Do you actually have the downloaded csv from linkedIn or is that part of your question?
In I think, if you do
File > Open... > CSV Files
Then all you can do is have a list of edges like this:
"A","B"
"B","C"
"C","D"
If instead you go to the Data Laboratory, then you can do import spreadsheet as a "Nodes Table" or an "Edges Table". The edges table csv file looks like this:
Source,Target,Type,Id,Label,Weight
145,147,Directed,465,,1.0
145,150,Directed,466,,1.0
145,159,Directed,467,,1.0
146,156,Directed,468,,1.0
There is a labs tool that LinkedIn provides here http://inmaps.linkedinlabs.com/ that draws a nice network graph. UPDATE - LinkedIn no longer offers this tool.