I’m so glad this thread was resurrected because I was just about to post the exact same request 
I think the ability to add properties to the relationships is very useful and important as well. One of the easiest examples I can think of are contacts/people entities. It is currently possible to define a many-to-many relationship between a contact entity and itself to define “related people”. However, it is not possible to say how two contacts are related to each other. That is to say, are they co-workers, family, friends, etc.
This will also be a good solution to another issue I raised earlier regarding denoting if an entity of one type is the same as another entity of a different type (semantic same as relation).
The example of parts is also very instructive as I can see it extended to area of physical asset management to define parts and assemblies to allow managing of maintenance records, etc.
An implementation of this should allow for one and two way edges that can ideally allow you to define a relationship between a brother and a sister very precisely (i.e. instead of a generic sibling relationship, allow to you same John is Mary’s brother and Mary is John’s sister). It would be also fantastic to be able to define these relationship types in a systematic way using a thesaurus/defined vocabulary that supports import/export. Finally, ability to query/search/filter based on this would be needed to make this useful at scale.
I am not sure if the underlying datastore for Fibery is graph-enabled, but I think having graph functionality is going to be critical long term.