Emergence of group size disparity in growing networks with adoption

Social and technical networks undergo constant evolution driven by both existing entities and newcomers. In academia, research papers are continually cited by new papers, while senior researchers integrate newly arrived junior researchers into their academic networks. Moreover, social systems can be influenced by external factors that could indirectly impact their growth patterns. For instance, systematic discrimination against certain groups in academia or managerial positions can impede their long-term growth, especially when combined with group-level preferences in hiring or adoption, as observed in our study. To address this, we introduce a network growth and adoption model where generalised preferential attachment and asymmetric mixing act as the two fundamental mechanisms of growth and adoption. We show analytically and numerically that these mechanisms can recover the empirical properties of citation and collaboration growth, as well as the inequalities observed in the growth dynamics of groups. This model can be used to investigate the effect of intervention in group mixing preferences to overcome the cumulative disparities in the group-level dynamics.