Scale-free and small-world networks in geographical research: A critical examination

A rapid surge of interest for networks in the late 1990s throughout natural and social sciences has witnessed the emergence and the diffusion of new concepts and measures. In this paper, we wish to examine how two recent models of networks (i.e. scale-free and small-world) have been integrated in the works of geographers, what have been the benefits, and whether such concepts are likely to increase their influence in further works on networks. First, we propose a critical review of the 'scale-free' and 'small-world' concepts, notably based on a review of the physics literature. The second section examines the spatial dimension in networks studies, and the third one evaluates how geographers have used these measures and concepts in their works. In conclusion, we question the benefits of these two models of networks to geography compared with other approaches such as the ones developed in sociology.

[1]  Ajay Mehra.  The Development of Social Network Analysis: A Study in the Sociology of Science , 2005 .

[2]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[3]  Denise Pumain,et al.  The Location of Multinational Firms in the European Urban System , 1993 .

[4]  C. Rozenblat,et al.  Opening the Black Box of Agglomeration Economies for Measuring Cities’ Competitiveness through International Firm Networks , 2010 .

[5]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[6]  Steven H. Strogatz,et al.  Small-world networks , 1999 .

[7]  Faraz Zaidi,et al.  Maritime constellations: a complex network approach to shipping and ports , 2012 .

[8]  Nigel Waters,et al.  Network and Nodal Indices. Measures of Complexity and Redundancy: A Review , 2006 .

[9]  Tore Opsahl,et al.  Clustering in weighted networks , 2009, Soc. Networks.

[10]  Alessandro Chessa,et al.  Modeling commuting systems through a complex network analysis: A study of the Italian islands of Sardinia and Sicily , 2010 .

[11]  Duncan J. Watts,et al.  Six Degrees: The Science of a Connected Age , 2003 .

[12]  Fahui Wang,et al.  Exploring the network structure and nodal centrality of China , 2011 .

[13]  Daniel J. Brass,et al.  Network Analysis in the Social Sciences , 2009, Science.

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

[15]  José S. Andrade,et al.  Erratum: Apollonian Networks: Simultaneously Scale-Free, Small World, Euclidean, Space Filling, and with Matching Graphs [Phys. Rev. Lett. 94 , 018702 (2005)] , 2009 .

[16]  Kongqing Yang,et al.  Geographical effects on cascading breakdowns of scale-free networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  R. Guimerà,et al.  Functional cartography of complex metabolic networks , 2005, Nature.

[18]  A K M Stoneham,et al.  The Small-World Problem in a Spatial Context , 1977 .

[19]  Mark Newman,et al.  Models of the Small World , 2000 .

[20]  Alessandro Vespignani,et al.  The effects of spatial constraints on the evolution of weighted complex networks , 2005, physics/0504029.

[21]  Michael Batty,et al.  Cities as Small Worlds , 2001 .

[22]  P. Haggett.  Network Analysis In Geography , 1971 .

[23]  L. Freeman,et al.  The Development of Social Network Analysis: A Study in the Sociology of Science , 2005 .

[24]  Gernot Grabher.  Trading routes, bypasses, and risky intersections: mapping the travels of `networks' between economic sociology and economic geography , 2006 .

[25]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[26]  F. H. W. Green,et al.  Structure of transportation networks , 1963 .

[27]  Nick Crossley,et al.  Small-World Networks, Complex Systems and Sociology , 2008 .

[28]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[29]  Cesar Ducruet,et al.  Inter-similarity between coupled networks , 2010, ArXiv.

[30]  Nick Crossley.  Book Reviews: Review article: The New Social Physics and the Science of Small World Networks , 2005 .

[31]  L. Barnett,et al.  Spatially embedded random networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  J. S. Andrade,et al.  Apollonian networks: simultaneously scale-free, small world, euclidean, space filling, and with matching graphs. , 2004, Physical review letters.

[33]  Daoli Zhu,et al.  Empirical analysis of the worldwide maritime transportation network , 2008, 0806.0472.

[34]  K. Kansky.  Structure of transportation networks : relationships between network geometry and regional characteristics , 1967 .

[35]  D. Sui.  Tobler's First Law of Geography: A Big Idea for a Small World? , 2004 .

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

[37]  Peter Nijkamp,et al.  Network Analysis of Commuting Flows: A Comparative Static Approach to German Data , 2007 .

[38]  Faraz Zaidi.  Analysis, Structure and Organization of Complex Networks , 2011 .

[39]  G. Melançon,et al.  Réseaux Multi-Niveaux : L'Exemple des Echanges Aériens Mondiaux de Passagers , 2005 .

[40]  Nadine Cattan,et al.  Attractivity and Internationalisation of Major European Cities: The Example of Air Traffic , 1995 .

[41]  Roger Stough,et al.  The Revenge of Distance: Vulnerability Analysis of Critical Information Infrastructure , 2003, cond-mat/0310427.

[42]  Koen Frenken,et al.  The Geography of Internet Infrastructure: An Evolutionary Simulation Approach Based on Preferential Attachment , 2010 .

[43]  César Ducruet,et al.  Cities in Worldwide Air and Sea Flows: A multiple networks analysis , 2011 .

[44]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[45]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

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

[47]  Marc Barthelemy.  Crossover from scale-free to spatial networks , 2002 .

[48]  Rajendra Kulkarni,et al.  Spatial Small Worlds: New Geographic Patterns for an Information Economy , 2003 .

[49]  Seth Bullock,et al.  Spatial embedding and the structure of complex networks , 2010, Complex..

[50]  Guy Melançon,et al.  A Small World Perspective on Urban Systems , 2013 .