Creating a data object relationship system

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I would like to store an object that has a name and some attribute and any kind of database and have another that that document relationship between between them

Let say this

Object A Object B Object C Object D

A is related to B A is related to D B is related to C

All relation have also attribute that give the relation order (uni (from,to) or (to,from) or bidrectional).

Then, I would like to do some query that will show me A is related to C by passing in B. A kind of path between 2 objects.

Kind of graph database like Neo4J

Thanks for your input

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Question is rather old but anyways:

The Neo4j documentation actually has an example that is very close to answering the question. http://docs.neo4j.org/chunked/stable/graph-algo-path-finding.html