Structural properties of planar graphs of urban street patterns

Alessio Cardillo, Salvatore Scellato, Vito Latora, Sergio Porta

Research output: Contribution to journalArticle

178 Citations (Scopus)

Abstract

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.
LanguageEnglish
Article number066107
Number of pages8
JournalPhysical Review E
Volume73
Issue number6
DOIs
Publication statusPublished - 7 Jun 2006

Fingerprint

streets
Planar graph
Structural Properties
Graph in graph theory
Minimal Spanning Tree
Relative Efficiency
Local Properties
Costs
Vertex of a graph
Spatial Distribution
Iron
Statistical property
Empirical Study
Triangulation
Counting
Extremes
Intersection
Grid
costs
Cycle

Keywords

  • structural properties
  • relational networks
  • urban street patterns

Cite this

Cardillo, Alessio ; Scellato, Salvatore ; Latora, Vito ; Porta, Sergio. / Structural properties of planar graphs of urban street patterns. In: Physical Review E. 2006 ; Vol. 73, No. 6.
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Structural properties of planar graphs of urban street patterns. / Cardillo, Alessio; Scellato, Salvatore; Latora, Vito ; Porta, Sergio.

In: Physical Review E, Vol. 73, No. 6, 066107 , 07.06.2006.

Research output: Contribution to journalArticle

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AB - 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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