Spectral Fingerprints of Street-Network Morphology: A Size-Adjusted Graph-Laplacian Descriptor of Urban Fabric

Abstract

Decades of space-syntax research have established that the topology of the street network conditions movement, co-presence and urban activity. The standard vocabulary for this -- integration, choice and connectivity -- summarises each street's position as a scalar centrality, yet two streets with identical centrality can sit in radically different morphological fabric. We introduce a compact, comparable, machine-learning-ready encoding of that local fabric: the spectral fingerprint, a fixed-dimensional kernel-density representation of the graph-Laplacian eigenvalue distribution of each node's k-hop ego subgraph, computed on the COINS dual graph of the street network. From it we derive two interpretable scalar readouts: the Mesh Index (MI), a normalised spectral entropy, and the Connectivity Resilience Index (CRI), the algebraic connectivity (Fiedler value). Both are corrected for an ego-subgraph-size confound that dominates raw spectral statistics. Applied to the full street network of Poznan, Poland (1,908 continuity-based strokes), the descriptor is robust to its encoding hyperparameters (spectral resolution and kernel bandwidth; Spearman rho >= 0.98) while remaining scale-dependent in its neighbourhood radius. The size adjustment leaves the Mesh Index near-orthogonal to integration (r = 0.06), carrying information classical centrality does not. The fingerprint separates morphological tissue types without supervision, and the Mesh Index is associated with the functional diversity of street-adjacent activity at the neighbourhood scale (r ~ 0.19, on open OpenStreetMap data). We delineate the method's scope honestly: it characterises what kind of activity a street's position affords, not the price that activity commands. It offers an information-theoretic morphological descriptor that complements space syntax and is directly consumable by modern graph-learning pipelines.