Role of Local Geometry in Robustness of Power Grid Networks.

We introduce a novel approach to study robustness of a power grid network employing the tools of topological data analysis (TDA). This approach not only enables one to incorporate intrinsic network properties such as electrical conductance but more importantly also offers a systematic and comprehensive framework to study the role of topology in its functionality and robustness. This is achieved by viewing the network as a weighted graph, equipping it with a nested simplicial complex structure and extracting topological summaries in the form of the Betti numbers and persistent diagrams. These summaries are then used to characterize network vulnerability under critical conditions such as targeted attacks.