Social media seems to have made all aspects of our personal lives into a matter of public concern, including our relationships. Some people however might not want to go public and there are many good reasons to avoid sharing your private life with strangers online.
One way to keep your relationship low profile is to avoid tagging your significant other. It is even possible to appear in photographs with someone with whom you are in a relationship holding hands, but if you do not tag your other half, Facebook and Twitter will not even notice. Ask your friends to avoid doing the same.
The most obvious method is to simply avoid posting private photos of you as a couple on social media sites at all if you want your private life to remain private. Be careful to avoid sharing too much information in a tweet and turn off your location. If you and your partner like to tweet about activities you do, negotiate so that only of you can tweet about doing something at the same time.