I'm having the same issues and found this question among others. From my research I cannot agree with this answer completely, so I felt I should point some things out, here.
Just to clarify: a graph database may seem structurally different from a relational or time series database, but it is possible to build Cypher queries that basically return graph data as tables with proper columns as it would be with any other supported data source. Therefore this sentence of the above mentioned answer:
So what you want to do is just not possible.
is not absolutely true, I'd say.
The actual problem is, there is no datasource plugin for Neo4j available at the moment. You would need to implement one on your own, which will be a lot of work (as far as I can see), but I suspect it to be possible. For me at least, this will be too much work to do, so I won't use any approach to read data directly from Neo4j into Grafana.
As a (possibly dirty) workaround (in my case), a service will regularly copy relevant portions of the Neo4j graph into a relational database (or a time series database, if the data model is sufficiently simple for that), which Grafana is aware of (see datasource plugins), so I can query it from there. This is basically the replication idea also given in the above mentioned answer. In this case you obviously end up with at least 2 different database systems and an additional service, which is not so insanely great, but at the moment it seems to be the quickest way to resolve the problem with the missing datasource plugin. Maybe this is applicable in your case, too.