I want to do a graph classification task. Those graphs are directed, and their edges have features. I knew little about graph representation methods, but I did some research, and find most of the works for graph classification seem to be based on undirected graphs. So is there a way to encode this kind of graph? Or any suggestions to encode this kind of graph?
Most methods generalize naturally to undirected graphs, some of the simple examples are GCN , GIN  and GAT . There are more sophisticated methods, but depending on the task, often they don't perform drastically different .
It really depends on you specific task what works best for you. You might want to try some different architectures and I'd start with the GCN or GIN. You could opt for a nice library that allows benchmarking all the different architectures quite quickly like deep graph library (DGL) or Torch-Geometric.