A Nontrivial Interplay between Triadic Closure, Preferential, and Anti-Preferential Attachment: New Insights from Online Data

Abstract: This paper presents an analysis of a temporal network that describes the social connections of a large-scale (~ 30,000) sample of online social network users, inhabitants of a fixed city. We tested how the main network formation determinants - transitivity, preferential attachment, and social selection - contribute to network evolution. Among other things, we found that opinion social selection does affect tie appearing whereas its impact on tie removing is rather unclear. We report that transitivity displayed the strongest effect on network dynamics. Surprisingly, a closer look revealed an intriguing and complex interplay between the transitivity, preferential attachment, and anti-preferential attachment mechanisms. For a given pair of unconnected nodes, if they have no mutual connections, then the probability of tie creation goes up with the sum of node degrees - that is exactly what the preferential attachment mechanism is assumed to do. Instead, if the nodes have at least one common friend, then the highest probability of tie appearing is achieved if both the nodes have only a few friends - a phenomenon that is called anti-preferential attachment. We attempted to explain this finding by appealing to the notions of social communities and leaders.