In The curl of graphs and networks (Gustafson and Haray, 1984) it is claimed to be shown that any digraph $G$ can be decomposed as the sum of three graphs $U_1 + U_2 + U_3$, where $U_1$ is divergence-free, $U_2$ is curl-free and $U_3$ is both curl and divergence free.
However I am having a hard time understanding the proposed definitions for curl and divergence, and the decomposition.
It would be immensely helpful if somebody could help me decipher the paper by providing an example of a digraph decomposition.
For example, how could one decompose the following weighted digraph?