The ability of additive manufacturing (AM) processes to produce components with virtually any geometry presents a unique challenge in terms of quantifying the dimensional quality of the part. In this paper, a novel spectral graph theory (SGT) approach is proposed for resolving the following critical quality assurance concern in the AM: how to quantify the relative deviation in dimensional integrity of complex AM components. Here, the SGT approach is demonstrated for classifying the dimensional integrity of standardized test components. The SGT-based topological invariant Fiedler number (λ2) was calculated from 3D point cloud coordinate measurements and used to quantify the dimensional integrity of test components. The Fiedler number was found to differ significantly for parts originating from different AM processes (statistical significance p-value <1%). By comparison, prevalent dimensional integrity assessment techniques, such as traditional statistical quantifiers (e.g., mean and standard deviation) and examination of specific facets/landmarks failed to capture part-to-part variations, proved incapable of ranking the quality of test AM components in a consistent manner. In contrast, the SGT approach was able to consistently rank the quality of the AM components with a high degree of statistical confidence independent of sampling technique used. Consequently, from a practical standpoint, the SGT approach can be a powerful tool for assessing the dimensional integrity of the AM components, and thus encourage wider adoption of the AM capabilities.