Remove Vertex
Deleting vertices with associated edges is currently not handled via C8QL while the graph management interface and the REST API offer a vertex deletion functionality.
However, as shown in this example based on the knows_graph, a query for this use case can be created.

When deleting vertex eve from the graph, we also want the edges eve -> alice and eve -> bob to be removed.
The involved graph and its only edge collection has to be known. In this case it is the graph knows_graph and the edge collection knows.
This query will delete eve with its adjacent edges:
LET edgeKeys = (FOR v, e IN 1..1 ANY 'persons/eve' GRAPH 'knows_graph' RETURN e._key)
LET r = (FOR key IN edgeKeys REMOVE key IN knows) 
REMOVE 'eve' IN persons
This query executed several actions:
- use a graph traversal of depth 1 to get the 
_keyof eve's adjacent edges - remove all of these edges from the 
knowscollection - remove vertex eve from the 
personscollection 
The following query shows a different design to achieve the same result:
LET edgeKeys = (FOR v, e IN 1..1 ANY 'persons/eve' GRAPH 'knows_graph'
            REMOVE e._key IN knows)
REMOVE 'eve' IN persons
The query has to be adjusted to match a graph with multiple vertex/edge collections.
For example, the city graph contains several vertex collections - germanCity and frenchCity and several edge collections -  french / german / international Highway.

To delete city Berlin all edge collections french / german / international Highway have to be considered. The REMOVE operation has to be applied on all edge collections with OPTIONS { ignoreErrors: true }. Not using this option will stop the query whenever a non existing key should be removed in a collection.
LET edgeKeys = (FOR v, e IN 1..1 ANY 'germanCity/Berlin' GRAPH 'routeplanner' RETURN e._key)
LET r = (FOR key IN edgeKeys REMOVE key IN internationalHighway
        OPTIONS { ignoreErrors: true } REMOVE key IN germanHighway
        OPTIONS { ignoreErrors: true } REMOVE key IN frenchHighway
        OPTIONS { ignoreErrors: true }) 
REMOVE 'Berlin' IN germanCity