UN staff face a difficult decision when they need to prioritize the 17 Sustainable Development Goals (SDGs). Faced with multiple constraints such as financial and human resources, the UN needs to make decisions by building an effective model. Our team developed the W17 relationship network model, the priority assessment model, and other models based on the W17 relationship network, and applied them to prioritize the goals of other companies and organizations. We discuss how the network of relationships changes under the assumption that no poverty goal is achieved, and obtain new priorities for the SDGs by reassigning values to indicators. We considered the impact of international crises on the network structure, discussing the impact of global pandemics, refugee movements, and climate change on the choice of priorities. The impact of these international crises on the progress of the UN's work was analyzed from a network perspective. Finally, we applied the relationship network construction model and the priority assessment model to prioritize the goals of other companies and organizations. We also performed a sensitivity analysis of the model. The percentage of synergy still accounts for more than 80% of our artificially determined indicator increments when they fluctuate in the 2% interval. This indicates that our model is stable within a reasonable range of variation.