Custom Access Permissions
Just use the Group module, and create a content type like "Connected Users". And then create a "group" for each user (using something like the user's name as its label), of group type "Connected Users".

Tune the permissions which come with the Group module (which are different from standard Drupal permissions!) to fit your needs.

Possibly you also want to use all sorts of integrations with modules such as the Rules module or the Views module (the Group module is entirely entity based, so those kind of integrations or virtually unlimited).

Voilà ...

PS: This answer applies for either Drupal 7, or Drupal 8.