Enrico,

You are correct that the gPPI is not symmetrical. A few possible reasons are: (1) The deconvolution process; (2) A might influence B, but B might not influence A; (3) difference in neurovascular coupling; (4) differences in the timing of the neural activity or BOLD signal. For example, the activity in B is due to the task effect plus some influence from A, while the activity in A is purely due to activity from the task. There will likely be some residual correlations in actual data, which directionality can't be determined from the results. However, if you had the anatomical pathways, you could then infer direction.

For graph theory, you generally use the entire row, not just the upper or lower triangle.

There is no clear consensus as to whether you should use the top or bottom triangle or to average the top and bottom triangle. Keep in mind that if you change the order of the seeds, then the upper and lower triangles would change. For example, if you switch the top and bottom rows, then most of the matrix stays the same, but the outside rows and columns will change.

To complicate matters further with gPPI, you might have 3 or more conditions, so it is unclear, unless you are using the difference of only 2 conditions, how to apply graph theory to multiple values for each edge.

Hope this doesn't confuse you too much and hopefully it will generate some discussion about how to apply graph theory to PPI.