Abstract: Connectivity and diagnosability not only closely related in definition, but also some well-known fault diagnosis theories are inspired by correlative connectivity. Firstly, a systematic overview of connectivities and diagnosabilities are given in this paper, which focus on the relationship between connectivities and diagnosabilities. Then, it concluds that diagnosabilities will increase with the improvement of correlation connectivity, and shows an important conclusion of obvious linear relationship in multiprocessor systems. Furthermore, the measurement of diagnosability can be simplified and many kinds of diagnosabilities of multiprocessor computer systems can be quickly calculated, if the linear relationship between diagnosability and correlation connectivity had be determined. Finally, the direction of future research on the correlation between connectivity degree and diagnostic degree is put forward. The research results have very important reference value for promoting the reliability of interconnection networks and promoting the application and popularization of interconnection networks.