Reverse order of summation for function on edges of a graph

Question

Let $V$ be the vertices of a graph and $N: V \to 2^V$ be the neighbor function for the graph. When is it true that

$$ \sum_{i \in V} \sum_{j \in N(i)} f(i,j) = \sum_{i \in V} \sum_{j \in N(i)} f(j,i) $$

?

Answer 1

When the graph is undirected. Then each of the sums equals $$\sum\{f(i,j):(i,j)\in V\times V, i\mbox{ is adjacent to }j \}.$$