the performance of different algorithms. Results: Although most algorithms did not differ significantly from each other, the TDDR and wavelet filtering turned out to be the most effective methods for FC and topological analysis, as evidenced by their superior denoising ability, the best ROC, and an enhanced ability to recover the original FC pattern. Conclusions: The findings of our study elucidate the varying impact of MA correction algorithms on brain FC analysis, which could serve as a reference for choosing the most appropriate method for future FC research. As guidance, we recommend using TDDR or wavelet filtering to minimize the impact of MA correction in brain network analysis.