For me it was, yes. For you, though, it might not have to be. Can you get some security classes in your coursework? (Does your institution even offer any?)
Luckily it offers two: Software security and cryptography. I have taken both. Should also probably mention that I live in Norway, so my question applies more to the European job market. Though I am of course interested hearing experiences from anywhere in the world.
I'm from Denmark and in a position similar to yours. I'm not newly graduated but new to the "it security" field. What I do is that, I try to go to conferences here in Copenhagen. Luckily my current employer endorses my endeavour and even sponsors some of the conferences or let me use some of my work time to attend.
But the point is I'm trying to get to know the field and the people in it. It's a small community - at least in Scandinavia, so I'm trying to use the human angle here. :)
(But truth be told I'm hoping to land a job at my current employer.)