The trading of LinkedIn shares on private exchanges puts its value at about $3 billion, well short of Groupon at $6 billion or Facebook at $50 billion. The reason is simple: The professional social network is a tiny company.

The S1 that LinkedIn filed with the SEC on Thursday as one of the steps to an initial public offering describes a company that's growing but has only modest revenue. For the first three quarters of 2010, sales were $161 million. LinkedIn made only $1.8 million because most of its costs soared.

The company also listed a number of business risks, the most important of which is that it may not be able to "successfully compete with other companies that are currently in, or may in the future enter, the online professional network space." The largest competitor could eventually be Facebook, which can mimic most LinkedIn features and has a much larger member base.

A number of analysts have said the LinkedIn IPO will test the waters for public offerings by other social networks. That's not necessarily so. LinkedIn may just be too small to be a real player in the sector.