According to the Neo4j data visualisation guide there is a possibility to set the parameter resultDataContents to "graph". ( https://neo4j.com/developer/guide-data-visualization/ Neo4j documentation for "resultDataContents")
This is exactly what I need for my application. Any idea how to do that with graphaware/neo4j-php-client, since I am not able to find it in documentation?
You can't. This format has been removed in v4 of the client due to its verbosity making the json body too large.
Also, chances are high that in v5 http will be removed from the client and focus on bolt only.
You can still issue cypher statements using pure curl or an abstraction layer as Guzzle. Or you can also create a wrapper that will create a graph representation based on the Result received from a Cypher query.