# Euclidean Distance

Euclidean distance measures the straight line distance between two points in n-dimensional space. The algorithm takes two vectors denoted by `ListAccum` and returns the Euclidean distance between them.

## Notes

This algorithm is implemented as a user-defined function. You need to follow the steps in Add a User-Defined Function to add the function to GSQL. After adding the function, you can call it in any GSQL query in the same way as a built-in GSQL function.

## Specifications

`tg_euclidean_distance_accum(A, B)`

### Parameters

Name Description Data type

`A`

An n-dimensional vector denoted by a `ListAccum` of length `n`

`ListAccum<INT/UINT/FLOAT/DOUBLE>`

`B`

An n-dimensional vector denoted by a `ListAccum` of length `n`

`ListAccum<INT/UINT/FLOAT/DOUBLE>`

### Output

The Euclidean distance between the two vectors.

### Time complexity

The algorithm has a complexity of O(n), where n is the number of dimensions of the vectors.

## Example

• Query

• Result

``````CREATE QUERY euclidean_example() FOR GRAPH social {
ListAccum<INT> @@a = [1, 2, 3];
ListAccum<INT> @@b = [4, 5, 6];
double distance = tg_euclidean_distance_accum(@@a, @@b);
PRINT distance;
}``````
``````{
"distance": 5.19615
}``````