Tara Smith at Aetiology has a neat post about networks, particularly in disease transmission. Studying networks allows you to see and analyze how entities, like people in a society or species in an ecosystem, interact. Sometimes, you discover neat and useful patterns. For example, many infectious diseases, including HIV in America, are primarily spread by hyper-connected individuals. Other times, a person does more than their share of disease transmission by simply shedding more of the infectious agent than other people. SARS is an example of this.
To me, the coolest application of network science is to ecological networks such as food webs. Neo Martinez, Jennifer Dunne and their colleagues at PEaCE Lab have done some fascinating work on food web structure. One of their basic results shows that you can create realistic food webs using very simple rules -- animals have a certain size and eat things that are a given fraction of that size. Their simulations also show that the ability of a food web to withstand species extinctions depends on how richly interconnected the species are.
A different approach to the study of ecological networks is that practiced by Bernie Patten and the Systems and Engineering Ecology group at the University of Georgia. Their work looks less at network structure than at dynamics and general principles. I'll be joining this group in mid-August, so expect more on ecological networks starting then.