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Electric power grids are evolving rapidly as increased emphasis is placed on integration of renewable resources into existing power infrastructures and as new paradigms for power production and distribution, such as microgrids, are developed. Resultant grid configurations must meet the needs and requirements of existing and evolving population distributions, feasible production facilities placement, and environmental stewardship associated with power transmission and distribution infrastructures. In most developed regions, large-scale transmission infrastructures are well established, and their geographic routing is increasingly difficult to alter or amend. Renewables integration, however, directs far more attention at the power distribution level. As more local power is produced, often intermittent in nature and sometimes by consumers themselves, power distribution becomes more problematic in several respects. Conceptually, “the grid” becomes less a fixed entity and more an ever-changing amalgam of sources, loads, and preferred routes among them. All such routes must meet certain fundamental physical requirements, such as current and voltage handling capabilities. For power quality and reliability reasons, however, they also need to be “stable” in several senses, and there is currently no comprehensive approach to selecting available or potential routes to optimize the resultant “stability” of the configuration, in any of the various senses. This work develops such an approach, applicable to the steady-state stability of grids subject to several simplifying constraints. That is, it provides a framework for analyzing the steady-state stabilities of all grid topologies for grids that meet those constraints. The approach is general and abstract in nature, as this work focuses not on particular commonly studied grids but instead on the characteristics of grid topologies that lend themselves to greater or lesser degrees of steady-state stability. As a baseline study, only grids having synchronous generators are considered, with the expectation that future work will adapt inertia-based models of renewable sources to this or a similar approach. Although the approach itself is the main contribution, several interesting discoveries have already been made regarding optimal configurations of some simple topologies and on quantifying how richness of grid interconnections influences grid steady-state stability.