Monozygotic twins share the same genotype; however, they can be phenotypically discordant on various traits. Studying discordant monozygotic twins allows the investigation of differences in associations between symptoms and psychopathological risk factors, controlled for shared genetic liability. The network approach to psychopathology suggests that depressive symptoms, along with risk and protective factors (e.g., cognition, daily activities), form a complex system of mutually interacting components. We compared monozygotic twins discordant for lifetime depression on their respective extended networks of depressive symptoms, cognitive functions, and daily activities (intellectual, physical, social), and evaluated if these networks differ in their associations between variables and in the role of each variable within the network. Regularized partial correlations investigated the networks’ composition in 147 monozygotic twin pairs discordant for depression from the Danish Twin Registry. Affected twins had stronger overall associations within their network of depressive symptoms, cognitive functions, and daily activities than their unaffected co-twins, while the importance of the network components’ associations did not differ between the co-twins. In affected twins, decreased frequency in experiencing happiness had the strongest association with remaining variables (i.e., the most influence in activating other network elements). Also, variables from different groups were significantly associated (e.g., loneliness with delayed memory, pessimism with low social activities, verbal learning with intellectual activities). In unaffected twins, both mood symptoms and cognitive functions were important, but between-groups associations were quasi-absent. These results suggest that external events affecting the ability to feel happiness likely trigger the psychopathological process (depression network activation), independently from the genetic predisposition to depression.