Coupling effect of nodes popularity and similarity on social network persistence.

Network robustness represents the ability of networks to withstand failures and perturbations. In social networks, maintenance of individual activities, also called persistence, is significant towards understanding robustness. Previous works usually consider persistence on pre-generated network structures; while in social networks, the network structure is growing with the cascading inactivity of existed individuals. Here, we address this challenge through analysis for nodes under a coevolution model, which characterizes individual activity changes under three network growth modes: following the descending order of nodes' popularity, similarity or uniform random. We show that when nodes possess high spontaneous activities, a popularity-first growth mode obtains highly persistent networks; otherwise, with low spontaneous activities, a similarity-first mode does better. Moreover, a compound growth mode, with the consecutive joining of similar nodes in a short period and mixing a few high popularity nodes, obtains the highest persistence. Therefore, nodes similarity is essential for persistent social networks, while properly coupling popularity with similarity further optimizes the persistence. This demonstrates the evolution of nodes activity not only depends on network topology, but also their connective typology.