Spatial Scaling and Cross-Modal Network Reconstruction Analysis for River-Road Systems using GraphSAGE

Abstract

With a rapidly urbanizing world, cities are increasingly evolving into complex socio-technological systems, emphasizing the need for integrated environment-technology approaches for sustainable smart-city development. Urban riverine zones are at the intersection of such human-nature interfaces where natural hydrological processes interact with the built environment. This study examines the spatial dynamics of two prominent networks, rivers and roads, in Ho Chi Minh City (HCMC) and Jakarta. First, a city-scale spatial scaling analysis was performed using Hack's law for river networks and an analogous length-area scaling for road networks. Both cities exhibit strong power-law behaviour in river networks ($R^{2} \simeq 0.96-0.98$) and moderate scaling in road networks ($R^{2} \simeq 0.38-0.48)$, indicating that arterial roads retain a partially tree-like hierarchical structure shaped by underlying hydrological geometry. Further, a cross-modal Graph Neural Network (GNN) with dual encoders was developed to quantify river-road coupling through road-edge reconstruction. Same-city experiments show weak but non-random predictability ($A U C= 0.527$ for HCMC; 0.577 for Jakarta), suggesting that river morphology provides limited yet detectable information about major road connectivity. Cross-city experiments reveal a strong asymmetry, models trained on Jakarta generalize moderately to HCMC $(A U C \simeq 0.596)$, whereas models trained on HCMC fail to transfer to Jakarta $(A U C \simeq 0.434)$. These findings indicate that hydrological constraints in Jakarta produce more learnable and transferable structural patterns than the smoother deltaic morphology of HCMC. This study demonstrates that combining scaling law with Cross-modal GNNs provides a powerful framework for understanding natural-engineered network intersections, offering actionable insights for resilient, informed smart-city planning.