Conferences and journals for 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.