Cotton-top tamarins (Saguinus oedipus) are characterized by a system of cooperative breeding where helpers, in addition to the reproductive pair, contribute to infant care. Grooming interactions between individuals play an important role in establishing social relationships, creating an interconnected social network in the group. We used social network analysis to investigate the social structure of two groups of cotton-top tamarins with different sizes and compositions and study whether they remain stable after the birth of new infants. We also investigated the possible correlation between the time spent carrying infants and an increase in the grooming centrality. We found that group A (n = 13) had a stable grooming network that showed consistent stability after the birth, although group B (n = 8 and no adult helpers) changed its grooming network and showed a lower density after the birth. Infant carrying was not correlated with increased grooming centrality after the birth. These findings highlight the usefulness of social network analysis in the study of group structure in cooperatively breeding primates and suggest that the birth of offspring has a greater impact on the stability of groups without adult helpers.