Are there detectable differences in brain activity when thinking about people of different degrees of closeness?
This domain is extensively explored as a "self-referential processing"
The largest difference between self vs. non-self is higher activation for self-relatad activation of medial posterior and frontal regions 
(e.g., https://davidcjohnson.files.wordpress.com/2011/04/self-ref-vs-valence.png?w=694&amp;zoom=2)
Those two regions are part of the Default Mode Network.

One of the most prominent researchers is Georg Northoff: 

https://scholar.google.ca/citations?user=-w-9zOQAAAAJ&amp;hl=en
You can check his reviews and found references to many additional studies.