Alexithymia is a multifaceted personality construct that reflects deficits in affect awareness (difficulty identifying feelings, DIF; difficulty describing feelings, DDF) and operative thinking (externally oriented thinking, EOT; restricted imaginal processes, IMP), and is associated with several common psychiatric disorders. Over the years, researchers have debated the components that comprise the construct with some suggesting that IMP and EOT may reflect constructs somewhat distinct from alexithymia. In this investigation, we attempt to clarify the components and their interrelationships using a large heterogeneous multilanguage sample (N = 839), and an interview-based assessment of alexithymia (Toronto Structured Interview for Alexithymia; TSIA). To this end, we used 2 distinctly different but complementary methods, bifactor modeling and network analysis. Results of the confirmatory bifactor model and related reliability estimates supported a strong general factor of alexithymia; however, the majority of reliable variance for IMP was independent of this general factor. In contrast, network analysis results were based on a network comprised of only substantive partial correlations among TSIA items. Modularity analysis revealed 3 communities of items, where DIF and DDF formed 1 community, and EOT and IMP formed separate communities. Network metrics supported that the majority of central items resided in the DIF/DDF community and that IMP items were connected to the network primarily through EOT. Taken together, results suggest that IMP, at least as measured by the TSIA, may not be as salient a component of the alexithymia construct as are the DIF, DDF, and EOT components.