For example, take the network below:

A -> B 5

C -> D 8

B -> E 4

D -> B 5

I'd like to sum all input flows (or upstream flows) for each edge so that the edges have an accumulated value, eg

A -> B 5

C -> D 8

B -> E 22 (4+13+5)

D -> B 13 (5+8)

If anyone has any suggestion on how to do this in either R or QGIS then that would be much appreciated!

Thanks

Adam