One of the defining characteristics of soft glassy materials is their ability to exhibit a yield stress, which can result in an overall elasto-visco-plastic mechanics. To design soft materials with specific properties, it is essential to gain a comprehensive understanding of the topological and structural failure points that occur during yielding. However, predicting these failure points, which lead to yielding, is challenging due to the dynamic nature of structure development and its cooccurrence with other complicated processes, such as local rearrangements and anisotropy. I will show a few exmaples of how employing a series of tools from network science can help better understand topology of plastic events in colloidal gels as a model for soft glassy materials during yielding. Our findings reveal that edge betweenness centrality can be utilized as a universal predictor for yielding across various state variables, including the volume fraction of solids, the strength, and the range of attraction between colloids.