Answer
At least two computers in the set of six
-connected to the same number of others.
Work Step by Step
--Because there are six computers,
-the number of other computers a computer is connected to is an integer between 0 and 5, inclusive.
-However,
0 and 5 cannot both occur.
-To see this, note that if some computer is connected to no others, then no computer is connected to all five others, and if some computer is connected
to all five others,
-then no computer is connected to no others.
--Hence, by the pigeonhole principle, because there are at most
-five possibilities for the number of computers a computer is
-connected to, there are at least two computers in the set of six
-connected to the same number of others.
