Relation among objects can be connected with at least one object feature, and a feature can describe one or more objects. Object relation with feature set form an undirected multigraph which can be represented as hypergraph. In our previous work, we developed adjaceny hyperedges matrix which are hypergraph model representing undirected multigraph so that we can identify the type of the object connection. In partial similar object collection, there may exist composite object relation, which is a relation among objects satisfying proper superset operation based on the set of object feature. Composite object relation is one form of abstraction (higher level) relation among objects. In composite object relation, each proper superset object has direct connection in the form of transitive path into objects in its own subset, and also form transitive closure. In this paper, we propose object connection algorithm and composite object relationship algorithm. The Objective of the first algorithm is to determine a collection objects dataset which is totally different, partially similar, or identical objects. The objective of the second algorithm is to identify composite objects relationship in a collection of objects, also to construct the objects that form connection as partially order set. Our experiments support our proposed algorithms.