Six cities have at least twice as many college graduates per square mile:
San Francisco 7,031
New York City 6,357
Washington, D.C. 3,395
Richard Florida, a regional development economist (known for his "Creative Class" concept) who compiled the data, thinks that this matters:
[S]pillovers in knowledge that result from talent-clustering are the main cause of economic growth. Well-educated professionals and creative workers who live together in dense ecosystems, interacting directly, generate ideas and turn them into products and services faster than talented people in other places can. There is no evidence that globalization or the Internet has changed that.
If Professor Florida is right, it is bad news for most of the Midwest (except Minneapolis-St. Paul and Chicago), the South (except Atlanta and Miami), and is bad news for Arizona, Nevada and Utah. But, it is good news for Denver, the major coastal cities and a handful of major urban inland cities (listed above). It is also probably good news for small towns that are homes to colleges or hospitals.
It also suggests that pro-infill zoning policies may actually seriously promote economic growth.
There are, however, issues with how you calculate the slippery concept in a meaningful way, because the way that one draws urban boundaries greatly impacts population density. For example, New York City would be no less vibrant if its boundaries also included 1000 square miles of water adjacent to it, nor would Denver be less vibrant if it also included 1,000 square miles of virtually uninhabited farmland, despite the dramatic change this would cause to the statistics.
International urban geographers often look a small areas (e.g. square kilometers), define the "defacto city" based on the area with high population density, and then look at the total population of the city. This is not an easy thing to do with publicly available statistics, however, and poses cause and effect loop issues when you are trying to measure the impact of [educated] population density, if not done carefully.