Facebook fanpage link building

Hi guys and good evening. I have a fb fanpage with strong social proofs and i'm in local competition only (real estate broker) so it's easy to dominate this small space since where i am the brokers are so bad with SMM or even SEO.

My question is : Is it worth building PR backlinks on my fb fanpage ?

Is it really gonna make any impact ? Thanks alot guys for your replies, I have huge respect for BHW.

SEO/link building is important for your fan page even though this is not a website
Even though your Facebook business page is not a website per se, it can be reached via search engines like Google. And that means that search engine optimization (SEO) of your page is just as important for your business website. No matter how good your products or services are, if no one can find you, you will not get customers.

Not worth it. Why would you build links for Facebook? Build links to your money site only. Everything else is a waste of time.