in a 14 GB database I have a few CITES relationships:
MATCH p=()-[r:CITES]->() RETURN count(r)
91
However, when I run
MATCH ()-[r:CITES]-() RETURN count(r)
it loads forever and eventually crashes with a browser window reload (neo4j desktop)
You can see the differences in how each of those queries will execute if you prefix each query with EXPLAIN.
The pattern used for the first query is such that the planner will find that count in the counts store, a transactionally updated store of counts of various things. This is a fast constant time lookup.
The other pattern, when omitting the direction, will not use the count store lookup and will actually have to traverse the graph (starting from every node in the graph), and that will take a long time as your graph grows.
As for what this gives back, it should actually be twice the number of :CITIES relationships in your graph, since without the direction on the relationship, each individual relationship will be found twice, since the same path with the start and end nodes switched both fit the given pattern.