> By Matthieu Latapy, Jean-Philippe Cointet and Adrien Friggeri
The study of information diffusion among individuals in a social network is a challenging task as there are different possible definitions for a given concept. Consider for example a blogger who publishes a piece of information on his website; there are mainly two ways of quantifying his influence.
First, we call the direct influence of a blogger the number of fellow bloggers who obtained the resource from the original blogger. We define the indirect influence as the number of bloggers who copied the resource from the original blogger, or from bloggers who got their copy from the original blogger, and so on.
If one considers the spreading tree associated with the diffusion process, the direct influence of a node is it degree, and the indirect influence is the size of the subtree rooted on that node.
This plot shows the correlation between direct (x axis) and indirect influence (y axis) of 492 blogs having spread a widget in the context of the Happy Flu experiment. One may imagine some cases in which a blog with a low direct influence would have a high indirect influence by infecting another blog which has a high indirect influence.
However, notice how this is not the case here: both quantities are strongly correlated. Moreover, the six blogs with the lowest correlation (i.e. blogs having a high indirect influence but a relatively low direct influence) are the six initial blogs which served as seeds for the experiment and therefore may be considered as a measurement artefact.
Finally, as both quantities are correlated, we may say they both quantify in the same way the influence of a blog.