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We analyzed the effects of crosslinking fraction and number of functional sites per hardener molecule on the stress recovery and topology of thermoset shape memory polymers (TSMPs) via coarse-grained molecular dynamics simulations. After systematically varying the quality of the crosslinked network by manipulating the number of unique epoxies reacted with each hardener, we found that two fingerprints correlate well with stress recovery of TSMPs. These fingerprints are the fraction of epoxy molecules connected to two distinct hardener molecules, and the fraction of molecules that are part of the largest or main network in the system. Their product can be used as a topological score ($S_{\text{topo}}$) to quantify the topological feature of the network. When analyzing stress recovery as a function of$S_{\text{topo}}$, we found a strong correlation between$S_{\text{topo}}$and recovery stress. Moreover, we observed that while a higher crosslinking fraction did frequently lead to a higher stress recovery, many exceptions existed. High functionality hardeners tend to exhibit higher stress recovery at similar$S_{\text{topo}}$, especially at high (>0.65)$S_{\text{topo}}$. These results suggest that increasing the number of functional sites per hardener molecule combined with improving the topology of the network with a method such as semi batch monomer addition can lead to an improvement in the stress recovery of TSMPs.