In group-living animals, social relationships are the result of the interactions between two individuals over time and can provide fitness benefits to both the participants. Recently, components of social relationships were identified in Old World primates and ravens through the use of principal component analysis (PCA). We employed PCA to identify components that define the social relationships in two communities of wild spider monkeys in the Yucatán Peninsula, Mexico and investigated whether characteristics of the dyads, such as age combination, sex combination and kinship, had an effect on the components obtained. We found two components. Component 1 had high positive loadings of proximity, grooming and subgroup index, which may reflect value or compatibility. Embrace and aggression rates loaded highly on Component 2, which was labelled risk. Component 1 was affected by kinship: kin had higher scores than non-kin. Both the components were affected by sex combination of the dyad. Male–male dyads had higher scores than female–male and female–female dyads. The results are in accordance with what is currently known about spider monkeys’ social relationships, but provide an additional perspective with the novel component of risk. In this respect, the two components are effective in capturing the ambiguous nature of male–male relationships in spider monkeys. Overall, this study offers further insight into the social patterns underlying the relationship quality in group-living animals and the usefulness of PCA in providing an objective assessment that reflects the animals′ perspective of their social interactions.