In the relational data model, a superkey is any set of attributes that uniquely identifies each tuple of a relation. Because superkey values are unique, tuples with the same superkey value must also have the same non-key attribute values. That is, non-key attributes are functionally dependent on the superkey.

The set of all attributes is always a superkey (the trivial superkey). Tuples in a relation are by definition unique, with duplicates removed after each operation, so the set of all attributes is always uniquely valued for every tuple. A candidate key (or minimal superkey) is a superkey that can't be reduced to a simpler superkey by removing an attribute.

For example, in an employee schema with attributes <code>employeeID</code>, <code>name</code>, <code>job</code>, and <code>departmentID</code>, if <code>employeeID</code> values are unique then <code>employeeID</code> combined with any or all of the other attributes can uniquely identify tuples in the table. Each combination, {<code>employeeID</code>}, {<code>employeeID</code>, <code>name</code>}, {<code>employeeID</code>, <code>name</code>, <code>job</code>}, and so on is a superkey. {<code>employeeID</code>} is a candidate key, since no subset of its attributes is also a superkey. {<code>employeeID</code>, <code>name</code>, <code>job</code>, <code>departmentID</code>} is the trivial superkey.

If attribute set K is a superkey of relation R, then at all times it is the case that the projection of R over K has the same cardinality as R itself.

Example

{| class="wikitable"

|+ English Monarchs

|-

! Monarch Name

! Monarch Number

! Royal House

|-

| Edward

| II

| Plantagenet

|-

| Edward

| III

| Plantagenet

|-

| Richard

| III

| Plantagenet

|-

| Henry

| IV

| Lancaster

|}

First, list out all the sets of attributes:

:• {}

:• {Monarch Name} &nbsp;

:• {Monarch Number} &nbsp;

:• {Royal House}

:• {Monarch Name, Monarch Number}

:• {Monarch Name, Royal House}

:• {Monarch Number, Royal House}

:• {Monarch Name, Monarch Number, Royal House}

Second, eliminate all the sets which do not meet superkey's requirement. For example, {Monarch Name, Royal House} cannot be a superkey because for the same attribute values (Edward, Plantagenet), there are two distinct tuples:

  • (Edward, II, Plantagenet)
  • (Edward, III, Plantagenet)

Finally, after elimination, the remaining sets of attributes are the only possible superkeys in this example:

  • {Monarch Name, Monarch Number} — this is also the candidate key
  • {Monarch Name, Monarch Number, Royal House} — this is also the trivial superkey.

In reality, superkeys cannot be determined simply by examining one set of tuples in a relation. A superkey defines a functional dependency constraint of a relation schema which must hold for all possible instance relations of that relation schema.

See also

  • Alternate key
  • Candidate key
  • Compound key
  • Foreign key
  • Primary key

References

Further reading

  • Relation Database terms of reference, Keys: An overview of the different types of keys in an RDBMS