# association end multiplicity

Association end multiplicity defines the number of entity type instances that can be at one end of an association.

An association end multiplicity can have one of the following values:

• one (1): Indicates that exactly one entity type instance exists at the association end.

• zero or one (0..1): Indicates that zero or one entity type instances exist at the association end.

• many (*): Indicates that zero, one, or more entity type instances exist at the association end.

An association is often characterized by its association end multiplicities. For example, if the ends of an association have multiplicities one (1) and many (*), the association is called a one-to-many association. In the example below, the PublishedBy association is a one-to-many association (a publisher publishes many books and a book is published by one publisher). The WrittenBy association is a many-to-many association (a book can have multiple authors and an author can write multiple books).

## Example

The diagram below shows a conceptual model with two associations: PublishedBy and WrittenBy. The association ends for the PublishedBy association are the Book and Publisher entity types. The multiplicity of the Publisher end is one (1) and the multiplicity of the Book end is many (*).

The ADO.NET Entity Framework uses a domain-specific language (DSL) called conceptual schema definition language (CSDL) to define conceptual models. The following CSDL defines the PublishedBy association shown in the diagram above:

<Association Name="PublishedBy">
<End Type="BooksModel.Book" Role="Book" Multiplicity="*" />
<End Type="BooksModel.Publisher" Role="Publisher" Multiplicity="1" />
</Association>