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~~How do I find idependent sets in a dataset~~

How do I find independent sets in a dataset

I have a dataset of car bookings like this:
~~> car_id, user_id~~
>
~~> 1, 1~~
>
~~> 2, 1~~
>
~~> 1, 2~~
>
~~> 3, 3~~
>
~~> 1, 2~~
>
~~> 3, 3~~
In this dataset, two separate groups/sets of cars and users don't overlap: One group consists of two vehicles (1,2) and two users (1,2) the other group has only one car (3) and one user (3). The groups are independent and have no overlap in users or vehicles. Lines in the datasets can repeat.
~~Now I have a much bigger dataset with many thousand cars and users. What is the most elegant/fastest algorithm/data structure to find those disjunct groups?~~
This is an actual problem, not a homework exercise. :-) (I code in python or julia.)

I have a dataset of car bookings like this:
| car_id | user_id |
| ------ | ------- |
| 1 | 1 |
| 2 | 1 |
| 1 | 2 |
| 3 | 3 |
| 1 | 2 |
| 3 | 3 |
In this dataset, two separate groups/sets of cars and users don't overlap: One group consists of two vehicles (1,2) and two users (1,2) the other group has only one car (3) and one user (3). The groups are independent and have no overlap in users or vehicles. Lines in the datasets can repeat.
Now I have a much bigger dataset with many thousands of cars and users. What is the most elegant/fastest algorithm/data structure to find those disjunct groups?
I code in Python or Julia.

algorithms julia python-3

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