The "Suggested Friends" application for Facebook recommends friends to users based on common networks between friends a user already has. When this feature is turned on, your Facebook page can appear to people as a suggestion, even if they haven't intentionally searched for you. Some users think this application is unnecessary and an invasion of privacy. The only way to turn this application off is to remove yourself from the search engine.
Log in to your account on the Facebook homepage. Click "Account" in the upper-right corner. Click "Privacy Settings" from the drop-down menu.
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Find the "How you connect" category on the Privacy Settings page. Click the "Edit Settings" link next to this heading.
Find the "Control Your Default Privacy" heading in the middle of the Privacy Settings page. Click "Custom." Click "Friends" from the drop-down menu, which is "Friends of Friends" by default.
Choose "Friends" from the drop-down menu in the "Who can look up your profile by name or contact info?" category. Click "Done."
Find the "Apps and websites" at the bottom of the Privacy Settings page. Click the "Edit Settings" link under this heading.
Scroll down to "Public Search" at the bottom of the page. Click "Edit Settings." Uncheck the "Enable Public Search" box.
Search for yourself with your full Facebook name on Google to make sure your changes have worked. Click on the Facebook link with your name. No information should appear. Sometimes it takes a few days for your changes to apply.
Your profile will not show up on "Suggested Friends," but the consequence is that Friends and Friends of Friends will not be able to search for you by name. Nothing will come up when your name is typed into the Facebook search engine. Gauge whether this is worth it to you before making changes.