Talking is the most common type of human interaction that people have in their daily life. Besides all conducted studies on the analysis of human behavior in different conditions, no study has been reported yet that analyzed how the brain activity of two persons is related during their conversation. In this research, for the first time, we investigate the relationship between brain activities of people while communicating, considering human voice as the mean of this connection. For this purpose, we employ fractal analysis in order to investigate how the complexity of electroencephalography (EEG) signals for two persons are related. The results showed that the variations of complexity of EEG signals for two persons are correlated while communicating. Statistical analysis also supported the result of analysis. Therefore, it can be stated that the brain activities of two persons are correlated during communication. Fractal analysis can be employed to analyze the correlation between other physiological signals of people while communicating.