Everything from ideas to communicable diseases spread through social networks, so understanding the processes that enable and influence this spread has immense practical value, even if the research involves... Facebook apps like Farmville.

In recent years, such studies have been revolutionized by the availability of data from computer networks, derived from games and social sites, that provide a far more complete picture of network effects. In the latest study of this sort, a pair of researchers analyzed the installation of Facebook applications in order to determine the point at which social influences start, and they came up with a remarkably specific answer: 55 downloads a day.

Facebook applications range from popular games to trivial decorations, and a number of them have become wildly popular, ending up with millions of installations. From the authors' perspective, however, these are cultural goods that people choose to install based on their exposure to the apps—and, given that the apps generally aren't advertised, most of that exposure comes purely through a user's social network. During the period the study examines (summer of 2007), Facebook automatically sent application install announcements to a user's network, which ensured that a user's social network came into play.

Facebook's public APIs also provided the researchers with an opportunity to get complete information on application installs. In the roughly two months they tracked users, the researchers tracked over a million app installs. Only a handful of applications were skipped due to data corruption issues, so the authors feel they've avoided the problem of selection bias that frequently afflict real-world studies.

To gauge the impact of social interactions, the authors turned to the field of fluctuation scaling. In the specific analysis they performed, adding a Facebook app was modeled as a coin flip-like process. At any point, a given user has a chance of deciding to install the app. If no social influences are at play, the analysis will spit out a probability that looks precisely like a coin-flip: 0.5. As social influences become increasingly important, that value will climb towards 1.0.

Below a certain level of download activity, social influences were minimal; the analysis returned a value of 0.55. The authors claim that, as far as they can tell, this distinct phase of non-social driven adoption had never been detected in any studies of network effects. They ascribe its previous invisibility to the fact that no other studies had complete access to all the relevant data; previously, these low-profile items were so hard to find, they didn't end up getting included in earlier work.

At a very specific point, however, a transition takes place. Once an app becomes popular enough, social forces kick in and the correlations among user downloads rise to 0.85. The transition takes place at a remarkably specific point: 55 installs a day. Once social influences kick in, that 0.85 figure stays in effect over two orders of magnitude, until the rate of downloading starts to tail off. To the authors, this suggests that social influences act as a binary, all-or-nothing influence.

The impact of social networks was independent of whether the app itself included a social component. So, a game that allowed friends to play against each other displayed similar dynamics to one that (in the authors' example) put a virtual lava lamp on your wall.

Not having seen anything like this before, the authors don't appear to know what to make of it. The discussion simply suggests that it's an inherent feature of social networks, and they don't even try to explain it. Until we have either an explanation or replication in other systems, however, it seems premature to conclude that these dynamics are an inherent feature of these networks.

PNAS, 2010. DOI: 10.1073/pnas.0914572107 (About DOIs).