Question: The [Neo4j Manual page on Constraints](http://neo4j.com/docs/stable/rest-api-schema-constraints.html) shows the `type` of each constraint as `UNIQUENESS`. Is there any other kind of constraint that can be applied?

Answer: 
Currently, in Neo4j **stable** version only `UNIQUENESS` constraint is supported.

But, in upcoming 2.3.0 release there will be new constraint added in Neo4j - `PROPERTY EXISTS`.

Example:

```
CREATE CONSTRAINT ON (book:Book) ASSERT exists(book.isbn)
CREATE CONSTRAINT ON ()-[like:LIKED]-() ASSERT exists(like.day)

```

Docs for new constraint can be found in 2.3.0-M03 release documentation - <http://neo4j.com/docs/2.3.0-M03/query-constraints.html>  

Also, you can checkout blog post by Neo where new constraints are presented - <http://neo4j.com/blog/neo4j-2-3-milestone-3-release/>

**Note:** new contraint will be available only for Enterprise version.
No, currently the only type of constraint available is uniqueness.