DARPA is seeking proposals that will address mathematical research on large networks and graphs with an emphasis on results that are applicable to social networks and other networks of interest to the DoD. The focus of the program will be three broad areas, namely: i. The theoretical underpinnings of the basic mathematics and dynamics of large networks and a framework for threat signature detection and identification; ii. Polynomial and sub-polynomial algorithm creation and development for exact and approximate solutions for DoD problems of interest; and iii. Graph and network techniques for other DoD networks of interest.