Interspecific dominance hierarchies have been widely reported across animal systems. High-ranking species are expected to monopolize more resources than low-ranking species via resource monopolization. In some ant species, dominance hierarchies have been used to explain species coexistence and community structure. However, it remains unclear whether or in what contexts dominance hierarchies occur in tropical ant communities. This study seeks to examine whether arboreal twig-nesting ants competing for nesting resources in a Mexican coffee agricultural ecosystem are arranged in a linear dominance hierarchy. We described the dominance relationships among 10 species of ants and measured the uncertainty and steepness of the inferred dominance hierarchy. We also assessed the orderliness of the hierarchy by considering species interactions at the network level. Based on the randomized Elo-rating method, we found that the twig-nesting ant species Myrmelachista mexicana ranked highest in the ranking, while Pseudomyrmex ejectus was ranked as the lowest in the hierarchy. Our results show that the hierarchy was intermediate in its steepness, suggesting that the probability of higher ranked species winning contests against lower ranked species was fairly high. Motif analysis and significant excess of triads further revealed that the species networks were largely transitive. This study highlights that some tropical arboreal ant communities organize into dominance hierarchies.