We have just published an experimental/theoretical work on the speed of information diffusion in social networks in Physical Review Letters. Specifically we have studied the impact of the heterogeneity of human activity in propagation of emails, rumors, hoaxes, etc. Tracking email marketing campaigns, executed by IBM Corporation in 11 European countries, we were able to compare their viral propagation with our theory (see below the campaigns details).

The results are very simple. Let me give you an example: the typical time between two emails sent by the same person is around 1 day. Traditional models of information diffusion will then yield to an infection speed of 1 day. However, some email computer viruses spread widely in a matter of hours (minutes, sometimes), while some viral propagation (for example the Veuve-Clicquot hoax) last for years. How can that occur? The reason is that traditional models are not correct because they neglect the large heterogeneity in the frequency of human activity: the average time between emails (1 day) does not actually represent the collectivity. In fact, most of us respond very quickly to emails, but some take a lot of time to do it. This fact (known and discovered previously by others) has a profound consequence in the way information spreads:

1. When information spreads “successfully”, in the sense that it propagates and reaches most of the collectivity (i.e. it surpasses the tipping-point), its propagation speed of is determined by the people that have higher activity.
2. However, when information reaches just a small fraction of the population (below the tipping-point), its propagation is controlled by those who take a lot of time to respond/forward and the spreading is very slow.

This phenomenon, as explained in our paper, has consequences for viral marketing, fads and hoaxes diffusion or opinion dynamics because the speed of their messages propagation depends strongly on the size of the sub-communities of very active and not-so active people. For example, in our campaigns (which were below the tipping-point yet successful from a viral marketing perspective), endogenous propagation of the commercial message lasted for months while the average time between getting the message and forwarding was only 1 day. We also found that messages do not “go viral”: They are viral because of the diffusion mechanism they use, but their spreading success largely depends on the social network propensity and heterogeneous behavior.

Finally, our work has some consequences for the way we model and understand human dynamics, since it shows that there is no such a thing as a typical time scale in the human dynamics. This is in sharp contrast with epidemic models, information diffusion models, etc. in which the heterogeneity in human activity and frequency is usually neglected, in favor of a more homogeneous picture of the activity of humans.

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