Conferences and journals for network science? I'd like to learn about the state of the art in network science and which problems researchers are actively working on. In particular, I'm interested in the applications, but the theory is also interesting.

I've found papers on scholar.google.com, and if I'm not mistaken most of the papers are published in application-specific conferences. For example, if network science is used to understand something related to cancer then the results are published in a medical journal. This is making it hard for me to get a consistent view and it's hard for me to get access to such a broad section of the literature (I'm not at a university so I keep hitting paywalls).

tl;dr: Where can I find conferences and journals that focus on network science?
I would say you are approaching it in the wrong way. Since network science (as Wikipedia defined it) is multidisciplinary concept, then I really doubt finding a consistent venue (conferences/ journals) for it.  This is specially true if you are interested in the application side.  If you are interested in the theory behind it, I see Graph Theory is the way to go.  

I have worked in different applications of what so called network science including bioinformatics, social networks. I only knew graph theory (I had no clue what genes really are). So this largely depends on the application domain.   

So simple steps to go:  


Pick an area/interesting problem related to your expertise/background. 
Read its literature.


If you saw a good paper related to your work, then keep an eye on the authors.