The occurrences of bugs are not isolated events, rather they may interact, affect each other, and trigger other latent bugs. Identifying and understanding bug correlations could help developers localize bug origins, predict potential bugs, and design better architectures of software artifacts to prevent bug affection. Many studies in the defect prediction and fault localization literature implied the dependence and interactions between multiple bugs, but few of them explicitly investigate the correlations of bugs across time steps and how bugs affect each other. In this paper, we perform social network analysis on the temporal correlations between bugs across time steps on software artifact ties, i.e., software graphs. Adopted from the correlation analysis methodology in social networks, we construct software graphs of three artifact ties such as function calls and type hierarchy and then perform longitudinal logistic regressions of time-lag bug correlations on these graphs. Our experiments on four open-source projects suggest that bugs can propagate as observed on certain artifact tie graphs. Based on our findings, we propose a hybrid artifact tie graph, a synthesis of a few well-known software graphs, that exhibits a higher degree of bug propagation. Our findings shed light on research for better bug prediction and localization models and help developers to perform maintenance actions to prevent consequential bugs.