In many taxa, individual social traits appear to be consistent across time and context, thus meeting the criteria for animal personality. How these differences are maintained in response to changes in population density is unknown, particularly in large mammals, such as ungulates. Using a behavioral reaction norm (BRN) framework, we examined how among- and within-individual variation in social connectedness, measured using social network analyses, change as a function of population density. We studied a captive herd of elk (Cervus canadensis) separated into a group of male elk and a group of female elk. Males and females were exposed to three different density treatments and we recorded social associations between individuals with proximity-detecting radio-collars fitted to elk. We constructed social networks using dyadic association data and calculated three social network metrics reflective of social connectedness: eigenvector centrality, graph strength, and degree. Elk exhibited consistent individual differences in social connectedness across densities; however, they showed little individual variation in their response to changes in density, i.e., individuals oftentimes responded plastically, but in the same manner to changes in density. Female elk had highest connectedness at an intermediate density. In contrast, male elk increased connectedness with increasing density. Whereas this may suggest that the benefits of social connectedness outweigh the costs of increased competition at higher density for males, females appear to exhibit a threshold in social benefits (e.g. predator detection and forage information). Our study illustrates the importance of viewing social connectedness as a density-dependent trait, particularly in the context of plasticity. Moreover, we highlight the need to revisit our understanding of density dependence as a population-level phenomenon by accounting for consistent individual differences not only in social connectedness, but likely in other ecological processes (e.g., predator-prey dynamics, mate choice, disease transfer).