The objective of this research is to develop methods to monitor and ensure the robustness of a class of cyber-physical systems termed "physical networks," such as electric, water, sewage, and gas networks. The approach is to analyze such networks using the mathematical formalism of graphical models. The project models a physical network as a graph, whose variables have a concrete physical interpretation, such as voltage, satisfying known physical laws, such as Kirchoff laws. The machinery of graphical models is used to develop methods to monitor and ensure the robustness of such networks, using the electric power network as a representative. By studying puzzling network-wide interactions, the project has the potential to clarify the role of complexity in large scale networks. Potential contributions will be made to the fields of distributed inference algorithms and fast numerical methods. Physical networks play a crucial role in modern society, and yet, often exhibit fragile behavior, such as black-outs in electric power networks, resulting in economic loss, as well as causing a security risk. This project seeks to understand the robustness behavior of such networks and to train a broad class of students in their theory and practice. Results from this research are to be incorporated into courses and disseminated via research publications. The Carnegie Mellon Conference on the Electricity Industry allows students to interact with faculty and electricity industry veterans. Interaction with the electricity industry aims to provide it with an understanding of cyber-intelligence, to ensure effective robustness monitoring capabilities in the power grid.