For the future, there are many interesting possibilities in the study of dynamical processes on networks (e.g. reaction-diffusion / message passing / synchronization) - for a high level treatment see this excellent review:
"... error tolerance is not shared by all redundant systems: it is displayed only by a class of in-homogeneously wired called scale-free networks, which include the World-Wide Web, the Internet6, social networks7 and cells8. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by un-realistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks ..."
A good understanding of Graph Theory would help too. The books "Graphs and Hypergraphs" by Claude Berge and "Random Graphs" by Bela Bollobás are among the most important in the area.
(1) M. Newman's publications contain a wealth of ideas and insights into these topics:
http://www-personal.umich.edu/~mejn/pubs.html
Also, much credit goes to Barabasi who made many contributions to this field and did much to popularize it (along with Watts and Strogatz)
http://www.barabasilab.com/pubs-revart.php
For the future, there are many interesting possibilities in the study of dynamical processes on networks (e.g. reaction-diffusion / message passing / synchronization) - for a high level treatment see this excellent review:
Critical phenomena in Complex Networks http://arxiv.org/abs/0705.0010