The sociality of cattle facilitates the maintenance of herd cohesion and synchronization, making these species the ideal choice for domestication as livestock for humans. However, livestock populations are not self-regulated, and farmers transfer individuals across different groups. Individuals consequently have to adapt to different group compositions during their lives rather than choose their own herd mates, as they would do in the wild. These changes may lead to social instability and stress, entailing potentially negative effects on animal welfare. In this study, we assess how the transfer of Highland cattle (Bos taurus) impacts individual and group social network measures. Four groups with nine different compositions and 18 individual transfers were studied to evaluate 1) the effect of group composition on individual social centralities and 2) the effect of group composition changes on these centralities. This study reveals that the relative stability of dyadic spatial relationships between changes in group composition or enclosure is due to the identities of transferred individuals more than the quantity of individuals that are transferred. Older cattle had higher network centralities than other individuals. The centrality of individuals was also affected by their sex and the number of familiar individuals in the group. This study reveals the necessity of understanding the social structure of a group to predict social instability following the transfer of individuals between groups. The developing of guidelines for the modification of group composition could improve livestock management and reduce stress for the animals concerned.