Observations of primate groups have shown that social learning can lead to the development of temporal stable traditions or even proto-culture. The social structure of primate groups is highly diverse and it has been proposed that differences in the group structure shall influence the patterns of social information transmission. While empirical studies have mainly focused on the psychological mechanisms of social learning in individuals, the phenomenon of information propagation within the group has received relatively little attention. This might be due to the fact that formal theories that allow actual testing have not been formulated, or were kept too simple, ignoring the social dynamics of multi-agent societies. We want to propose a network approach to social information transmission that (1) preserves the complexity of the social structure of primate groups and (2) allows direct application to empirical data. Results from simulation experiments with artificial group structures confirm that association patterns of group-members influence the expected speed of information transmission during the propagation process. Introducing a forgetting rate shows that under certain conditions the proportion of informed individuals will reach a stable rate in some systems while it will drop to zero in others. This suggests that the likelihood to observe temporal stable traditions shall differ between social systems with different structure.