I found this interesting. What I would love to have seen, however, is a probe into the dynamics. You did a nice abstraction over time as you measured property X as age was varied. I would have loved to have seen the manner in which topics and ideas spread over your network.
For instance: If an event occurred in New York, say, how long would it have taken to spread to San Francisco? If there were no progression, topic times would center around the same time. This would indicate that people were getting their information from national, not local sources (e.g. the evening news), then talking about it on facebook. On the other hand, if a local topic was spread on facebook alone, we should see some sort of progression.
It's possible that this progression could take more interesting forms besides geolocation, but that might require a more extensive network. A simple experiment would work like this: A few thousand people who are not friends but have a similar interest (say an interest in Elizabeth Warren) post independently a video of her. This particular esoteric interest is unlikely to be valued a priori by their friends, but perhaps they are compelled to repost the information. What's the threshold of "esotericness" such that it won't "go viral?" Is there a way to predict virality as a function of how popular it is to begin with? Is there no actual progression across the network, but rather a small bump in topic expression, until it is picked up by larger media sources at which point the entire network is inundated with people reposting Elizabeth Warren recaps from HuffPo et al?
The reason this is interesting is that it sheds insight into the role of social networks: are we fundamentally disposed toward central sources like the NYTimes, or is facebook a fundamental sharing mechanism? That is, do I post on facebook just to have my views expressed, validated, and challenged, so that they might change the world over a few years? Or do I post on facebook to have my views propagate across the world much more quickly?
Finally, a question: How did you estimate the power law? I know how difficult it is to do this (e.g. not linear regression on a log-log scale). Did you compare the power law fit to other, similar distributions, like lognormal? Preferential attachment is indeed a beautiful theoretical result, because it implies the existence of power law degree distributions. Unfortunately, many networks are not as well represented by power laws as by alternative distributions, which casts doubt on the preferential attachment hypothesis as is. (Also, many sampling methods give rise to fictive power laws). That said, a fat tail can still be interesting.
In any case, this is a beautiful piece of work.