A.6 Graphic Files. A Scale-Free Transportation Network Explains the City-Size Distribution. Figure 6. The Interstate route map (abridged).

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1 A Scale-Free Transportation Network Explains the City-Size Distribution A. Graphic Files Figure. The Interstate route map (abridged). Figure. A typical airline s route configuration (pre-merger Continental Airlines).

2 A Scale-Free Transportation Network Explains the City-Size Distribution 0. x # New York # Chicago # Houston # Philadelphia 0.0 # Los Angeles 0. x (a) Linear Scale 0 0. # New York # Los Angeles #0 Beaumont, TX #99 University City, MO 0.0 # New Amsterdam, IN 0. #0 Hillsboro, TX 0. # Harristown, IL # Sutton, NE 0.0 (b) Log Scale Figure 8. Frequency plot of the city-size distribution. Dots are size proportionate. See table for explanation of the cities selected in the figure. source: US Census 000.

3 A Scale-Free Transportation Network Explains the City-Size Distribution Figure 9. Population density by CBSA (persons/km ). source: Census 000.

4 A Scale-Free Transportation Network Explains the City-Size Distribution Distribution log LH KS log step geo/arith θ BIC AIC ˆr ˆδ Belgium /.09 Belgium / Belgium.8 0/.09 Belgium / Belgium / MA / MA / MA.9 0/.00 MA / MA / CBSA /.008.0e+0.0e+0 CBSA /.008.8e+0.8e+0 CBSA.8 0/.008 CBSA /.008.9e+0.89e CBSA /.008.0e+0.0e+0 Places /.9e-0.9e+0.9e+0 Places /.9e-0.9e+0.9e+0 Places.8 0/.9e-0 Places /.9e-0.0e+0.00e Places /.9e-0.e+0.e+0 Places Lognormal as Degree Dist /.9e-0.9e+0.9e+0 Places GEV as Degree Dist /.9e-0.9e+0.9e+0 Table. Model Comparison Row color corresponds to the line colors in figures to. denotes a statistic the higher value of which indicates a better fit and, the other way around. In the first row, log LH denotes the average of the log of likelihood values, KS denotes the Kolomogorov-Smirnov statistic, log step measures the geometric mean of the step F(s i ; θ) F(s i ; θ) in the logarithmic scale. Geo/arith measures the ratio between geometric mean and arithmetic mean of the step. The closer the geometric mean is to the arithmetic mean, the better the fit is. It is zero for Places due to multiple cities having the same size. θ counts the number of parameters. BIC and AIC stand for Bayesian and Akaike Information Criteria for detecting overfitting. Boldface with white foreground marks the winner and boldface with black foreground denotes the runner-up among the five distributions tested. See the last paragraph in section. for an explanation of the last two rows.

5 A Scale-Free Transportation Network Explains the City-Size Distribution Arlon Beringen Genk Mouscron Antwerp # Antwerp # Genk # Mouscron # Beringen 0. 0 (a) #9 Arlon Figure. Model Comparison (Belgium) Enid, OK Beaumont, TX Huntsville, AL Anchorage, AK Tulsa, OK St. Louis (a) New York.00 # New York #8 St. Louis #8 Tulsa, OK # Beaumont, TX # Huntsville, AL #8 Anchorage, AK # Enid, OK Figure. Model Comparison (MA)

6 A Scale-Free Transportation Network Explains the City-Size Distribution # New York #8 St. Louis # Beaumont, TX # Green Bay, WI New York St. Louis 0.0 Beaumont, TX Green Bay, WI 0. Sunbury, PA Hinesville, GA Andrews, TX #8 Sunbury, PA 0.0 # Hinesville, GA #9 Andrews, TX 0. (a) Figure. Model Comparison (CBSA) New York Beaumont, TX University City, MO 0.0 Hillsboro, TX Harristown, IL Sutton, NE New Amsterdam, IN 0. #0 Beaumont, TX# New York #99 University City, MO #0 Hillsboro, TX # Sutton, NE # Harristown, IL (a) 0. # New Amsterdam, IN Figure. Model Comparison (Places).00