The goal of this study is to identify, review, and analyze the published research works that used network analysis as a tool for understanding the human collaboration on different levels of software development. This study and its findings are expected to be of benefit for software engineering practitioners and researchers who are mining software repositories using tools from network science field. We conducted a systematic literature review, in which we analyzed a number of selected papers from different digital libraries based on inclusion and exclusion criteria. We identified $35$ primary studies (PSs) from 4 digital libraries, then we extracted data from each PS according to a predefined data extraction sheet. The results of our data analysis showed that not all of the constructed networks used in the PSs were valid as the edges of these networks did not reflect a real relationship between the entities of the network. Additionally, the used measures in the PSs were in many cases not suitable for the used networks. Also, the reported analysis results by the PSs were not, in most cases, validated using any statistical model. Finally, many of the PSs did not provide lessons or guidelines for software practitioners that can improve the software engineering practices. Although employing network analysis in mining developers' collaboration showed some satisfactory results in some of the PSs, the application of network analysis needs to be conducted more carefully. That is said, the constructed network should be representative and meaningful, the used measure needs to be suitable for the context, and the validation of the results should be considered. More and above, we state some research gaps, in which network science can be applied, with some pointers to recent advances that can be used to mine collaboration networks.