# The scaling of attention networks

Cheng-Jun Wang *,
Lingfei Wu

December 2015

### Abstract

We use clicks as a proxy of collective attention and construct networks to study the temporal dynamics of attention. In particular we collect the browsing records of millions of users on 1000 Web forums in two months. In the constructed networks, nodes are threads and edges represent the switch of users between threads in an hour. The investigated network properties include the number of threads $N$, the number of users $UV$, and the number of clicks, $PV$. We find scaling functions $PV \sim UV^{\theta_1}$, $PV \sim N^{\theta_3}$, and $UV \sim N^{\theta_2}$, in which the scaling exponents are always greater than 1. This means that (1) the studied networks maintain a self-similar flow structure in time, i.e., large networks are simply the scale-up versions of small networks; and (2) large networks are more “productive”, in the sense that an average user would generate more clicks in the larger systems. We propose a revised version of Zipf’s law to quantify the time-invariant flow structure of attention networks and relate it to the observed scaling properties. We also demonstrate the applied consequences of our research: forum-classification based on scaling properties.

Publication

*Physica A*: Statistical Mechanics and its Applications. 448:196–204, doi: 10.1016/j.physa.2015.12.081

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