Aggregation refers to combining the assembled parts of a single part. In terms of Object Management Technology, aggregation may be defined as representing the object classes as a hierarchy such that the object class at the root may only be visualized by aggregating other object classes in the hierarchy or in otherwords aggregation relates an assembled class and a component class.

Now, aggregation is transitive as well as antisymmetric. i.e. if A is a part of B, B is a part of C, then A is a part of C (transitivity); if A is a part of B then B is not a part of A (antisymmetric). Consider the object diagram of a word processing application –

The object diagram is such that sentences are aggregated to paragraphs which are then aggregated to document. Now, sentence is a part of paragraph, paragraph is a part of document, then sentence is also a part of document. This proves transitivity. Sentence is a part of paragraph, but paragraph is not a part of sentence. This proves Anti-symmetricity.

An example of Aggregation

We shall represent the object diagram of a multilevel hierarchical aggregation for the representation of a microcomputer. A microcomputer has 1 or > 1 monitor/s, a system , a keyboard and an optional mouse. Now, the system class may further contain a chasis, a CPU or a combination of RAM and an optional fan. The corresponding object diagram is a shown –Microcomputer