Edge definitions for a graph database

We will be receiving data that conveys the following information:

Object1 **is related to** Object2
Object1 **has relationship ID R1** with Object2

Both Object1 and Object2 are further related to arbitrary number of objects. The 'axis' of is related to will be used to answer a query, such as, 'Who is related to Object1', recursively. And, the 'axis' of has relationship ID R1 will be used to answer a query, such as, 'Who are the parties to the relationship ID R1'.

I have introductory knowledge in Neo4j and the question is not so much about code that does CRUD on such a graph. It seems that, number of edges should be equal to types of queries that (can be foreseen) will run between two vertices.

Can you please guide me a design pattern to define this database?