BackgroundSocial relations influence mental health through different pathways. To capture the complexity of social relations, it is beneficial to consider both the structural (e.g., reachability of social network and social integration) and functional (e.g., instrumental and emotional support) aspects of the concept. Both aspects are rarely investigated simultaneously. This study aimed to examine the association between the structural and functional aspects of social relations and poor mental health.MethodsThe study was designed as a cross-sectional register study. We used data on mental health and social relations from 15,839 individuals aged 16–92 years with a mean age of 49.0 years (SD 17.9) who responded to The North Denmark Region Health Survey 2013 among residents in Northern Jutland, Denmark. The 12-Item Short-Form Health Survey measured mental health; a cut-off point of 44.5 was used to dichotomize participants into poor and good mental health. The categorization of social relations was inspired by Berkman et al.’s conceptual model of social relations and health. The analyses were performed with survey logistic regression.ResultsWe found that 21.6% (n = 3422) of participants reported poor mental health, and 59% (n = 2020) of these were women. Being in contact with family and friends less than once a month statistically significantly increased the risk for poor mental health (Family OR = 1.78, 95% CI = 1.51–2.10 and Friends OR = 2.65, 95% CI = 2.30–3.06). The individuals who were not in contact with their network as often as they liked had a significantly higher risk for poor mental health (OR = 2.40, 95% CI = 2.20–2.62). Lack of instrumental support was associated with a higher risk for poor mental health (OR = 2.81, 95% CI = 2.26–3.48). We found an interaction between age and emotional support; the youngest population had the highest risk for poor mental health when they did not have access to emotional support (Young OR = 5.26, 95% CI = 3.91–7.09; Adult OR = 3.69, 95% CI = 3.17–4.30; and Elderly OR = 2.73, 95% CI = 2.23–3.34).ConclusionsBoth structural and functional aspects of social relations were associated with poor mental health in our study. Rarely being in contact with friends and a lack of network reachability were associated with poor mental health. Likewise, low levels of emotional and instrumental support were associated with poor mental health.Electronic supplementary materialThe online version of this article (10.1186/s12889-017-4871-x) contains supplementary material, which is available to authorized users.