What is community: 

Roots: etymological. The origin of the word "community" comes from the Latin munus, which means the gift, and cum, which means together, among each other. So community literally means to give among each other. 

It is embodied in spirit, action and human nature. Putting students in a group is not community, nor does it thrive if each person cannot freely imagine themselves giving and receiving. Confusing community with and organizational structure is somewhat fatal.