Background: Peer relationships are important for children's mental health, yet little is known of their etiological underpinnings. Here, we explore the genetic influences on childhood peer network characteristics in three different networks defined by rejection, acceptance, and prosocial behavior. We further examine the impact of early externalizing and internalizing trajectories on these same peer network characteristics. Methods: Participants were 1,288 children from the Dutch 'Generation R' birth cohort. At age 7, we mapped out children's classroom peer networks for peer rejection, acceptance, and prosocial behavior using mutual peer nominations. In each network, genetic influences were estimated for children's degree centrality, closeness centrality and link reciprocity from DNA using Genome-wide Complex Trait Analysis. Preschool externalizing and internalizing trajectories were computed using parental ratings at ages 1.5, 3, and 5 years. Results: Of the three network properties examined, closeness centrality emerged as significantly heritable across all networks. Preschool externalizing problems predicted unfavorable positions within peer rejection networks and having fewer mutual friendships. In contrast, children with preschool-internalizing problems were not actively rejected by their peers, but were less well-connected within their social support network. Conclusions: Our finding of significant heritability for closeness centrality should be taken as preliminary evidence that requires replication. Nevertheless, it can orient us to the role of genes in shaping a child's position within peer networks. Additionally, social network perspectives offer rich insights into how early life mental health trajectories impact a child's later functioning within peer networks.