Even though Facebook suffered social commerce fails with the Delta ticket window and the now-shuttered Facebook Deals, Facebook social shopping applications for Facebook still keep popping up.

A new study from Sociable Labs shows that 50% of shoppers are logged into Facebook while shopping on an e-commerce site. While that’s interesting data in and of itself, the study does not prove any correlation between sharing on Facebook and shopping on e-commerce sites. In other words, businesses may see that their customers are on Facebook – because, really, who isn’t on Facebook, save for the very paranoid – yet the idea of sharing what you buy through the world’s largest social network has not, and will not, become a part of the Facebook user’s experience. Unless it centers around an e-commerce site like EBay that people already know and trust.

Social commerce dashboards like Payvment allow Facebook users to launch free stores on their Facebook pages. Payvment believes in f-commerce, and aims to create a “virtual mall” out of Facebook. More than 100,000 sellers use the app.

Earlier this week a UK-based social commerce app called Shopcade launched. It offers seamless integration with Facebook, 40 million products, real cash rewards and gaming aspects that are supposed to make shopping fun. In an e-mail interview with Shopcade, CEO Nathalie Gaveau suggests that there’s still an opportunity to personalize the Facebook shopping experience, and says that is why Shopcade will succeed.

Yet, no matter how much social commerce app creators believe that a personalized f-commerce is the key, there’s still a fundamental problem. Facebook began as a space to connect with friends and family, not as a virtual mall. Social commerce evangelists wrongly conflate the social graph and the interest graph in an effort to make f-commerce viable.

In a ReadWriteWeb guest post from David Rogers, a consultant, speaker, author of “The Network Is Your Customer” and a current professor at Columbia Business School, explains the difference between the social graph and the interest graph.

“A social graph is a digital map that says, ‘This is who I know.’ It may reflect people who the user knows in various ways: as family members, work colleagues, peers met at a conference, high school classmates, fellow cycling club members, friend of a friend, etc. Social graphs are mostly created on social networking sites like Facebook and LinkedIn, where users send reciprocal invites to those they know, in order to map out and maintain their social ties.”

The interest graph is a digital map that explains what a user likes.

“Interest graphs are generated by the feeds customers follow (e.g. on Twitter), products they buy (e.g. on Amazon), ratings they create (e.g. on Netflix), searches they run (e.g. on Google), or questions they answer about their tastes (e.g. on services like Hunch).”

The social web, and especially Facebook, has wrongly conflated the two. This is precisely why social commerce apps on Facebook are not taking off.

If anything, integrating a familiar e-commerce platform like EBay into the Facebook ecosystem is how social commerce may actually start to work. It makes Facebook feel less mall-like and more like a space where online transactions can occur.

The Facebook-EBay integration could be seamless and easy. To turn up the personalization aspect a bit, EBay cleverly acquired recommendation technology Hunch.

With the EBay-Facebook integration, Facebook will be able to gather data without actually handling the transactions. In effect, Facebook will not become a virtual mall – that would skew too far from its original purpose. Instead, Facebook will work behind the scenes to gather data on consumer purchasing patterns. So forget social commerce concept already – it’s not going to work.