The last several decades have witnessed a remarkable growth in the algorithmic theory of networks, from combinatorial algorithms for shortest paths, network flows, cuts and partitions to models of random graphs, Internet, social graphs, biological networks, and the small-world phenomena. The rise of Big Data and its unprecedented scale is forcing a rethink of many of the algorithms and theories. This research thrust will build algorithmic foundations and theories that can scale to networks with millions of nodes and billions of edges, and will analyze specific characteristics of social and biological networks so that we can engineer algorithms to real networks.

Biological systems can be represented as networks of interacting units. Thus, we have gene regulatory networks, protein-protein interaction networks, signaling networks, metabolic networks, neuronal networks, and food webs. Understanding how they evolve and function is a core question in modern biology and requires approaches that bring together data and scientific approaches from disparate fields. 

Storage, retrieval, analysis and visualization of Network Science data pose formidable research and development challenges. In particular, the underlying data model for Network Science applications is based on graph-structured data. Queries on such data sets are based on the structural properties of graphs, in addition to the values of attributes. Managing, programming and visualizing of complex networked datasets is another significant research problem.

Networks provide the natural framework to model the dynamical processes and interactions arising in large-scale multi-agent systems. We are developing a Network Science of dynamical systems, while targeting natural large-scale networks (ranging for cellular regulatory networks to ecosystem level networks), artificial networks (including sensor networks, networks of robots, and the power grid), and societal networks (such as online social networks and networks of influence and opinion).

The last two decades have been a particularly productive period for network analysis in the social sciences. While the roots of formal graph modeling of social behavior go back a half a century or more, most of the early work was devoted to developing formalisms and tool building. That started to change a generation ago as network analysis was applied to a much wider variety of practical problems in the disciplines. Now the rise of the Internet and the increasing availability of Big Data promise to transform the scientific study of social networks yet again.