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A contact is someone you wish to follow, a feature that was announced on June 15, 2004. As addressed in the FAQ, adding someone as a contact is a simple way to keep track of their contributions on the site. You can have up to 750 contacts. To add a contact, go to that person's profile page and click on the "Add user as a contact" link there. You can choose what your relationship is with this user, or leave that part blank.* This structure is based on based on the XHTML Friends Network (XFN) creator structure. Those relationship options are as follows:
friendship: contact, acquaintance, friend, none (either/or)
physical: met (yes/no)
professional: co-worker, colleague (yes/no)
geographical: co-resident, neighbor, none (either/or)
family: child, parent, sibling, spouse, kin, none (either/or)
romantic: muse, crush, date, sweetheart (yes/no)
When you add a user as a contact and set a relationship status, this information will be visible on your own user page as well as your usercontacts page. Contacts you have added are listed in your profile with the phrase "Links to", and people who have added you as a contact are listed under "Linked by".
When you are logged in and viewing MetaFilter.com in "standard" view, you can easily see some of the site actions of your contacts in your Contact Activity sidebar on the front page. You can see if they make a new post to MetaFilter or any sub-site and if that new post gets 12 or more favorites, make a comment that gets 12 or more favorites, get a "best answer" in AskMe, or add contacts. You can also see their activity on the My Contacts page, where you can also filter which activities you wish to appear on the Contact Activity sidebar. If you prefer, you can completely hide the Contact Activity sidebar, from the (hide) link at the top of the sidebar. If you have made someone a mutual contact -- you have linked them and they have linked you -- you will be able to tag each other's posts in AskMe and MeFi.
The most common reason to add someone as a contact is that you enjoyed a comment or post they made, and you want to see future things they post. There is no obligation to be reciprocal if someone has added you as a contact. Disabled accounts will remain as contacts, but user names will be marked with a black background/highlight.
* Note that a few users like to select jokey answers for the "what is your relationship" question, for example "crush" or "spouse" for people they don't know. Do not be alarmed if someone does this; it is a common friendly joke, as seen in the mass enspousening of 2009, and the following anniversaries (year 1, year 2, year 3). It is also fine to ask them not to do that.