ER isomorphisms and uniqueness conditions

Given a collection of entity types (database tables) there is usually more than one way to model their associations. Consequently, two data models may appear different while essentially they are the same. To simplify the task of comparing data models, necessary and sufficient conditions are defined for a collection of entity types to have a unique Entity Relationship Diagram (ERD). The sufficient conditions for uniqueness are translated into modeling constraints that can be easily used to build an Entity-Relationship model. It is shown that the constraints do not prevent the representation of information requirements except for rare types of involuted relationships that seldom appear in the real world. Additionally, sufficient conditions are established for two ERDs to be isomorphic. All of this is done under the assumption that relationships are degree 2 or less. The results are extended to models containing relationships of higher degree.