LinkedIn connections and connection levels are as old as LinkedIn itself. The underlying idea of the Social Network is based on connections!
You would think that LinkedIn (founded in 2002) has figured out the search for connection levels by now. But if you trust connection search – for example, routinely search for the second level members to connect with – you are up for disappointment: connection search has multiple issues. Here is a summary; these things (or rather, bugs) are good to keep in mind.
A. Search for each connection level vs. no level selection is not the same