I don't believe they support SQL. They're somewhat more like pattern-matching on graphs. Most of their query language pages have compare/contrast examples with an equivalent SQL query. e.g. Neo4j's Cypher query language [1], or Apache Tinkerpop Gremlin (seriously) [2] used by Amazon Neptune.
I don't think the most popular ones support hypergraphs, although that sounds cool. I did see HypergraphDB [3] though! Need to read more about that.