Regional water and road networks reveal geometric and topological divergence patterns

Buried beneath nearly every city street lies a hidden second city: a lattice of water pipes that keeps taps running, hydrants charged, and industries supplied. For decades, planners have assumed that this subterranean network simply shadows the road grid above it—pipes laid along streets, following their geometry, their hierarchy, and their logic. A new comparative study challenges that assumption in a strikingly quantitative way, showing that the relationship between roads and water pipelines is not a universal constant of urban form but a regional fingerprint, shaped by colonial legacies, informal settlement growth, and the location of water infrastructure itself.

The research, published in the journal Discover Cities, was led by Zhangliang Deng of Heze University in China, together with Christopher Thomas Lloyd and Jim Wright of the University of Southampton, Lorna-Grace Okotto of Jaramogi Oginga Odinga University of Science and Technology, and Joseph Okotto-Okotto of VIRED International in Kenya. The team conducted one of the first empirical comparisons of road and water pipeline network structure across cities in the Global South and the Global North, using real pipeline data from four cities on three continents: Kigali in Rwanda and Kisumu in Kenya representing sub-Saharan Africa, and La Rochelle in France and Vancouver in Canada representing the Global North.

To make the comparison rigorous, the researchers converted both road and pipeline networks into dual graphs—a mathematical representation in which each street or pipe segment becomes a node, and connections are drawn between segments that share an endpoint. This representation allows centrality measures, the workhorses of network science, to be computed directly for the infrastructure segments themselves rather than for intersections. The team calculated three such measures: degree centrality, which counts how many connections a segment has; betweenness centrality, which quantifies how often a segment lies on shortest paths through the network and thus how critical it is to overall flow; and closeness centrality, which measures how efficiently a segment can reach all other parts of the network. Each metric captures a different dimension of structural importance—connectivity, flow loading, and accessibility, respectively.

The first major finding emerged from the D-measure, a graph-similarity metric developed by Schieber and colleagues and published in Nature Communications in 2017. The D-measure quantifies how dissimilar two networks are by comparing their node-to-node distance distributions, their connectivity heterogeneity, and their centrality profiles, returning zero for topologically equivalent graphs. Because it is largely insensitive to network size, it enabled fair comparison between networks of very different scales—from La Rochelle’s compact 28-square-kilometre footprint to Kigali’s sprawling 730 square kilometres. The results showed high structural similarity across all eight networks, with most similarity values between 0.8 and 0.9. But a clear regional split appeared: road networks from the two African cities were most similar to each other, and the two Northern road networks clustered together, while water pipeline networks remained remarkably similar across all four cities regardless of region. Road and water networks were also more similar to each other in the Northern cities than in the African ones, with Kigali’s road network showing the lowest similarity to water networks overall.

That regional divergence in road networks carried through to the centrality statistics. Mean degree centrality of road networks hovered near four, generally exceeding that of pipeline networks, and Vancouver’s networks showed the highest connectivity of the four cities. More tellingly, the pattern of betweenness flipped between regions: in Kigali and Kisumu, water pipelines carried higher betweenness than roads, whereas in La Rochelle and Vancouver the opposite held. The authors interpret this as evidence that the African case cities lack the primary high-capacity road corridors that dominate Northern networks—a finding consistent with prior work showing that informal settlements, which house roughly 79 percent of Kigali’s population and about 60 percent of Kisumu’s, tend to be topologically isolated, with poor connectivity to the surrounding urban fabric. Kigali’s road network, with an exceptionally narrow range of closeness values, may even approximate a tree-like structure resembling a minimum spanning tree, a signature of largely self-organised growth and, possibly, of the city’s hilly terrain.

