Beyond preferential attachment: falling of stars and survival of superstars.

Numerous studies over the past decades established that real-world networks typically follow preferential attachment and detachment principles. Subsequently, this implies that degree fluctuations monotonically increase while rising up the 'degree ladder', causing high-degree nodes to be prone for attachment of new edges and for detachment of existing ones. Despite the extensive study of node degrees (absolute popularity), many domains consider node ranks (relative popularity) as of greater importance. This raises intriguing questions-what dynamics are expected to emerge when observing the ranking of network nodes over time? Does the ranking of nodes present similar monotonous patterns to the dynamics of their corresponding degrees? In this paper, we show that surprisingly the answer is not straightforward. By performing both theoretical and empirical analyses, we demonstrate that preferential principles do not apply to the temporal changes in node ranking. We show that the ranking dynamics follows a non-monotonous curve, suggesting an inherent partition of the nodes into qualitatively distinct stability categories. These findings provide plausible explanations to observed yet hitherto unexplained phenomena, such as how superstars fortify their ranks despite massive fluctuations in their degrees, and how stars are more prone to rank instability.

Segregation and polarization in urban areas.

Social behaviours emerge from the exchange of information among individuals-constrained by and reciprocally influencing the structure of information flows. The Internet radically transformed communication by democratizing broadcast capabilities and enabling easy and borderless formation of new acquaintances. However, actual information flows are heterogeneous and confined to self-organized echo-chambers. Of central importance to the future of society is understanding how existing physical segregation affects online social fragmentation. Here, we show that the virtual space is a reflection of the geographical space where physical interactions and proximity-based social learning are the main transmitters of ideas. We show that online interactions are segregated by income just as physical interactions are, and that physical separation reflects polarized behaviours beyond culture or politics. Our analysis is consistent with theoretical concepts suggesting polarization is associated with social exposure that reinforces within-group homogenization and between-group differentiation, and they together promote social fragmentation in mirrored physical and virtual spaces.