Veterans of the U.S. military tend to be underrepresented at the nation's selective four-year institutions and overrepresented at community colleges and for-profit institutions, according to a new report from Ithaka S+R.

Student veterans accounted for about 5 percent of all undergraduate and graduate student enrollment in 2016, the report found, but represented 13 percent of students enrolled at for-profits. And nearly one in three veterans who receive GI Bill benefits attend for-profits.

In contrast, veterans are half as likely as their peers to enroll in colleges with high graduation rates. For example, the report said just 10 percent of veterans who receive the GI Bill attend institutions with a graduation rate of at least 70 percent (using graduation rates based on 150 percent of the normal time to degree).

As Inside Higher Ed columnist Wick Sloane has written often, few veterans attend highly selective colleges. Just 722 undergraduate veterans were enrolled at the nation's 36 most selective private institutions, according to the report.

"Relatively few veterans are enrolled at the highest graduation-rate and wealthiest colleges and universities today, for a variety of reasons," the report said. "But veterans will have the greatest chance of succeeding and earning a degree if they go to the most selective school possible given their potential. It seems incumbent on us as a nation to make sure that veterans have access to the educational opportunities for which they are ready when they are ready."