A graph theory based similarity metric enables comparison of subpopulation psychometric networks

Network psychometrics leverages pairwise Markov random fields to depict conditional dependencies among a set of psychological variables as undirected edge-weighted graphs. Researchers often intend to compare such psychometric networks across subpopulations, and recent methodological advances provide invariance tests of differences in subpopulation networks. What remains missing, though, is an analogue to an effect size measure that quantifies differences in psychometric networks. We address this gap by complementing recent advances for investigating whether psychometric networks differ with an intuitive similarity measure quantifying the extent to which networks differ. To this end, we build on graph-theoretic approaches and propose a similarity measure based on the Frobenius norm of differences in psychometric networks' weighted adjacency matrices. To assess this measure's utility for quantifying differences between psychometric networks, we study how it captures differences in subpopulation network models implied by both latent variable models and Gaussian graphical models. We show that a wide array of network differences translates intuitively into the proposed measure, while the same does not hold true for customary correlation-based comparisons. In a simulation study on finite-sample behavior, we show that the proposed measure yields trustworthy results when population networks differ and sample sizes are sufficiently large, but fails to identify exact similarity when population networks are the same. From these results, we derive a strong recommendation to only use the measure as a complement to a significant test for network similarity. We illustrate potential insights from quantifying psychometric network similarities through cross-country comparisons of human values networks. (PsycInfo Database Record (c) 2026 APA, all rights reserved).