Assortative and preferential attachment lead to core-periphery networks

Abstract

Core-periphery is a key feature of large-scale networks underlying a wide range of social, biological, and transportation phenomena. Nodes in the core have an influential position in the network, and thus, the periphery can be under structural disadvantage if the groups are aligned with external attributes such as gender or economic status. Despite its prevalence in empirical data, it is unclear whether core-periphery is a consequence of fundamental network evolution processes. While preferential attachment can create degree heterogeneity indistinguishable from core-periphery, it does not explain why cores and peripheries are aligned with some external node attribute, i.e., why specific groups of nodes gain dominance and become cores. We show that even small amounts of assortative attachment, e.g., homophily in social networks, can break the symmetric effect of preferential attachment and that the interplay of the two mechanisms leads to one of the groups emerging as a prominent core. A systematic analysis of the phase space of the proposed model reveals the levels of assortative and preferential attachment necessary for a group to become either core or periphery. We find that relative group size is significant, with minority groups typically having a disadvantage on becoming the core for similar assortative attachment levels among groups. We also find that growing networks are less prone to develop core-periphery than dynamically evolving networks and that these two network evolution mechanisms lead to different types of core-periphery structures. Analyzing five empirical networks, our findings suggest that core nodes are highly assortative, illustrating the potential of our model as a tool for designing and analyzing interventions on evolving networks.