A Framework Based on Graph Cellular Automata for Similarity Evaluation in Urban Spatial Networks

TL;DR

This paper introduces GCA-Sim, a novel framework using graph cellular automata to evaluate similarity in urban spatial networks, outperforming existing methods in clustering and revealing urban morphological insights.

Contribution

The paper presents a new similarity evaluation framework based on graph cellular automata and a differentiable logic-gate network, tailored for urban spatial networks.

Findings

Submodels outperform existing similarity methods with Silhouette scores above 0.9.

Planning-led street networks are less homogeneous than organic ones.

Degree centrality aligns more with land value over iterations.

Abstract

Measuring similarity in urban spatial networks is key to understanding cities as complex systems. Yet most existing methods are not tailored for spatial networks and struggle to differentiate them effectively. We propose GCA-Sim, a similarity-evaluation framework based on graph cellular automata. Each submodel measures similarity by the divergence between value distributions recorded at multiple stages of an information evolution process. We find that some propagation rules magnify differences among network signals; we call this "network resonance." With an improved differentiable logic-gate network, we learn several submodels that induce network resonance. We evaluate similarity through clustering performance on fifty city-level and fifty district-level road networks. The submodels in this framework outperform existing methods, with Silhouette scores above 0.9. Using the best submodel, we further observe that planning-led street networks are less internally homogeneous than organically grown ones; morphological categories from different domains contribute with comparable importance; and degree, as a basic topological signal, becomes increasingly aligned with land value and related variables over iterations.