Social networks play a vital role in linking individuals from all over the world. Locating the critical nodes within a social network remains a challenge due to the wide range of network sizes. To address this problem, several measures of centrality have been established. Locating the critical nodes is vital for controlling infection, encouraging or inhibiting the flow of information, and other processes. In this study, we compare ten newer and previously established centrality measures to find out the superior measure of centrality according to accuracy and distinguishing capability. Thus, four experiments are performed on distinct social networks employing ten measures, with the assessment metrics to investigate the efficacy of the measures. According to the experimental results, the extended gravity index and gravity index measures are more accurate than the other measures. In the future, we will endeavor to apply the experimentation to the newly established measures that have been introduced during our research to improve our findings.