On second thought, I'm not even sure what "transitive" means here. It seems like it should mean that if you trust your friend's movie recommendations then you trust your friend's friends' movie recommendations? Or maybe something like:

   trustsMovieRecs(A, B) and trustsMovieRecs(B, C) => trustsMovieRecs(A, C).

Their movie recommendations are likely some function that takes their friends' movie recommendations as input (along with watching them), but that's more like an indirect dependency than a transitive closure.