Strong, stable social bonds in primates are characterized by high levels of social affiliation, low levels of aggression, minimal stress, and affiliative reciprocity within the dyad. In relatively well-studied catarrhine monkeys, these bonds tend to form most frequently between kin, animals close in age, and animals close in rank. This results in patterns of affiliation in which kin, similarly aged animals, and like-ranked animals tend to affiliate and patterns of aggression and submission where animals tend to aggress more toward nonkin and closely ranked animals, and submit more toward distantly ranked animals. However, literature on how affiliative and agonistic relationships are organized in platyrrhine primate species like brown capuchin monkeys is limited and conflicting. In this study, we used social network analyses to characterize how age, sex, maternal kinship, and dominance rank relate to the patterns of submissive, aggressive, contact, and grooming interactions in a group of captive brown capuchin monkeys. Like catarrhine monkeys, brown capuchin monkeys showed a steep linear dominance hierarchy, tended to affiliate with kin, similarly aged animals, and like-ranked animals, and tended to aggress more toward nonkin. However, our monkeys showed a pattern of affiliation and grooming down the hierarchy that is inconsistent with grooming up the hierarchy patterns often seen in catarrhine monkey groups, suggesting that brown capuchins do not compete for access to higher ranking social partners. Higher ranking monkeys were most central to the aggression network, and lower ranking monkeys were most central to the submission network. Mid-ranking monkeys were the most central to the contact network, suggesting that they may play an important role in the affiliative cohesion of the group. These results inform our understanding of brown capuchin social behavior specifically, and of how demographic factors relate to social organization in platyrrhine primates generally.