a b s t r a c tIn social animals, fission is a common mode of group proliferation and dispersion and may be affected by genetic or other social factors. Sociality implies preserving relationships between group members. An increase in group size and/or in competition for food within the group can result in decrease certain social interactions between members, and the group may split irreversibly as a consequence. One individual may try to maintain bonds with a maximum of group members in order to keep group cohesion, i.e. proximity and stable relationships. However, this strategy needs time and time is often limited. In addition, previous studies have shown that whatever the group size, an individual interacts only with certain grooming partners. There, we develop a computational model to assess how dynamics of group cohesion are related to group size and to the structure of grooming relationships. Groups' sizes after simulated fission are compared to observed sizes of 40 groups of primates. Results showed that the relationship between grooming time and group size is dependent on how each individual attributes grooming time to its social partners, i.e. grooming a few number of preferred partners or grooming equally or not all partners. The number of partners seemed to be more important for the group cohesion than the grooming time itself. This structural constraint has important consequences on group sociality, as it gives the possibility of competition for grooming partners, attraction for high ranking individuals as found in primates' groups. It could, however, also have implications when considering the cognitive capacities of primates.