Source-linked AI summary
Self-organization versus top-down planning in the evolution of a city
Marc Barthelemy, Patricia Bordin, Henri Berestycki, Maurizio Gribaudi
TL;DR
Cities may reflect both self-organization and central planning, complicating naive models of urban dynamics. Using Paris as a case study, the paper compares planned Haussmann transformations with natural evolution and finds that planning reorganized centrality through large-scale, unconstrained road changes.
Problem
Central planning interventions in cities may limit models that treat urban evolution as self-organized, making Paris under Haussmann a critical test case.
Method
The study analyzes Paris’s street network by applying physical quantitative measures to compare Haussmann’s planned transformation with its natural evolution.
Results
The main quantitative signature of central planning is a spatial reorganization of centrality, while most network indicators follow smooth evolution dominated by densification.
Takeaways & Limitations
Central planning operates through large-scale road creation and destruction that connects distant important nodes, after which natural processes continue on the modified network.
Takeaways & Limitations
The study needs more data at a larger spatial scale to determine whether Haussmann’s modifications were optimal or inevitable.
Abstract
from arXiv · showhide
Interventions of central, top-down planning are serious limitations to the possibility of modelling the dynamics of cities. An example is the city of Paris (France), which during the 19th century experienced large modifications supervised by a central authority, the `Haussmann period'. In this article, we report an empirical analysis of more than 200 years (1789-2010) of the evolution of the street network of Paris. We show that the usual network measures display a smooth behavior and that the most important quantitative signatures of central planning is the spatial reorganization of centrality and the modification of the block shape distribution. Such effects can only be obtained by structural modifications at a large-scale level, with the creation of new roads not constrained by the existing geometry. The evolution of a city thus seems to result from the superimposition of continuous, local growth processes and punctual changes operating at large spatial scales.
Introduction
The paper examines whether Paris’s street-network evolution can be modelled as self-organization despite major central-planning interventions during the Haussmann period. It reconstructs the network across more than 200 years to compare planned transformations with other phases of urban evolution.
- Paris’s complex urban dynamics reflect interactions among many diverse agents, raising the possibility that cities emerge through self-organization.
- Central planning, understood as a top-down process controlled by a central authority, can leave long-standing traces in city evolution.
- The study focuses on Paris’s street network over more than 200 years, especially the major transformations supervised by Baron Haussmann in the 19th century.
- The authors use physical quantitative measures to compare Haussmann’s planned transformation with the city’s “natural” evolution during other periods.
- Historical maps are digitized into a GIS to reconstruct detailed road systems, including minor streets, at six moments from 1789 through 2010.The corresponding years are 1789, 1826, 1836, 1888, 1999, and 2010.
- The analysis uses a common inner-Paris area of roughly 34 km^2, while noting that larger-scale study is needed to capture the city’s complete evolution.
Results
Across 1789–2010, Paris’s street network generally evolved through smooth densification, while Haussmann’s main signatures were a spatial redistribution of centrality and altered block shapes.
- Quantitative analysis targeted node, edge, and total-length evolution, new-link typology, betweenness-centrality impact, spatial centrality redistribution, and block geometry.
- About 3,000 nodes in 1836 became about 6,000 in 1888, while total length rose from about 400 kms to almost 700kms during the Haussmann period.The increase occurred over about 50 years and corresponded essentially to population growth.
- The rescaled average route distance decreased with time and network size, indicating easier navigation as the network became denser when junction delays are neglected.
- Most new links represented densification across all periods, with only a small exploration peak in 1836–1888, making Haussmann’s period broadly comparable to earlier periods.
- Node betweenness-centrality distributions remained smooth overall, but Haussmann works dramatically redistributed the spatial structure of centrality between 1836 and 1888.After Haussmann, the reorganized centrality pattern remained largely stable until the present.
- Haussmann’s new roads and avenues were approximately 6% of the present network’s total length yet produced a major reorganization of centrality.
- Before Haussmann, block-shape values centered around φ = 0.5, whereas from 1888 the distribution flattened and values φ < 0.25 increased, indicating more elongated shapes.The changes followed new roads and avenues that destroyed parts of the original pattern.
