Introduction - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 3

diffusion of ideas between these scientific communities. Similarly, many researchers
in sociology, mathematics and physics, such as Rashevsky, Landau, Landahl,
Lazerfeld, Merton, Moreno, and White in sociology and Erdos, Rényi, and Rapoport
in mathematics, continued to develop the field of network analysis to evaluate
network structure and the relative position of different network nodes. However,
their structural network theories exerted little influence on research in social
geography and spatial analysis, which focused investigations at the territorial scale
( Chorley & Haggett , 1969 ).
Networks, which are organised through both direct links and indirect paths,
induce topological proximities that simultaneously integrate spatial, social, cul-
tural and organisational dimensions. Although the spatial systems approaches that
emerged in the 1970s and the new paradigms of the 1990s have increasingly
examined networks in which the “space of flows” interacted with the “space of
places” ( Castells , 1996 ), the framework guiding empirical studies of “networks in
spatial systems” continues to lack relevant tools and concepts.
Network synergies based either on the similarities or complementarities between
and within cities create specialised and relatively stable proximities between these
entities ( Powell , 1990 ). Interrelations between geographical levels of organisation
also provide information regarding the equilibrium or disequilibrium of the territo-
ries that emerge at different geographical scales. From a geographical perspective
that focuses on spatial interactions, the concepts and methods of the small-world
model are particularly relevant because these interactions can be described and
studied using large volume exchange and similarity matrices.
To the best of our knowledge, the field of geography has not employed this type
of empirical model, which integrates a “network theory” approach with specialised
methods. This perspective is based on Small-World Theory (Sect. 1.1 below),
Scaling laws (Sect. 1.2 ), and multilevel approaches (Sect. 1.3 ), which lead to the
multiscale (Sect. 1.4 ) and multidimensional (Sect. 1.5 ) analyses that are presented
in this volume.

1.1 “Small-World” Networks

Networks develop privileged links between subset of nodes that subsequently are
distinct from other nodes, while the network globally establishes a “small-world”
web. This “small world” approach first appeared in the Hungarian writer Karinthy's
“Chain-links” story, which described a fictional world in which all individuals were
connected with each other through five acquaintances (Karinthy, 1929, as cited
in Newman, Watts, & Barabasi , 2006 ). The Milgram experiment, which involved
sending a document from a random panel of “starting persons” to a “target person”,
empirically evaluated the “six degrees of separation” concept ( Milgram , 1967 ;
Travers and Milgram, 1969 ) and was inspired by Pool and Kochen, who addressed
this problem in a 1958 working paper that was not published until 1978 ( Pool
& Kochen , 1978 , cited in Newman et al. , 2006 ). The “small world” model was