If the diagonal elements of the adjacency matrix are not equal to zero, then for example there could be information flow from the x-axis of scout-1 to the y-axis of scout-1.
Indeed. Since the signals are different along the X and Y directions, we compute a non-zero value.
However, I personally believe that the diagonal elements of the adjacency matrix should be equal to zero, since there is no information flow from a scout to itself regardless of the scout's source direction.
This is only a convention. If you don't want to see these non-zero diagonals, you can decide to ignore them. Alternatively, if they are really bothering you in the displays, you can explicitly set them to zero. This would require writing a script to edit the connectivity matrix saved in the TF field.
https://neuroimage.usc.edu/brainstorm/Tutorials/Connectivity#On_the_hard_drive
I should note that when there are constrained sources, the diagonal elements of the adjacency matrix in Brainstorm are set equal to zero. Shouldn't that also be true for the unconstrained sources?
What do you believe?
I don't believe in anything here. I just explained why you observe zero diagonals in the constrained case, and non-zero in the unconstrained case. At the moment, we don't have a better way to estimate the connectivity from unconstrained source maps. If this is not satisfying, as I already mentioned, you can use a constrained model instead: simpler data structures, simpler algorithms, possible minor loss in spatial accuracy (or fake impression of precision).