如果我在拓扑上对DAG进行排序，我可以减少邻接矩阵的一半吗？

I think I have understood a particular situation as described below, but I lack the theoretical knowledge to conduct a proof and I couldn't find any source that mentions it. If my understanding is correct, I can save half the space on my adjacency matrix, if it isn't I'm likely to have pretty weird bugs. So I'd like to be sure, and I'd appreciate if someone with a more solid background could review my reasoning.I think I have understood a particular situatio