Product manager at fraud detection company Simility here. I'm very surprised Facebook hasn't put more effort into curbing fake accounts, makes me think it's very low priority for them. We have social network customers who are much smaller than FB, yet have gotten their fake account rates far below FB's.
One effective strategy we've employed not mentioned here is category mapping: if an account of type A, only targets accounts of type B for likes (especially if they ignore categories C, D, etc.), this is usually a high indicator of fraud. For example, one very common strategy is to create a fake account for an attractive female to friend many male accounts (especially relatively new accounts unaware of these tactic). This can be easily detected by analyzing the gender and account age of all targets and coming up with a diversity score. Low diversity score = likely fraudster.
One effective strategy we've employed not mentioned here is category mapping: if an account of type A, only targets accounts of type B for likes (especially if they ignore categories C, D, etc.), this is usually a high indicator of fraud. For example, one very common strategy is to create a fake account for an attractive female to friend many male accounts (especially relatively new accounts unaware of these tactic). This can be easily detected by analyzing the gender and account age of all targets and coming up with a diversity score. Low diversity score = likely fraudster.