We find that the flow of attention on the Web forms a directed, tree-like structure implying the time-sensitive browsing behavior of users. Using the data of a news sharing website, we construct clickstream networks in which nodes are news stories and edges represent the consecutive clicks between two stories. To identify the flow direction of clickstreams, we define the “flow distance” of nodes (L_i), which measures the average number of steps a random walker takes to reach the ith node. It is observed that L_i is related with the clicks (C_i) to news stories and the age (T_i) of stories. Putting these three variables together help us understand the rise and decay of news stories from a network perspective. We also find that the studied clickstream networks preserve a stable structure over time, leading to the scaling between users and clicks. The universal scaling behavior is confirmed by the 1,000 Web forums. We suggest that the tree-like, stable structure of clickstream networks reveals the time-sensitive preference of users in online browsing. To test our assumption, we discuss three models on individual browsing behavior, and compare the simulation results with empirical data.

Two classes of scaling behaviours, namely the super-linear scaling of links or activities, and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded. We implement some realistic extensions to the basic model to offer more accurate predictions for cities of various scaling behaviours and the Zipf distribution reported in the literature and observed in our empirical studies. All of the empirical results can be precisely recovered by our model with analytical predictions of all major properties. By virtue of these general findings concerning scaling behaviour, our models with simple mechanisms gain new insights into the evolution and development of complex networked systems.