Here are some excellent papers that every researcher in this area should read. They present a logical introductory material into the field and describe latest achievements as well as currently unsolved issues of complex networks.
Book in complex networks that a newbie should read:
1. D. Easley, J. Kleinberg. Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, 2010.
Core papers in complex networks:
2. Wattz, D.J. & Strogatz, S.H. Collective dynamics of small world networks. Nature 393, 440–442(1998).
3. Barabasi, A.L. & Albert, R. Emergence of scaling in random networks. Science 286, 509(1999).
4. Strogatz, S.H. Exploring complex networks. Nature 410, 268–276(2001).
Review and state of the art:
5. Albert, R. & Barabasi, A.L. Statistical mechanics of complex networks. Reviews of modern physics 74, 47–97(2002).
6. Newman, M.E.J. The structure and function of complex networks. Arxiv preprint cond-mat/0303516 (2003).
For an account of the activity in this field we refer to the followin recent review:
7. Boccaletti, S. et al. Complex networks: structure and dynamics. Physics Reports 424, 175–308(2006).