The second analytical stage moved from pure topology into geometric space. The researchers overlaid pipeline and road layers and, to cope with positional uncertainty in the data, performed a sensitivity analysis: they drew buffers of increasing width around every street segment, in one-metre increments, and tracked how much pipeline length fell inside each buffer. Using segmented regression, they identified a breakpoint separating rapid from slower pipeline capture, which they took as the effective road width—11 metres for both Kigali and Kisumu, 7 metres for La Rochelle, and 10 metres for Vancouver. At these optimal widths, the proportion of pipeline lying co-located with roads ranged dramatically: 92.6 percent in Vancouver, 76.8 percent in Kigali, 74.2 percent in La Rochelle, and just 67.7 percent in Kisumu. The Northern cities, in other words, bury their pipes far more faithfully beneath their streets.

To quantify the coupling between the two systems, the team then extracted paired centrality values for co-located road–pipeline segments and fitted them with total least squares (TLS) regression. Unlike ordinary least squares, which assumes the explanatory variable is error-free, TLS minimises perpendicular distances to the fitted line, making it appropriate when no causal direction exists between the two variables—as is the case for roads and pipes, which influence each other rather than one determining the other. Only closeness centrality showed a sufficiently strong Pearson correlation to warrant this analysis. Across all four cities the slopes were positive: streets with high closeness tend to sit above pipelines that also have high closeness. But the slopes were steeper in the African cities, and the residual analysis revealed a systematic pattern in all four: from the urban core outward, pipeline closeness falls faster than road closeness. A Global Moran’s I test, validated with 999 Monte Carlo permutations, confirmed that these deviations were strongly and significantly spatially clustered in every city, with autocorrelation values between 0.928 and 0.957.

Mapping the outliers onto real neighbourhoods gave the pattern a human geography. Negative deviations—pipelines weaker than the roads above them—concentrated in peripheral areas such as Nyagahinga in Kigali, a low-density residential zone slated for future densification where roads exist but pipe infrastructure lags behind. Positive deviations clustered around major water facilities: Rugarama and Masaka in Kigali sit near the Nzove and Karenge water supply systems, Nyamasaria in Kisumu lies close to the private Nyamasaria Water Works, and Kibuye, Kisumu’s principal market district, hosts the city’s most important water tanks. At the upper tail, exceptionally high pipeline closeness appeared in historically integrated neighbourhoods such as La Genette in La Rochelle, a historic district outside the old city walls, and Shaughnessy in Vancouver, an affluent residential enclave. Pipeline structure, in short, is sculpted by the distribution of water facilities and urban communities, producing a heterogeneity that roads do not share.

The implications reach well beyond network theory. Contemporary planning practice often treats streets as the organising skeleton for all underground utilities, and street-led slum upgrading programmes assume that improving road connectivity will pull water and sanitation infrastructure along with it. These findings suggest that assumption holds better in the Global North than in sub-Saharan African cities, where pipelines obey organisational logics that diverge substantially from street patterns. Planners, the authors argue, should consider a settlement’s position within the wider urban network—its connectivity and its proximity to major water infrastructure—rather than relying on road layout alone as a proxy. The results also matter for asset management: because roughly two-thirds to nine-tenths of pipeline length shadows roads, excavation and renewal projects frequently interact with pipe segments of varying structural importance, and knowing where high-closeness road–pipeline pairs occur could help prioritise maintenance and reduce the risk of accidental damage where utility records are incomplete or outdated.

Why pipeline networks across all four cities converged so strongly—despite radically different histories, from La Rochelle’s medieval port morphology to Kisumu’s railway-borne origins—remains an open question, and one the authors suggest may reflect shared international norms in hydraulic engineering design. The study is explicitly exploratory, built on four cities and limited by data quality variations in OpenStreetMap and municipal pipeline records, and by the well-known caveat that topology alone captures only part of infrastructure performance. But as the first quantified, cross-regional comparison of its kind, it lays down a template: a workflow combining dual-graph topology, buffer-based co-location analysis, TLS regression, and spatial autocorrelation testing that can be scaled to many more cities as pipeline data becomes available. In a century when most urban growth will happen in the Global South, understanding that water does not simply follow the street may prove essential to building cities that work.