Atlantic Cities includes this "brainiest cities" ranking. They actually mean metropolitan areas and they refer to Richard Florida's work. But getting the spatial units right matters.
This time, "density" is not mentioned as the key ingredient, although Florida evokes the importance of population density in much of his work. I have noted several times at this blog that metropolitan area densities (which almost everyone uses) are a lousy proxy. Aggregation causes problems, in some cases big problems.
Mr. Demographia refers me to 2000 urbanized area density data for 461 U.S. areas. Their average density was 2163 people per square mile, with standard deviation of 878 and coefficient of variation of 0.41.
Also for 2000, we can get PUMS area (PUMA) densities for each of the metropolitan areas. The Los Angeles metro area can be cut up into 111 of them. Their average 2000 population density was 6857 people per square mile, with standard deviation of of 5869 and coefficient of variation of 0.86.
Here, there is more density variation within than between metropolitan areas.