In science, rejection is normal
In the news: A coupla guys played around with some #2 pencils and Scotch tape and won a Nobel Prize in physics. Talk about easy science! This is what happens when you work in a field with such low-hanging fruit that you run out of testable hypotheses.
Okay, kidding aside…
The initial NY Times report noted that the first paper on graphene that the researchers wrote was rejected by Nature before later being published in Science. 
It would be easy to fit that into a narrative that is common in movies and in science journalism: the brilliant iconoclasts rejected by the hidebound scientific establishment.
Far more likely though is a much more mundane explanation: scientists see their work rejected all the time. It’s just part of how science works. The review process is not perfect, and sometimes you have to shop a good idea around for a while before you can convince people of its merit. And the more productive you are, the more rejection experiences you will accumulate over a career.
It’s a good reminder that if you’re a working scientist (or trying to start a career as one), don’t get too worked up about rejection.
 Puzzling sidenote: For some reason that part no longer appears in the article on the NY Times website, but since there’s no correction statement I’ll still assume that it’s true and they just edited it out of a later edition for some reason. The rejection anecdote still appears on the PBS website.