Fledgling cities are finding that trying to reinvent themselves after losing large swaths of industry sectors takes one critical ingredient in order for the transformation to work: College students.

Take Dayton, Ohio, for instance. This once thriving metropolitan city has only 24 percent of adult residents with four-year degrees, well below the average of 32 percent for U.S. metro areas, according to Brookings Institution analysis, and sitting on one side of a growing divide among U.S. cities, in which a small number of metro areas vacuum up a large number of college graduates and the rest are struggling to keep those they have.

The winners are metro areas like Raleigh, N.C., San Francisco and Stamford, Comm., where more than 40 percent of the population has a college degree. The Raleigh area has a booming technology sector and several major research universities; San Francisco has been a magnet for college graduates for decades; and metropolitan Stamford draws highly educated workers from white-collar professions in New York.

The divide shows signs that college graduates gravitate to places with many other college graduates and the atmosphere that creates.

"This is one of the most important developments in the recent economic history of this country," said Enrico Moretti, an economist at the University of California, Berkeley, who recently published a book on the topic, "The New Geography of Jobs," told the New York Times.

College students tend to have longer life expectancies, higher household incomes, lower divorce rates and fewer single-parent families than those with less education, and cities where they cluster tend to exhibit those patterns strongly.