I think integration is definitely a cultural thing, since in my anecdotal experience, the level of integration seems to vary wildly with country of origin.

When I was in grad school, the Chinese students formed their own secret society to the extent that non-Chinese might never even know their name. Indians also had a secret society, but unlike most of the Chinese, they individually interacted with the outside world. Israelis, Russians, Koreans and various flavors of African all integrated more or less completely with the outside world.

In concrete terms, Chinese math students joined the Chinese soccer team and had Chinese advisers. Indians had secret Indian parties, but they played on the Math soccer team. Russians invited people of every nationality to the Russian vodka drinking parties.