Empirical studies on network equilibria There have been a number of papers in the literature (pioneered by Sanjeev Goyal, Jackson, Kranton, amongst others) emphasising the role and importance of network structure in economics, the equilibrium arising therein and the relationship between the topology and other graph properties and the equilibrium.

Such networks arise in a number of cases, for example, research collaboration, social networks, crime networks, etc. My question is what published empirical studies have tested the hypothesis presented by the theory? Do such studies also find that the graph properties are critical, as predicted by the theory? Or is network effects in economics a theory-only area?
Because the notion of pairwise stability is so important in the theory of network formation and equilibrium, there has been a few attempts to test it in experimental setups. I know at least two papers:


Myopic or farsighted? An experiment on network formation, by Georg KIRCHSTEIGER1, Marco MANTOVANI, Ana MAULEON and Vincent VANNETELBOSCH.
Departures from Best Response in Market-like Link Formation: An experimental study, by Margherita Comola and Marcel Fafchamps.


The first is a discussion paper. A word of warning regarding the second : the version of the paper that is linked is very much a draft. You might want to have a look to get an idea of what the authors plan on doing, but don't rely on it too much. I attended a talk where Fafchamps presented the paper this week, and he told us that they initially got the wrong data from their experiment. They only realized it rather recently and had to revise the whole paper. Because the linked draft is from February 2014, there are chances it is still based on the the old data (I did not read it).

For some field experiments on networks in development economics, you might want to have a look at other papers by Fafchamps : 
http://web.stanford.edu/~fafchamp/index.html. I am not sure these explicitly test equilibrium concepts though, but they might.