Fig 1.
Structure of the database used as an input to the algorithms studied in the paper.
The database consists in the history of interactions (like, comments) of Facebook users with Facebook pages. In this form, it corresponds to a bipartite graph whose edges have a time tag (i.e. when the interaction happened) and therefore can be multiple (each user can comment at different times the same page).
Fig 2.
Future activity (i.e., number of posts) of Facebook pages as a function of Impact ranking.
The PopRank algorithm can also predict how many comments will be posted on that page and the number of users will comment its posts. In particular, we show the results for α = −1/2.
Fig 3.
Residuals of the linear fit in Fig 2 as a function of the Impact Ranking.
Scientific and conspiracy pages show a similar behavior with respect to the residuals. On the contrary, the Impact ranking shows a slight discriminative power since, on average, conspiracy pages have a lower ranking respect to scientific ones.
Fig 4.
Mean squared error in predicting the activity using the simple popularity measure or using the Impact, as a function of the exponent α in the PopRank algorithm.
Negative exponents give better results.
Fig 5.
The correlation between Impact and future activity is roughly independent from users’ polarization level.
We divide users according to their polarization and we count the number of users, belonging to a given group, that comments a given page. The PopRank algorithm can predict such values with similar performances across the groups, and always overperforming a simpler measure of Popularity.