Neo4j had a great demo, load up the IMDB database, then solve six degrees of Kevin Bacon with SQL vs with Cypher. The Cypher is a one liner that runs immediately, the SQL is a mess that almost brings down the database.
For certain types of queries, recommendation engines being a prime example, graph databases are awesome.
For one, Neo4j is an implementation and SQL is not. As for clarity, SQL, although by far the most widespread query language is a shitty language in many respects... again a separate issue from the relational model.
In any case you’re conflating a storage engine and a query language. There’s no reason an RDBMS implementation cannot be tuned for graphs, and there is no inherent lack of generality in the relational model which seems to be the prior posters claim. Whether Neo4j is a useful piece of software is a different topic.
For certain types of queries, recommendation engines being a prime example, graph databases are awesome.