Predictive models using traditional statistical methods have largely failed to describe suicide etiology. Network theory, which conceptualizes factors as mutually interacting, reinforcing elements of a complex outcome, can model relationships between transdiagnostic and neurocognitive vulnerability factors. The present study used a network approach to produce an atheoretical model of psychological factors and their interrelationships within a population of ideators and non-ideators. We developed two network models (i.e., suicidal ideators and psychiatric controls) describing the relationships between a diverse set of risk factors and symptom measures for a population of psychiatric outpatients. We compared networks using three measures of network structure (i.e., network structure invariance, global strength invariance, edge invariance) and described the differences. Network structures for ideators (N = 229) and non-ideators (N = 454) were stable and accurate. In non-ideators, cognitive-affective depression symptoms (Expected Influence [EI]: 2.06), trauma avoidance (EI: 1.08), and negative affect (EI: 0.81) were most influential to the psychological network. In ideators, cognitive-affective depression symptoms (EI: 1.77), intolerance of uncertainty-negative self-referent implications (EI: 1.29), and negative affect (EI: 1.19) were most influential. Invariance testing did not indicate significant differences in overall network structure between ideators and non-ideators (p = .111), but did indicate significant differences in node strength (p = .013). Significant differences in node EI were detected for intolerance of uncertainty-negative self-referent implications, anxiety sensitivity physical concerns, thwarted belongingness, worry, and negative affect. These findings indicated differences in network structures for suicidal psychiatric outpatients and provide crucial directions for future research on therapeutic targets for suicidal thoughts and behaviors.