RJ,
>> the results of a paired t-test
I assume that you're comparing two groups. So, it would be a conventional two-sample (not paired) t-test.
>> The results look off in the sense that connectivity shows in regions like the ventricles, cerebellum, and even outside the brain. Is this correct?
The results in some of those regions you mentioned are likely random noise, especially when sample sizes are not large.
Gang