Background: Open Source Software is the building block of modern software. However, the prevalence of project deprecation in the open source world weakens the integrity of the downstream systems and the broad ecosystem. Therefore it calls for efforts in monitoring and predicting project deprecations, empowering stakeholders to take proactive measures. Challenge: Existing techniques mainly focus on static features on a point in time to make predictions, resulting in limited effects. Goal: We propose a novel metric from the user-repository network, and leverage the metric to fit project deprecation predictors and prove its real-life implications. Method: We establish a comprehensive dataset containing 103,354 non-fork GitHub OSS projects spanning from 2011 to 2023. We propose repository centrality, a family of HITS weights that captures shifts in the popularity of a repository in the repository-user star network. Further with the metric, we utilize the advancements in gradient boosting and deep learning to fit survival analysis models to predict project lifespan or its survival hazard. Results: Our study reveals a correlation between the HITS centrality metrics and the repository deprecation risk. A drop in the HITS weights of a repository indicates a decline in its centrality and prevalence, leading to an increase in its deprecation risk and a decrease in its expected lifespan. Our predictive models powered by repository centrality and other repository features achieve satisfactory accuracy on the test set, with repository centrality being the most significant feature among all. Implications: This research offers a novel perspective on understanding the effect of prevalence on the deprecation of OSS repositories. Our approach to predict repository deprecation help detect health status of project and take actions in advance, fostering a more resilient OSS ecosystem.