Arity: How Many Entities in a Relationship?

"Arity" refers to the number of entities involved in a relationship. Most relationships are binary, having two entities involved.

Some relationships are unary, i.e. they are reflexive or recursive, referring from one entity back to itself.

And other conceptual relationships involve more than two entities - three, four, or occasionally more.

Logical modeling reduces all relationships to binary form (unary is binary self-binary).

According to Codd90 (p. 477), "The major problem with the entity-relationship approach is that one person's entity is another person's relationship." Date95 (p.363) agrees , saying "[the ER approach] is seriously flawed because the very same object can quite legitimately be regarded as an entity by some users and a relationship by others.".

The Information Engineering (IE) methodology from James Martin reduces complex relationships to simple entity pairs. While classic Entity Relationship modeling provides for attributes on relationships, IE requires that any "relationship" which has either attributes of its own or other relationships attached to it must be simplified into the underlying entities pairs. For the same reason, PowerDesigner does not support "associative entities" as something different from any other entity; they are merely the resolution of complex relationships.

This is quite similar to the algorithmic mapping which the ORM method performs in transforming a "conceptual" model into a logical data model. Complex relationships can be described conceptually in a number of ways but they cannot be housed in current relational database structures.