Increases in depressive and suicide-related symptoms among United States adolescents have been recently linked to increased use of smartphones. Understanding of the brain mechanisms that underlie the potential smartphone dependence may help develop interventions to address this important problem. In this exploratory study, we investigated the neural mechanisms underlying potential smartphone dependence in a sample of 19 adolescent volunteers who completed self-assessments of their smartphone dependence, depressive symptoms, and sleep problems. All 19 adolescents underwent diffusion MRI that allowed for assessment of white matter structural connectivity within the framework of connectomics. Based on previous literature on the neurobiology of addiction, we hypothesized a disruption of network centrality of three nodes in the mesolimbic network: Nucleus Accumbens, anterior cingulate cortex, and amygdala. Our results showed positive correlations between the node centrality of the right amygdala and self-reported smartphone dependence, between smartphone dependence and sleep problems, and between sleep problems and depressive symptoms. A higher phone dependence was observed in females compared to males. Supported by these results, we propose a model of how smartphone dependence can be linked to aberrations in brain networks, sex, sleep disturbances, and depression in adolescents.