Quantifying the Influence of Websites Based on Online Collective Attention Flow

The availability of network big data, such as those from online users＇ surfing records, communication records, and e-commerce records, makes it possible for us to probe into and quantify the regular patterns of users＇ long-range and complex interactions between websites. If we see the Web as a virtual living organism, according to the metabolic theory, the websites must absorb ＂energy＂ to grow, reproduce, and develop. We are interested in the following two questions： 1） where does the ＂energy＂ come from？ 2） will the websites generate macro influence on the whole Web based on the ＂energy＂？ Our data consist of more than 30 000 online users＇ surfing log data from China Internet Network Information Center. We would consider the influence as metabolism and users＇ attention flow as the energy for the websites. We study how collective attention distributes and flows among different websites by the empirical attention flow network. Different from traditional studies which focused on information flow, we study users＇ attention flow, which is not only a ＂reversed＂ way to study Web structure and transmission mode, but also the first step to understand the underlying dynamics of the World Wide Web. We find that the macro influence of websites scales sub-linearly against the collective attention flow dwelling time, which is not consistent with the heuristics that the more users＇ dwelling time is, the greater influence a website will have. Further analysis finds a supper-linear scaling relationship between the influence of websites and the attention flow intensity. This is a websites version of Kleiber＇s law. We further notice that the development cycle of the websites can be split into three phases： the uncertain growth phase, the partially accelerating growth phase, and the fully accelerating growth phase. We also find that compared with the widespread hyperlinks analysis models, the attention flow network is an effective theoretical tool to estimate and rank websites.