This is not a circular reference.
It would be if emails would have a strong integrity relationship to invitations and invitations an independent strong integrity relationship back to emails (for example).
EDIT: regarding the design
As Hank Holterman points out the question is if your design is normalized to desired extent.
Assiming tables: primary keys such as
users: id
emails: id, users_id
invitations: id, users_id, emails_id
and assuming foreign keys on table_id fields and that no other constraints are placed on the tables (such for example only a part of a key being unique) then you have modelled the following:
- for each user there can be several e-mails and you can not have emails with no corresponding user record
- for each email there can be several invitations and you can not have invitations with no corresponding e-mail nor user record (note: from the above definition we can not know if the user_id refers to entry in emails or in users)
Now only you can say if those rules correspond to the ones from the real world situation that you are trying to model.
One way to look at the database design is - there is actually no wrong database design, you can almost always find data that would make something that looks like an error justified. That's why without taking both rules (in form of sentences) and the tables (E-R diagram, description of tables and relationships) it is impossible to say if there is a problem in design (though it is possible to give suggestions from personal experience).
To illustrate - the above note that it is not clear which table user_id refers to might seem easy to answer. And the common answer, considering that you said that every invitation has a mail, is that it should refer to user_id from the mail table.
Otherwise there could exist an invitation for which user_id recorded on the invitation and the user_id recorded for a mail are different.
Normally, this should make a red light labelled 'normalize your data' go flashing in your mind. But, often unspoken assumption here is that the email_id determines the user_id, and that might not be true(!).
This depends on the semantics of your data (the predicate of each table) - for example if you are trying to model a situation where it is possible to send invitation to one person, and receive an e-mail reply from another person (for example inviting people through secretary and receiving direct replies), then the red light switches off and all is fine - that is what really happened and that is what you are going to allow for in your design.