A novel method of stability analysis was proposed by threshold gain analysis based on a transfer matrix theory in this study. The results reveal that long coupling delays need weak coupling strength, whereas short coupling delays need strong coupling strength. To analyze the linewidth of mutually injection-locked semiconductor lasers under weak coupling, an analytical method based on noise correlation analysis is used. The results show that the coupling delay and coupling strength are the main factors affecting the linewidth; however, the phase difference has less influence on the linewidth, which can be used for fine adjustment.