A new way of measuring the hidden geometry of city streets suggests there may be no such thing as an optimal urban layout. Their analysis, published in EPJ Data Science, found that grid cities pack people in most densely, organically grown cities show the strongest hierarchical structure, and linear cities minimise the detours travellers must make. No single design won on every count.
The metric builds on a long line of urban theory. Architect Christopher Alexander argued that cities which grow organically over centuries tend to display a “living structure”: far more small elements than large ones, arranged in a recurring hierarchy. Earlier work by Bin Jiang and colleagues formalised this idea using the head/tail breaks algorithm, a classification scheme designed for the heavy-tailed distributions that arise naturally in urban systems. The algorithm repeatedly splits a set of values into a small “head” above the mean and a large “tail” at or below it, and the resulting ht-index counts how many hierarchical levels the data contains. Applied to street networks, previous studies found that organically developed cities such as Amsterdam and Rome are more hierarchical than fully planned ones such as Brasilia and Chandigarh.
The researchers, Cameron Dobbie and Anders Johansson, saw a weakness in how those earlier studies ranked streets. They used connectivity, simply how many other roads each road touches, which can flatter a quiet peripheral road connected to many neighbours while ignoring a busy through-route at the city’s heart. The researchers instead turned to betweenness centrality, a network measure introduced by Freeman in 1977 that scores each element by how many shortest paths pass through it. Their “road betweenness” works on named roads rather than individual segments, reflecting how humans actually navigate: people generally take the shortest path while trying to stay on the same road for as long as possible. Where several equally short routes exist, credit is split between them, and each road’s contribution is weighted by the distance a journey spends on it.
To test the metric, the researchers applied it to six real cities loaded from OpenStreetMap data: London, Rome and Tokyo as famously organic examples, and Chicago, Phoenix and Salt Lake City as strict grids. Because such analyses are notoriously sensitive to boundary choices, they did not rely on a single map cut-out. Instead they sampled 31 partially overlapping hexagonal areas, each roughly 2.6 square kilometres, centred on a triangular grid with one-kilometre spacing in each city, and averaged the results. In every case the road betweenness values followed a heavy-tailed distribution, justifying the head/tail breaks approach. The organically developed cities scored clearly higher on the living metric than the grid cities, with the two groups well separated, confirming that the measure can distinguish organic from planned morphologies using the road network alone.
The metric is deliberately narrow in what it claims to measure. The authors stress that a low score does not mean a city is unpleasant, and a high score does not guarantee liveability. Manhattan would likely score similarly to Chicago, yet is widely regarded as a vibrant place to live. The living metric captures one specific structural property, the extent of hierarchy in the road betweenness distribution, and the researchers explicitly warn against reading it as a proxy for quality of life, safety or pleasantness, which depend on countless factors beyond any street map.
The second half of the study tackles a gap the authors identify in most urban analysis: it is almost always applied to cities that already exist, leaving open the question of how hypothetical designs would perform. As a proof of concept they built CitySprout, an open-source procedural generator based on Lindenmayer systems, the rule-based, recursive method famously used to model plant growth and later adapted for road generation by Parish and Müller. CitySprout expands a road network node by node according to user-defined production rules, with stochastic choices of branching behaviour, deflection angles and distances, so a single grammar, or ruleset, can produce many city variations. Four grammars were defined: an Organic grammar inspired by cities like London, a Grid grammar of perfectly straight orthogonal streets, a Hex grammar with six equiangular arms radiating from the centre like the avenues of Paris, and a Line grammar loosely inspired by The Line project in Saudi Arabia’s Neom development, with a long linear spine.
For each grammar the team generated 40 cities with a nominal population of one million, using a calibrated constant of 340 people per road-kilometre derived from London, which treats population as proportional to total road length. They then measured three complementary metrics: population density as a proxy for space efficiency, the living metric, and mean circuity, the ratio of network distance to straight-line distance averaged over all node pairs, which captures travel efficiency. A leave-one-seed-out check confirmed the sample of 40 was stable, with changes in means and medians well below one percent.
The results underline how metric-dependent any judgement of urban form must be. Grid cities were the most space efficient; the minimum population density among them exceeded the maximum of every other grammar, as expected when population scales with road length and square blocks leave fewer unusable gaps. Organic cities scored highest on the living metric, mirroring the real-city results, while Hex cities scored surprisingly low, because the roads within each wedge are bounded by the six arms and cannot run uninterrupted across the city, flattening their betweenness distributions. On travel efficiency, Line cities excelled, since travellers simply reach one of three long spine roads and ride them straight across the city, producing very low mean circuity. Grid cities measured a median mean circuity of 1.3034, close to the theoretical rectilinear value of 4 divided by pi, roughly 1.2732, with the small excess attributed to the cities growing square rather than circular. Organic cities showed by far the widest spread of circuity values, and across all grammars higher population density correlated with lower circuity, since densely packed roads offer more efficient route choices.
The study also examines why optimising a road network alone cannot guarantee a successful city. Planned cities offer cautionary tales on both sides: Brasilia’s original design failed to absorb rapid migrant-driven growth, pushing workers to underserved peripheries with lasting socio-spatial segregation, while Songdo in South Korea expected 250,000 residents by 2020 but had yet to reach 220,000 as of 2024. Washington D.C., planned in 1791 but continuously adapted since, shows that ongoing development can offset the typical pitfalls of car dependency and monotony. Milton Keynes ranked second among large UK cities on quantitative health measures yet is often described as soulless, a contrast the authors use to illustrate how poorly metrics capture lived experience. Modelling cities as flat, two-dimensional road networks also ignores high-rise population and terrain, and the generated cities’ road spacing is wider than in real ones, so their metric values cannot be compared directly with empirical cities.
The broader conclusion is that optimising a road network inherently converges on different answers depending on which metric is prioritised, so no single optimal urban form exists. Linear cities performed well on all three metrics studied, but the authors caution that such an extreme departure from existing cities makes their real-world success impossible to predict. The living metric and CitySprout are offered as tools for exploring trade-offs before construction begins, with future work planned to incorporate empirical travel-demand data and to calibrate the generator’s rules against the junction spacing and branching patterns of real cities.
Subject of Research: A new road-network metric quantifying hierarchical living structure and its application to real and procedurally generated city layouts
Article Title: Comparing urban network morphologies: a new living metric and a framework for evaluating procedurally generated city layouts
Article References: Dobbie, C., & Johansson, A. (2026). Comparing urban network morphologies: a new living metric and a framework for evaluating procedurally generated city layouts. EPJ Data Science, 15(1), Article 76. https://doi.org/10.1140/epjds/s13688-026-00694-7
Image Credits: AI Generated
DOI: 10.1140/epjds/s13688-026-00694-7
Keywords: urban networks, road betweenness, living metric, head/tail breaks, procedural city generation, L-systems, CitySprout, population density, mean circuity, urban morphology, city planning, The Line
News Source: Denise Maddox. (October 29, 2026). New Metric Ranks City Street Networks by Their Hidden Hierarchical Structure. Scienmag.
