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

arXiv: https://arxiv.org/abs/2511.00768 · HTML: https://mlsanity.com/paper/2511.00768/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 70 references that are in the map.
- First posted on arXiv 2 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks](https://mlsanity.com/paper/1611.01890/) (2016)
- [Deep Differentiable Logic Gate Networks](https://mlsanity.com/paper/2210.08277/) (2022)
- [A Survey on Metric Learning for Feature Vectors and Structured Data](https://mlsanity.com/paper/1306.6709/) (2013)
- [NetLSD: Hearing the Shape of a Graph](https://mlsanity.com/paper/1805.10712/) (2018)
- [Convolutional Differentiable Logic Gate Networks](https://mlsanity.com/paper/2411.04732/) (2024)
- [Learning Graph Cellular Automata](https://mlsanity.com/paper/2110.14237/) (2021)
- [SimA: Simple Softmax-free Attention for Vision Transformers](https://mlsanity.com/paper/2206.08898/) (2022)
- [Random walks and diffusion on networks](https://mlsanity.com/paper/1612.03281/) (2016)
- [DELTACON: A Principled Massive-Graph Similarity Function](https://mlsanity.com/paper/1304.4657/) (2013)
- [NoisyGL: A Comprehensive Benchmark for Graph Neural Networks under Label Noise](https://mlsanity.com/paper/2406.04299/) (2024)
- [An information-theoretic, all-scales approach to comparing networks](https://mlsanity.com/paper/1804.03665/) (2018)
- [Quantifying Spatial Homogeneity of Urban Road Networks via Graph Neural Networks](https://mlsanity.com/paper/2101.00307/) (2021)
- [Deep Clustering Using the Soft Silhouette Score: Towards Compact and Well-Separated Clusters](https://mlsanity.com/paper/2402.00608/) (2024)

## Abstract (arXiv)

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.