<p>Predicting the stability of superheavy nuclei remains a major challenge owing to limited experimental accessibility and substantial uncertainties among existing theoretical nuclear models. In this work, we introduce a network science–based framework in which nuclear decay chains, constructed from evaluated nuclear data, are represented as directed weighted networks, which allows for the analysis of topological properties alongside conventional nuclear descriptors. We find a statistically significant negative association between betweenness centrality and a structural stability score, indicating that nuclei occupying more topologically peripheral positions within the decay network tend to be relatively more stable. This behavior highlights known regions of enhanced relative stability within the analyzed transuranic domain and provides a qualitative network-based trend consistent with the expected movement toward the long-discussed superheavy stability region. Rather than identifying isolated topological clusters, the framework maps topological peripherality to localized regions of high stability determined by nuclear shell effects. Sensitivity analyses with respect to stability-score weighting schemes confirm the robustness of these trends. Rather than replacing existing nuclear models, the proposed approach provides a complementary, system-level perspective that captures collective decay patterns beyond single-nucleus descriptions. These results suggest that simple network measures can serve as useful qualitative indicators of relative nuclear stability and may help prioritize regions for further theoretical and experimental investigation.</p>