System of systems (SoS) are networked integration of constituent systems that together achieve new capabilities not possible through the operation of any single system. SoS can be found across all aspects of modern life such as power grids, supply chains, and disaster monitoring and tracking services. Their resilience (being able to withstand and recover from disruptions) is a critical attribute whose evaluation is nontrivial and requires detailed disruption models. Engineers rely on heuristics (such as redundancy and localized capacity) for achieving resilience. However, excessive reliance on these qualitative guidelines can result in unacceptable operation costs, erosion of profits, over-consumption of natural resources, or unacceptable levels of waste or emissions. Graph-theoretic approaches provide a potential solution to this challenge as they can evaluate architectural characteristics without needing detailed performance simulations, supporting their use in early stage SoS architecture selection. However, no consensus exists as to which graph-theoretic metrics are most valuable for SoS design and how they should be included in the design process. In this work, multiple graph-theoretic approaches are analyzed and compared, on a common platform, for their use as design tools for resilient SoS. The metrics central point dominance, modularity, specialized predator ratio, generalization, vulnerability, and degree of system order are found to be viable options for the development of early stage decision-support tools for resilient SoS design.