The U.S. Army depends on a broad array of interacting physical, informational, cognitive, and social networks. Nevertheless, fundamental understanding about these networks is primitive. This gap between what is known and what is needed to ensure the smooth operation of complex networks makes the Army's transformation to a force capable of network-centric operations (NCO) problematic. To help address this problem, the Army asked the National Research Council to find out whether identifying and funding and network science and research could help close this gap. This book presents an assessment of the importance and content of network science as it exists today. The book also provides an analysis of how the Army might advance the transformation to NCO operations by supporting fundamental research on networks. The study finds that networks are indispensable to the defense of the United States. In addition, there is no science today that offers the fundamental knowledge necessary to design large, complex networks in a predictable manner. The study also concluded that current federal funding of network research is focused on specific applications and not on advancing fundamental knowledge.