# CardinalityBoundaryAdherence

If there are two connected tables, the *cardinality* refers to the number of connections between a parent row and the child. This metric measures whether the cardinality of the synthetic data follows the min/max values as determined by the real data.

## Data Compatibility

* **Foreign Key** : This metric is meant for foreign keys
* **Primary Key** : This metric validates that the foreign key values are found in the primary key

This metric ignores missing values in the foreign key.

## Score

* **(best) 1.0**: The cardinality of the synthetic data is always in the min/max bounds as determined by the real data.
* **(worst) 0.0**: The cardinality of the synthetic data is never whether the min/max bounds.

The example below shows a distribution of cardinality values for real and synthetic data (black and green, respectively). The real data has a min cardinality of 0 and a max of 4. Since the synthetic data is contained within these bounds, the score is 1.0.

<figure><img src="https://2284413265-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FrNLha4DaPNwVJ930KhmB%2Fuploads%2FssNJ7NMzwhmuwTTwFbQX%2FCardinality%20Shape%20Similarity.png?alt=media&#x26;token=055d1b10-aac1-476c-a4de-bda89d8f040c" alt=""><figcaption></figcaption></figure>

## How does it work?

In a multi table setup, there is a parent and child table. The parent contains a primary key that uniquely identifies every row while the child contains a foreign key that refers to a parent row. The foreign keys may repeat, as multiple children can reference the same parent.

<figure><img src="https://2284413265-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FrNLha4DaPNwVJ930KhmB%2Fuploads%2Fzgh0ueeuAcfMiZNH26B7%2Fsdmetrics-metrics-metrics-glossary-cardinality-shape-similarity_Mar%2010%202026.png?alt=media&#x26;token=d5318596-f927-4c76-9074-bc21c4e6ccbb" alt=""><figcaption><p>The parent table contains primary keys while the child table has foreign keys that refers to them. Each parent row has a different number of children based on the references. For example, <code>User_00</code> has 1 child row, <code>User_01</code> has 2, <code>user_02</code> has 0 and so on.</p></figcaption></figure>

This metric computes the cardinality \[1] of each parent row. That is, it computes the number of children that each parent rows has so that each parent row is associated with an integer ≥ 0.  This yields a set of values for both the real data, *r*, and the synthetic data, *s*. The score is based on the proportion of rows in *s* that follow the min/max boundary.

$$
score = \frac{| s, s\ge min(r) \text{ and } s\le max(r)|}{| s|}
$$

## **Usage**

{% hint style="success" %}
**Recommended Usage:** The [Diagnostic Report ](https://docs.sdv.dev/sdmetrics/data-metrics/diagnostic/diagnostic-report)applies this metric to applicable columns.
{% endhint %}

To manually apply this metric, access the `column_pairs` module and use the `compute` method.

```python
from sdmetrics.column_pairs import CardinalityBoundaryAdherence

CardinalityBoundaryAdherence.compute(
    real_data=(real_table[['primary_key']], real_table[['foreign_key']]),
    synthetic_data=(synthetic_table[['primary_key']], synthetic_table[['foreign_key']])
)
```

**Parameters**

* (required) `real_data`: A tuple of 2 pandas.DataFrame objects. The first represents the primary key of the real data and the second represents the foreign key. *For a composite key, provide multiple columns in each pandas.DataFrame object.*
* (required) `synthetic_data`: A tuple of pandas.DataFrame objects. The first represents the primary key of the synthetic data and the second represents the foreign key. *For a composite key, provide multiple columns in each pandas.DataFrame object.*

## References

\[1] <https://en.wikipedia.org/wiki/Cardinality_(data_modeling)>


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