I believe an interesting metric would be the ratio FC/AC, as it shows the propension to take part in collaborations.

Let's take an example with 3 countries (resp. institutions) A, B and C. Each has two authors noted A1, A2, B1, B2, C1, C2.

A1 and B1 publish together (AC +1, FC +0.5 each),
A2 and B2 publish together (AC +1, FC +0.5 each),
C1 and C2 publish together (AC +1, FC +1)

Country FC AC AC/FC
/Institution
----------------------------------
A 1 2 2
B 1 2 2
C 1 1 1

For an equal amount of work (1 paper), the ratio is double for countries (resp. institutions) with mixed teams (A,B).
For large number of publications, differences in the ratio AC/FC reveal habits about publishing with foreign countries (resp. different labs).