Large networks of dynamical systems are becoming ubiquitous in modern technology. In modeling, analysis, and control of these systems, it is of fundamental importance to understand the interplay between dynamical properties of the network and the underlying network structure.

In this talk, I will introduce a framework for identification and design of network topologies that strike a balance between network performance and network sparsity. The developments will be motivated by two problems that arise in optimal design of sparse consensus networks and optimal localized control of vehicular formations. I will then demonstrate how combination of tools and ideas from optimization, control engineering, and graph theory can be used to obtain new methods for analysis and design of large dynamic networks.