Can anybody please name some common applications of Complex Networks (aka. network science) preferably related (but not limited) to computer science?

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Christian L. Staudt

An extensive survey is provided by http://arxiv.org/pdf/0711.3199.pdf

Alex Shackelford

Im not really sure what you mean by complex networks, but Ive been working for Internet service providers for the past year, and I know if you figured out how to network neighborhoods of people together, where they would efficiently share bandwidth, I think that would be very useful.

Valdis E Krebs

Take a look at the blog -- http://thenetworkthinkers.com

Many applications of network analysis are illustrated there. Most from real client engagements.