Table 1 Urban indicators and their scaling relations.

Columns show measured exponent ranges (see table S3 for details). Also shown are predicted values for D = 2, H = 1 (the simplest theoretical expectation) and for general D, H. Agglomeration effects vanish as Embedded Image (14). The larger range for the observed land-area exponent is likely the result of different definitions of the city in space and distinct measurement types. See table S3 and supplementary text for specific values of observed exponents, discussion, and additional data sources.

Urban scaling relationsObserved exponent rangeModel
(D = 2, H = 1)
Model
D, H
Land area
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[0.56,1.04]Embedded ImageEmbedded Image
Network volume
Embedded Image
[0.74,0.92]Embedded ImageEmbedded Image
Network length
Embedded Image
[0.55,0.78]Embedded ImageEmbedded Image
Interactions per capita
Embedded Image
[0.00,0.25]Embedded ImageEmbedded Image
Socioeconomic rates
Embedded Image
[1.01,1.33]Embedded ImageEmbedded Image
Network power
 dissipation Embedded Image
[1.05,1.17]Embedded ImageEmbedded Image
Average land rents
Embedded Image
[0.46,0.52]Embedded ImageEmbedded Image