Many times you may have noticed that people get self-obsessed. Every time they tend to talk about themselves. They have "I, Me and Myself" in them which is not good at times. It gets really harmful if you are in a relationship. These types of people are called as Narcissists. They are really weak when it comes to handling criticism. No one with this behaviour can take NO from anyone.
Here we have listed some of the major pointers to look out for, as reported by The Independent:

1. They might make you feel bad about yourself.
2. Don't assume or expect a narcissistic partner to be genuinely happy for you.
3. They only like to talk about themselves basically they are self-obsessed. 
4. If you're dating someone extremely self-absorbed, your date night conversation will most likely revolve around his or her achievements, success and interests.
5. Constant praise makes them happy.
6. Narcissists always want to be the centre of attention.
7. They always demean towards other people.
8. Egocentrics often obsess over the negative aspects of other people's lives.
9. Narcissists often think they can do a better job than others.
10. They are sensitive and also overreact.