Are social networks typically good expanders? I am interested in the combinatorial properties of social networks as graphs. People have looked at things such as the distribution of the degrees, the clustering coefficient and the compressibility of these graphs. One basic question is: Are these graphs typically good expander graphs?

Has anyone checked, say, the facebook graph's spectral gap? Or the spectral gap of other large real-world networks? I am hoping that someone can point me in the right direction to learn about this topic.
Social networks typically have many vertices with just one or two connections to the rest of the graph. Such vertices will typically lead to a bad spectral gap. 

What you could hope for is good vertex/edge expansion for sufficiently large sets. However, if you have tightly-knit communities within the network, then again you would expect low expansion. 

I'm not sure if it quite answers your question, but the following empirical paper looks at exactly expansion-like properties in social networks. The answer seems to vary from network to network.
http://fragkiskos.me/papers/expansion_SNSMW11.pdf

I'm sure there is other work out there along these lines, possibly disguised using alternate terminology ("community structure", cut sizes, etc).