The role of relatedness in structuring animal societies has attracted considerable interest. Whilst a significant number of studies have documented kin recognition in shoaling fish under laboratory conditions, there is little evidence that relatedness plays a significant role in structuring social interactions in wild populations that are characterised by fission-fusion dynamics. Previous work has tended to compare relatedness within and among entire shoals. Such an approach however, does not have the ability to detect social sub-structuring within groups, which appears to be a major factor driving the social organisation of fission-fusion animal societies. Here, we use social network analysis combined with DNA microsatellite genotyping to examine the role of relatedness in structuring social relationships in a wild population of guppies (Poecilia reticulata). Consistent with previous findings, female-female dyads formed the strongest social relationships, which were stable over time. Interestingly, we also observed significant co-occurrence of male-male interactions, which is in contrast to previous work. Although we observed social sub-structuring in the population, we found no evidence for relatedness playing a significant role in underpinning this structure. Indeed, only seven first-degree relative dyads were identified among the 180 fish genotyped, indicating that the majority of individuals do not have a first-degree relative in the population. The high genetic diversity observed in this population is indicative of a large effective population size typical of lowland guppy populations. We discuss our findings in the context of the evolution of social organisation and the mechanisms and constraints that may drive the observed patterns in wild populations.