The emerging area of network biology is seeking to provide insights into organizational principles of life. However, despite significant collaborative efforts, there is still typically a weak link between biological and computational scientists and a lack of understanding of the research issues across the disciplines. This results in the use of simple computational techniques of limited potential that are incapable of explaining these complex data. Hence, the danger is that the community might begin to view the topological properties of network data as mere statistics, rather than rich sources of biological information. A further danger is that such views might result in the imposition of scientific doctrines, such as scale-free-centric (on the modeling side) and genome-centric (on the biological side) opinions onto this area. Here, we take a graph-theoretic perspective on protein-protein interaction networks and present a high-level overview of the area, commenting on possible challenges ahead.