A graph-theoretic framework for quantitative analysis of angiogenic networks

The endothelial tube formation assay is an established in vitro model for evaluating angiogenesis. Although widely used, quantification of angiogenic behavior in such assays remains semi-empirical and often lacks spatial, topological, and structural context. Here, we present a graph-theoretic framework to quantify network morphology, temporal dynamics, and spatial heterogeneity in tube formation assays. We simulated two distinct angiogenic network morphologies using human umbilical vein endothelial cells (HUVECs) seeded at two densities and imaged at 2, 4, and 18 h post-seeding. Skeletonized images were converted to mathematical graphs from which 11 graph-based metrics were extracted. This framework captured both morphological differences and temporal progression. Sparse networks exhibited significantly higher average node degree (p = 0.00079), clustering coefficient (p = 0.00109), and tortuosity (p = 0.0171), whereas dense networks showed greater node and edges counts (p = 0.00109). Over time, networks evolved from fragmented forms at 2 h to integrated structures at 18 h, as reflected by increased largest component size (p = 0.00216), connectivity index (p = 0.00216), and efficiency (p = 0.0152). ROC AUC analysis revealed that metrics such as average degree (AUC = 0.98) and clustering coefficient (AUC = 0.96) effectively distinguished between sparse and dense morphologies, while component-based metrics perfectly separated 2- and 18-hour networks (AUC = 1.00). Radial zone analysis revealed that vascular distribution becomes more compartmentalized over time, with increasing standard deviation and coefficient of variation. This approach provides a sensitive and scalable method for quantifying angiogenic dynamics, offering insight into both therapeutic efficacy and disease-related vascular remodeling.