Structural properties of planar graphs of urban street patterns
Open accessAbstract
Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological, and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street patterns of different world cities. Samples are turned into spatial valued graphs. In such graphs, the nodes are embedded in the two-dimensional plane and represent street intersections, the edges represent streets, and the edge values are equal to the street lengths. We evaluate the local properties of the graphs by measuring the meshedness coefficient and counting short cycles (of three, four, and five edges), and the global properties by measuring global efficiency and cost. We also consider, as extreme cases, minimal spanning trees (MST) and greedy triangulations (GT) induced by the same spatial distribution of nodes. The measures found in the real and the artificial networks are then compared. Surprisingly, cities of the same class, e.g., grid-iron or medieval, exhibit roughly similar properties. The correlation between a priori known classes and statistical properties is illustrated in a plot of relative efficiency vs cost.
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The comparative investigations in Cardillo et al. 2006 and Porta et al. 2006 reveal scale-free degree distributions for the vertices of spatial graphs if the ICN principle is implemented.
“The comparative investigations in (Cardillo et al. 2006 andPorta et al. 2006) reveal scale-free degree distributions for the vertices of spatial graphs if the ICN (intersection continuity negotiation) principle is implemented.”
From A Network Approach to Link Visibility and Urban Activity Location (2018) · cites this paper as Cardillo et al. 2006
In “Graph local properties” (p. 4), Cardillo et al. say they do not expect scale-free degree distributions in their planar street networks because spatial embedding limits the number of streets at an intersection. The Introduction (p. 1) defines their graph vertices as street intersections; it does not describe an ICN-based result that would support the cited claim. (LLM, conf=0.88)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredSeveral studies found scale-free degree distributions in street networks using other graph representations.
“Several studies also found scale-free degree distributions in street networks, using other graph representations (Cardillo et al. 2006;Carvalho and Penn 2004;Porta et al. 2006).”
From A Network Approach to Link Visibility and Urban Activity Location (2018) · cites this paper as Cardillo et al. 2006
Cardillo et al. represent street intersections as nodes and streets as edges (Introduction, p. 1). In Graph local properties (p. 4), they say they do not expect scale-free degree distributions in these planar street networks because spatial embedding limits node degree; they do not report finding one. (LLM, conf=0.90)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measured
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Percentages, sums and reported differences re-computed from the paper’s own numbers.
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- Authors
- Cardillo, A., Scellato, S., Latora, V., & Porta, S.
- Affiliations
- University of Catania (IT)
- Politecnico di Milano (IT)
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2006-06-07
- Volume
- 73
- Issue
- 6
- Pages
- 066107-066107
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W1976668093
- Cited by
- 370
- References
- 38
- Citations by year
- 2026: 8 · 2025: 11 · 2024: 15 · 2023: 16 · 2022: 17 · 2021: 14 · 2020: 26 · 2019: 19 · 2018: 47 · 2017: 31 · 2016: 22 · 2015: 19 · 2014: 14 · 2013: 24 · 2012: 12
- FWCI
- 47.08
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review E (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Building and Construction › Urban Design and Spatial Analysis
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Complex Network Analysis Techniques
- Social Sciences › Urban Studies › Global Urban Networks and Dynamics
- Keywords
- planar graphs, complex networks, cycle counting, global efficiency, minimum spanning tree, greedy triangulation, medieval towns
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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