Interspecific dominance hierarchies have been widely reported across animal systems. While some dominant individuals (winners) get to monopolize resources, during dyadic interactions, they can increase their relative fitness as compared to subdominant individuals (losers). 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. Furthermore, it can be challenging to infer and quantify reliable dominance hierarchies from observed interactions. This study seeks to examine whether arboreal twig-nesting ants competing for nesting resources in a Mexican coffee agricultural ecosystem are arranged in a dominance hierarchy. Using network analysis, we quantified interactions between ten species by measuring the uncertainty and steepness in the dominance hierarchy. We also assessed the orderliness of the hierarchy by considering species interactions at the network level. Based on the Elo-ranking 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. We quantified the uncertainty in the dominance hierarchy and found that the hierarchy was intermediate in its steepness, suggesting that the probability of higher ranked individuals winning contests against lower ranked individuals 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 self-organize into dominance hierarchies.