Social influence on selection behaviour: Distinguishing local- and global-driven preferential attachment - Fig 1

<p>(Color online) <b>a,</b> An example of user-business bipartite network with social structure to illustrate the Yelp data set and the research scenario. On the user layer, each user may establish friendships with others and those friends are the target user’s local neighbourhood. On the other hand, the whole user layer is the global environment for each user. The interactions between the user and business layer represented by the bipartite links, are the comment behaviours. Although it is impossible to know exactly each user’s real-world consumption for those businesses, we assume the online comment behaviour could largely reflect what those users have selected (consumed). <b>b,</b> The distribution of the businesses’ final global popularity, i.e. popularity at the end <i>t</i> = <i>T</i> of the Yelp data set, <i>GP</i>(<i>T</i>). As what have been observed from most networks, the global popularity distribution displays a power-law form with slope of −1.7. <b>c,</b> Local popularity of selection behaviours <i>LP</i>(<i>c</i>) versus the expected local popularity <i>LP</i>^<i>exp</i>. The red dashed line shows the condition that <i>LP</i>(<i>c</i>) = <i>LP</i>^<i>exp</i>. While the local popularity of the random experiments and global-driven preferential attachment (GPA) model are very similar to the expected value, the empirical local popularity is significantly higher which suggests that the users tend to select locally popular businesses. <b>d,</b> The distribution of real-time local popularity <i>LP</i>(<i>c</i>). For the empirical data, the local popularity follows the power-law distribution with slope of −2.7. On the other hand, the local popularity of the GPA model being very similar to the random experiment, cannot reproduce the empirical observation.