Pardon my question if it seems too general... I'm new to networks in general, but recently I came across a type of network called citations network. However, I couldn't figure out why we do citation analysis or what kind of special information we can get out of it.
One simple example of an application of citation analysis is ranking. Imagine you do a keyword search over a collection of scientific articles, How do you rank the result set from most relevant to least? A measure one could use is the amount of citations an article has or the quality of the citations it has and also the quality of the articles the paper refers to. This problem is closely related to the problem of ranking web pages according to its hyperlinks.
Not sure if this is relevant to what you're investigating, but I believe reading up on Bibliometrics might give you some insight into citation analysis. This type of analysis is used within research/academia to identify trends in topics of interest.
Interestingly, I was reading this article yesterday which analyzed and mapped the shift in research priority within the neuroscientific community. Hopefully this helps!