A Small World Perspective on Urban Systems - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 18

globalization has been developed at a worldwide scale for stock exchange, while
“global value chains” of production are developing, most of the time, at a continental
scale, leveraging from “regional” international trade arrangements ( Dicken, Kelly,
Olds, & Yeung , 2001 ; Doz, Santos, & Williamson , 2001 ).
The hypothesis we just stated suggests that all transformations strongly depend
on the internal and external relations of network components, calling for a study of
the relative positions of places in networks and at different geographical scales.
Geographical interactions can be studied through multi-dimensional networks,
which can be considered as graphs. To date, most geographical network stud-
ies were based either on gravity models ( Wilson , 1967 ) or on general indexes
of graph connectivity or accessibility ( Kansky , 1963 ). Graph theory and more
particularly Watts' theory of small-world networks ( Watts , 1999 ) can feed this
trend of research and enrich spatial analysis as a complement to systems theory.
Networks indeed organize through direct links or by indirect paths, inducing
topological proximities that simultaneously involve spatial, social, cultural or
organizational dimensions. Network synergies, either based on the similarities
or the complementarities between or inside cities, create specialized and more
or less stable proximities between these entities ( Powell , 1990 ). Interrelations
between geographical scales of organization also allow an understanding of the
equilibrium or disequilibrium of territories emerging at different geographical
scales. The concepts and methods of the small-world theory are particularly relevant
to geography, in which spatial interaction is mainstream and where interactions
can be described and studied using large numbers of exchanges or similarity
matrices. As far as we know, this type of empirical approach combining a conceptual
approach of the “small-world theory” and dedicated tools has not been developed in
geography.
Multi-level analyses and the visualization of graphs bring new questions. How do
networks link similar actors, reinforcing their social proximities as well as spatial
specializations and segregations? In this sense, how do networks (not only transport
and communication networks but also social and economic networks) increase
the anisotropy of space? How far are networks from random processes, instead
creating densely connected groups of nodes separated from others, like “small-
world” networks ( Watts , 1999 ; Watts & Strogatz , 1998 )? What are the properties
of these networks, and what consequences can we infer for geographical places,
especially for cities?
In this presentation, we will stress the advantages of analyzing and visualizing
networks using their network properties (Sect. 2.2 ). Then, we will underline
topological positions in a static state as well as from a dynamic perspective
(Sect. 2.3 ) and transfer them onto properties of city systems (Sect. 2.4 ). The final
section discusses levels of organizations, taking into account empirical findings on
hierarchical clustering (Sect. 2.4 ).