Scaling of human behavior in the portal browsing. |
Anna Chmiel ^{1,2}, Kamila Kowalska ^{3}, Janusz A. Hołyst ^{1,2} |
1. Warsaw University of Technology, Faculty of Physics, Koszykowa 75, Warszawa 00-662, Poland |
Abstract |
We investigate the behavior of users at the web portal. We focus on the transitions between two subpages, using the information about the path of the users. We construct a weighted network whith portal subpages being its nodes and the weights of edges defined as a number of transition from a vertex to one of its neighbors. We scrutinize the properties of such a network as a distribution of weights and strenghts that corresponds to the power-law relation, as well as the statistics of users behavior. The latter brings interesting results: the average number of distinct subpages visited during the n-th step of a visit scales as a square root relation. Moreover, the way of choosing the next subpage and the browsing pattern at the portal can be understood as a special attracting walk on the weighted network. We show there is an agreement between the real data and the results of numeric simulation of attracting walk with the number of steps less than thirty. Finally, we use the rate equation to perform analytical calculation which fits the data from simulation |