Heterogeneity of Human Activity Levels Gives Rise to Power-Law Distribution in Online Social Networks

It is well established that the distribution of social ties (degree) of an individual in a social network follows a power-law. How this heavy-tailed distribution arises in practice, however, has not been conclusively demonstrated. Mechanisms of ``preferential-attachment'' and optimization are often cited as the origin of heavy-tailed degree distributions. Our data indicate that there is a different cause for these phenomena. For different social networks we find an intrinsic relationship degree and activity (number of posts, edits etc): The degree distribution is entirely random except for its mean value which depends deterministically on the volume of the users' activity. This suggests that heavy-tailed degree distribution is a consequence of the intrinsic activity of users. More importantly, human activity deterministically affects the mean success at establishing links in a social network, and the specific degree of a given user is otherwise random following a ``maximum entropy attachment'' model.