Smart-grids are made up of two interdependent constituents: a power production and distribution network catering to a geographic area and a communication network that helps regulate and control the power-grid from which it derives its electricity. Thus, failures in one of the two networks can lead to failures in the other and in some cases cause a cascade or domino effect, bringing down the entire system completely. In this work, we present a theoretical framework to model and study the structural properties of such interdependent networks based on a topological interpretation  of the Moore-Penrose pseudo-inverse of the graph Laplacians (L +). Using this framework, we study how the way in which node pairs in two networks are coupled or "glued" together (thereby introducing interdependence) affects the overall robustness of the resulting interdependent networks. Our study leads to some surprising (and somewhat counter-intuitive) results.