I just can't think of one. Almost any "natural" monopoly (roads, healthcare, power grid, network cable, etc) I think should be done by local government, not private business, because structural aspects of society aren't effective platforms for competition if they just supply the foundations to build markets upon.
Actually, I just thought of one - maybe agriculture. While it is structural, it isn't an inherent infrastructure because it has specialized purpose. The post green revolution has demonstrated (though I imagine it is the result of regulation this happens) that megafarms are the most efficient way to organize modern farming. This naturally leads to a few big players because the cost of equipment to properly maximize productivity of land has high expenses (though they aren't at a comparable scale to say, a road network, or laying fiber in a city - one tractor, plow, tiller, etc plus the seed, silos, barns, etc, but these are tools to maximize productivity, not infrastructure).
It might be the product of land ownership and zoning, but I'm only familiar with my local zoning code, which has a large Mennonite population, so most of the farmland in the region is restricted from being sold for other purposes. The midwest is a much different story that I'm not familiar with.
That is all I'm saying. If you agree with that, we aren't arguing anything.
... social networking?
I don't think in a decade the closed social networks will last, for the interopt reason. The value proposition of a common platform of profiles is too strong long run not to take over.
If the capital costs are low, this isn't as much of problem. With some understanding investors and creditors an entrant can match the incumbent.
But when you have to build millions or billions of dollars of stuff just to get started, that's much harder to arrange.