API - Add Primary Contact to Company Account

Hello,

We have a custom built Application Form which allows our Members to essentially setup to 'Parties' at once, one for their Personal details (Main Contact) and one for the Company Party.

Everything is working great but I'm really struggling to identify how to link the two records together.

In our older setups which don't use the API, there seems to be 2 areas that cause the link:

Name.CO_ID (in the database) contains the ID of the company record within the Primary Contacts record.

There also seems to be a line within a 'Relationships' table within the database which I think is what provides the Primary Contact the ability to interact with the Company Record.

Is it possible to link the two create Parties via the REST Api?

Many thanks,
Alex.