I am new to this and I wanted to ask, when should we invite co-authors and when should we write alone?
Can somebody invite a co-author to join an article about a project solely done by the main author? Perhaps for the purposes of gaining more experience in publishing,building professional relationships?

What are the rules?

Thank you

You can add a co-author whenever you want but they have to be contributing something substantial to the project ie design, data collection, writing, supervision etc.

Generally people don't add co-authors after data collection has finished in order to build a relationship - it would be more common to do this at project design stage.

Unless you were going to ask them to contribute with some specific expertise - e.g., to do the statistical analysis/part of it.

Absolutely. But I am assuming this person is in between Masters and PhD or some such situation given that they are the sole author of their work. What is the situation Artmate?