Real computer networks at what layer?  The Internet is, at the AS level (arguably the topmost level), a small-world network with some extremely high-degree nodes.  As the layers get closer to actual wires, the graph becomes more linked to geography and less linked to the social layer (social is kind of the wrong word - is it really a social network when the entities being "friends" are multinational corporations?).  In the extreme case, a local ethernet is a logical tree that is (probably) a subgraph of the physical pattern of wire connections, and that pattern of wire connections is probably not too many wires more than a tree.

"Real computer networks" come in lots of flavors and layers.  Some of them look like social networks, some don't.  For more on this, I immodestly refer you to chapter 2 of my dissertation - http://home.manhattan.edu/~peter.boothe/thesis.pdf