Abstract When the estimated strength of social associations corresponds to the proportion of time spent together, strong links, those that take up most of the recorded time of individuals, are compulsorily transitive and tend to occur in clusters. However, I describe three ways in which the frequency and position of strong associations apparently offset the expected transitivity of strong links in published association networks from 26 species of vertebrates. Instead of occurring in groups of three, strong links were mostly isolated. When they did occur in clusters, the clusters were small. The phenomena increased in intensity as the overall number of links of all strengths and the overall network transitivity increased. Since stable transitive motifs are beneficial to cooperation, these results can help explain why cooperative behaviors are not more frequent than they are in group‐living vertebrates. Inversely, stable transitive motifs may be rare and small because the benefits of cooperation do not overcome the costs associated with these motifs. The summary statistics developed for this study captured information not conveyed by other network‐level metrics; thus they may help quantify the socio‐spatial structure of populations and potentially tease apart the environmental, species‐specific, and individual drivers.