Preferential attachment and the spreading influence of users in online social networks

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Identifying influential users who lead to large-scale spreading in online social networks (OSNs) is of theoretical and practical significance. Many methods have been proposed to measure the influence of users, but little literature studies the interplay of the global influence of users and their local connections. In this paper, we particularly focus on the assortative and disassortative preference. The results in this paper can address three main issues in this area: (i) What is the difference in spreading influence between ordinary and core users? (ii) What is the distribution of influential users? (iii) How do they evolve from a fresh user to a powerful influencer? The k-shell hierarchy is adopted to quantify the global spreading influence of users. Firstly, we find that the global influence varies dramatically among users in disassortative OSNs, but the variation is relatively small in assortative OSNs. Hence, ordinary users also possess high influence in assortative OSNs. Secondly, we empirically and theoretically prove that the global influence of users follows a power-law distribution. Moreover, many users concentrate on the core in assortative OSNs, but few users locate at the core in disassortative OSNs. Thirdly, it is found that users in assortative OSNs gain influence over time and gradually upgrade to core members. In disassortative OSNs, the core users gain much influence along with network growth but other users scatter among all hierarchical levels. The results are verified on real OSN datasets and the state-of-the-art OSN model.