Discussion
Paris’s street network shows mostly smooth evolution, but Haussmann-era planning produced a large-scale reorganization of centrality and street geometry. The findings support a combination of local self-organized growth and punctual, city-scale interventions.
- Most network indicators evolved smoothly through densification, despite the major Haussmann-era perturbation.
- Haussmann planning reorganized the most central nodes by creating roads and avenues that crossed existing geometry at various angles.
- Natural road growth is generally local, whereas Haussmann modifications occurred rapidly at large spatial scales by connecting important, distant network nodes.
- Before 1836, block-shape distributions were stable; during Haussmann’s period, small-φ blocks became more abundant, indicating elongated rectangles and triangles.
- Before Haussmann, road angles clustered around two values separated by approximately 90 degrees; by 1888, diagonals and intermediate angles were more common.
- The study leaves open whether Haussmann’s modifications were optimal or inevitable, and calls for more data at a larger spatial scale.
Methods
The study reconstructs Paris’s historical street networks as temporal spatial graphs and evaluates their structure using route-distance, betweenness-centrality, link-impact, and block-form measures.
- Temporal network data: Paris’s street networks are represented as primal graphs Gt, with street junctions as nodes and road segments as links at each time.The temporal graph records newly added junctions and streets between successive snapshots.
- Route distance: Average route distance dR measures the mean shortest weighted path length between node pairs, with edge weights given by Euclidean street lengths.The weighted shortest path minimizes total path length and expresses average walking distance through the network.
- Betweenness centrality: Betweenness centrality measures how often a link or node participates in shortest paths, thereby quantifying its contribution to organizing network flows.For links, g(e) counts shortest paths containing the edge; node BC is defined analogously.
- Link impact: The impact δ(e*) of a newly added link is the relative variation in average edge betweenness caused by removing that link from the graph.The procedure compares average edge betweenness before and after removal of e*.
- Block geometry: Block form factor φ is the ratio of block area to the area of its circumscribed circle, decreasing as the block becomes more anisotropic.The measure captures the geometric shape of urban blocks.
Population and nodes
Paris’s node count increased sharply during the Haussmann period and showed a linear relationship with population in the analyzed area.
- Population and nodes: The number of nodes N was proportional to population P, with dN/dP = 0.0021.Because the historical areas differ, the population comparison supports only the order of magnitude.
Type of new links
The proportions of different new-link types changed smoothly over time, and the Haussmann period was not radically distinct by this measure.
- Type of new links: The evolution of the proportions of different types of new links was rather smooth across the studied periods.The figure classifies new links according to the number of newly connected nodes.
- Type of new links: The Haussmann period was not radically different from previous periods in the proportions of new-link types.The figure notes that denser networks have smaller E2 values.
- Type of new links: Figure 9 compares the evolution of Paris’s node count with population and shows a linear fit with r2 > 0.99.The plotted relationship is between the number of nodes and population.
Stability of the BC distribution
Vertex betweenness-centrality distributions remained stable in shape across the historical snapshots, while average BC decreased slightly over time.
- Stability of the BC distribution: The average vertex BC decreased slightly across the studied time snapshots.The decrease indicates greater navigability in the system.
- Stability of the BC distribution: The overall probability distribution of vertex BC remained constant in time.The distribution’s overall shape and tail stayed the same across all snapshots.
Most central nodes: stability of spatial patterns
The identified spatial patterns of Paris’s most central nodes remain robust across the tested α values, with α = 10 providing an intermediate view.
- Most central nodes are defined by gv > max gv/α.
- The spatial patterns remain relatively robust when α varies between 5, 10, and 15.
- α = 10 represents an intermediate situation displaying interesting spatial patterns.
Spatial pattern of the most central edges
The spatial pattern of the most central edges is consistent with the pattern obtained from central nodes across the considered dates.
- Most central edges are selected using ge > max ge/α with α = 20.
- The most central-edge patterns are presented for the different dates in Fig. 13.
- The edge-centrality pattern is naturally consistent with the pattern obtained from node centrality.
- For four time points, the spatial pattern of the most central nodes is robust to the value of α.