Co-evolution of Density and Topology in a Simple Model of City Formation

We study the influence that population density and the road network have on each others’ growth and evolution. We use a simple model of formation and evolution of city roads which reproduces the most important empirical features of street networks in cities. Within this framework, we explicitly introduce the topology of the road network and analyze how it evolves and interact with the evolution of population density. We show that accessibility issues -pushing individuals to get closer to high centrality nodes- lead to high density regions and the appearance of densely populated centers. In particular, this model reproduces the empirical fact that the density profile decreases exponentially from a core district. In this simplified model, the size of the core district depends on the relative importance of transportation and rent costs.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[2]  C. Nash-Williams,et al.  Random walk and electric currents in networks , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  J. H. V. Thunen,et al.  Von Thunen's isolated state , 1967 .

[4]  B. Berry,et al.  Central places in Southern Germany , 1967 .

[5]  B. Ripley,et al.  Pattern Recognition , 1968, Nature.

[6]  A. Dixit,et al.  Monopolistic competition and optimum product diversity , 1977 .

[7]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[8]  Godfried T. Toussaint,et al.  The relative neighbourhood graph of a finite planar set , 1980, Pattern Recognit..

[9]  Ronald L. Graham,et al.  On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.

[10]  Mischa Schwartz,et al.  Telecommunication networks: protocols, modeling and analysis , 1986 .

[11]  Jan K. Brueckner,et al.  THE STRUCTURE OF URBAN EQUILIBRIA: A UNIFIED TREATMENT OF THE MUTH-MILLS MODEL* , 1987 .

[12]  Bernard Derrida,et al.  Statistical properties of randomly broken objects and of multivalley structures in disordered systems , 1987 .

[13]  Bernard Derrida,et al.  Distribution of local magnetisations in random networks of automata , 1987 .

[14]  Allen C. Goodman,et al.  An econometric model of housing price, permanent income, tenure choice, and housing demand , 1988 .

[15]  R. Graham,et al.  The Shortest-Network Problem , 1989 .

[16]  C. Itzykson,et al.  Statistical Field Theory , 1989 .

[17]  C. Itzykson,et al.  Statistical Field Theory: Random geometry , 1989 .

[18]  P. Armbruster,et al.  Creating Superheavy Elements , 1989 .

[19]  Coniglio.  Fractal structure of Ising and Potts clusters: Exact results. , 1989, Physical review letters.

[20]  B. Duplantier,et al.  Statistical mechanics of polymer networks of any topology , 1989 .

[21]  Godfried T. Toussaint,et al.  Relative neighborhood graphs and their relatives , 1992, Proc. IEEE.

[22]  H. Stanley,et al.  Modelling urban growth patterns , 1995, Nature.

[23]  Alessandro Flammini,et al.  Universality Classes of Optimal Channel Networks , 1996, Science.

[24]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[25]  A. Rinaldo,et al.  Fractal River Basins: Chance and Self-Organization , 1997 .

[26]  Adrian Bejan,et al.  Streets tree networks and urban growth: Optimal geometry for quickest access between a finite-size volume and one point , 1998 .

[27]  J. S. Andrade,et al.  Modeling urban growth patterns with correlated percolation , 1998, cond-mat/9809431.

[28]  Donald L. Turcotte,et al.  Fractal River Basins–Chance and Self‐organization , 1998 .

[29]  P. Krugman,et al.  The Spatial Economy , 1999 .

[30]  Amos Maritan,et al.  Size and form in efficient transportation networks , 1999, Nature.

[31]  Philip Ball,et al.  The Self-Made Tapestry: Pattern Formation in Nature , 1999 .

[32]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[33]  J R Banavar,et al.  Topology of the fittest transportation network. , 2000, Physical review letters.

[34]  A. Venables,et al.  The Spatial Economy: Cities, Regions, and International Trade , 2000 .

[35]  K. Goh,et al.  Universal behavior of load distribution in scale-free networks. , 2001, Physical review letters.

[36]  M. Barthelemy.  Betweenness centrality in large complex networks , 2003, cond-mat/0309436.

[37]  Marc Barthelemy,et al.  Spatial structure of the internet traffic , 2003 .

[38]  B. Palsson,et al.  Genome-scale models of microbial cells: evaluating the consequences of constraints , 2004, Nature Reviews Microbiology.

[39]  Christophe Claramunt,et al.  Topological Analysis of Urban Street Networks , 2004 .

[40]  Colin McDiarmid,et al.  On the Number of Edges in Random Planar Graphs , 2004, Combinatorics, Probability and Computing.

[41]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[42]  Richie Khandelwal,et al.  PATTERNS IN NATURE , 2005 .

[43]  P. Prusinkiewicz,et al.  Modeling and visualization of leaf venation patterns , 2005, SIGGRAPH 2005.

[44]  Michael Batty,et al.  Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals , 2007 .

[45]  K Sneppen,et al.  Networks and cities: an information perspective. , 2005, Physical review letters.

[46]  A. Clauset,et al.  Scale invariance in road networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  David Levinson,et al.  Self-Organization of Surface Transportation Networks , 2006, Transp. Sci..

[48]  Michael T. Gastner,et al.  Optimal design of spatial distribution networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Pablo Jensen.  Network-based predictions of retail store commercial categories and optimal locations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[50]  V. Latora,et al.  The Network Analysis of Urban Streets: A Primal Approach , 2006 .

[51]  V. Latora,et al.  The backbone of a city , 2005, physics/0511063.

[52]  V. Latora,et al.  Structural properties of planar graphs of urban street patterns. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  V. Latora,et al.  Centrality measures in spatial networks of urban streets. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  Dirk Helbing,et al.  Scaling laws in the spatial structure of urban road networks , 2006 .

[55]  Michael T. Gastner,et al.  The spatial structure of networks , 2006 .

[56]  Guy Theraulaz,et al.  Topological patterns in street networks of self-organized urban settlements , 2006 .

[57]  Alessandro Flammini,et al.  Modeling urban streets patterns , 2007 .

[58]  David M Levinson,et al.  Density and Dispersion: The Co-Development of Land Use and Rail in London , 2007 .

[59]  D. Helbing,et al.  Growth, innovation, scaling, and the pace of life in cities , 2007, Proceedings of the National Academy of Sciences.

[60]  Alessandro Flammini,et al.  Modeling urban street patterns. , 2007, Physical review letters.

[61]  Ravindra K. Ahuja,et al.  Network Flows , 2011 .

[62]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[63]  October I.  Physical Review Letters , 2022 .