In the technology age, people believe everything is quantity-driven. We often think that if someone has a ton of Facebook friends, it means he or she is popular. Seeing a person with many connections on LinkedIn could mean she is very well-connected. However, the presence of 500-plus connections on LinkedIn and 1,000 Facebook friends can be deceptive. Do those people personally know that many people? It's pretty unlikely.
Having an exorbitant number of connections can make others question whether you really know that many people or are just trying to increase your numbers for show. High numbers aren't going to get you the job you want, but substantive relationships will.