<p>The performance of polymer networks is directly determined by their structure. Understanding the network structure offers insights into optimizing material performance, such as elasticity, toughness, and swelling behavior. Herein, in this study we introduce the Dijkstra algorithm from graph theory to characterize polymer networks based on star-shaped multi-armed precursors by employing coarse-grained molecular dynamics simulations coupled with stochastic reaction model. Our research focuses on the structure characteristics of the generated networks, including the number and size of loops, as well as network dispersity characterized by loops. Tracking the number of loops during network generation allows for the identification of the gel point. The size distribution of loops in the network is primarily related to the functionality of the precursors, and the system with fewer precursor arms exhibiting larger average loop sizes. Strain-stress curves indicate that materials with identical functionality and precursor arm lengths generally exhibit superior performance. This method of characterizing network structures helps to refine microscopic structural analysis and contributes to the enhancement and optimization of material properties.</p>