Postgres can handle a lot of generic 'graph' use cases. Unless you have very specialized needs, focusing on complex algorithms and very big network data, it's not at all clear that you'll need more than that.
My use case a few years ago was such that _every_ dedicated graph engine I tried would just OOM on the test set of ~10M nodes, which I attributed to insufficient pruning. Postgres was able to handle it, and still worked on the production set of ~1.5B nodes. The SQL took some tuning, and wasn't _pretty_, but it did _work_ where nothing else did...