BUILDINGS AS GRAPHS

Source: Courtesy of Faculty, Wassim Jabi.

This seminar explores the proposition that architecture is fundamentally relational. Buildings and cities are not merely collections of objects; they are structured fields of spatial, functional, environmental, and social relationships. Graphs provide a rigorous and computationally tractable way of making these relationships explicit. The course equips participants with the conceptual and technical tools required to represent architectural and urban systems as graphs and to apply graph machine learning (GML) methods to extract insight from them.

We begin with an introduction to graph theory. Nodes, edges, directionality, weighting, centrality, adjacency matrices, Laplacians, and spectral properties are introduced not as abstract mathematics, but as operational constructs for spatial reasoning. We examine how rooms, façades, circulation routes, structural systems, and even urban districts can be modelled as graphs at multiple scales.

The seminar then focuses on representing buildings and urban spaces as graphs. We discuss dual graphs, visibility graphs, connectivity graphs, and multi-layer graphs that combine geometric, topological, and semantic information. Graph analysis methods are introduced, including space syntax measures, isovists, shortest paths, centrality metrics, clustering, and community detection, with applications in layout optimisation, accessibility analysis, environmental performance, and urban morphology.

A dedicated module addresses the derivation of graphs from 3D models. Participants will extract relational structures from IFC models and computational geometry workflows using TopologicPy, translating boundary representations into graph data structures enriched with attributes.

We then consider dataset construction. Real-world data versus synthetic data is discussed, including sampling strategies, bias, data sparsity, and scalability. Particular attention is given to feature engineering: continuous versus categorical attributes, one-hot encoding, normalisation, graph-level versus node-level features, and hierarchical dictionaries.

The course introduces graph machine learning: why GML is required when conventional ANN or CNN architectures are insufficient for non-Euclidean data; how message passing, neighbourhood aggregation, and graph convolutions operate in principle; and how embeddings are learned. We examine common tasks such as node classification, edge prediction, and graph regression within architectural contexts.

Practical sessions cover hyperparameters, loss functions, overfitting, regularisation, and the standard workflow of training, validation, and testing. We conclude with model evaluation, explainability, ethical considerations in AI for the built environment, and the integration of GML into design workflows and digital twins.

We will also examine a GraphRAG-inspired generative workflow in TopologicPy, where annotated ResPlan house plans are converted into attributed graphs and stored in a graph database. Graph-native queries, pattern extraction, and subgraph similarity are used to structure generative constraints. Precedent graphs inform the synthesis of new spatial graphs through learned relational patterns and typological embeddings, enabling graph-to-graph generation of coherent residential layouts.

By the end of the seminar, participants will possess a coherent end-to-end understanding of graph-based modelling and machine learning as a methodological foundation for computational design and urban analysis.

Learning Objectives

At course completion the student will:

• Learn the fundamentals of Graph Theory 
• Learn the fundamentals of Graph Machine Learning 
• Learn how to represent buildings as graphs
• Learn how to work with graph databases
• Explore different applications of GraphML