A Small World Perspective on Urban Systems - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 23

if there are not such direct materialized exchanges, interdependencies also occur
through indirect effects. Therefore, some local chains create tangled networks,
allowing very integrated local systems of territories (see Chap. 12 ).
At the inter-urban scale, interdependencies also make sense in mutual ex-
changes (symmetric or not), increasing proximities in terms of space (e.g., local
or regional economical networks) or specialization (e.g., worldwide clusters
linked through multinational firms' global value chains or through research
centers). These new proximities stimulate the growth of exchanges, strengthening
the closeness of some specific groups of cities or territories in spatial, economic,
social or cultural proximities.

￿ Homophily: Networks between actors, territories or cities with similar attributes

have a greater probability of occurring. These exogenous criteria actually interact
with networks because exchanges could also transform places as they transform
individuals with imitative behaviors and diffusions of many types of ideas,
concepts and technologies.

￿ Range: In parallel to homophily, diversity of the elements of places and cities

linked by networks seems essential to the reproduction and renewal of territorial
systems. This diversity could be seen in terms of exogenous (for example, the
diversity of activity sectors) and endogenous characteristics (the diversity of links
to other places).

2.4.2 Urban Systems As Scale-Free Networks - Hierarchies

of Individuals

There is evidence in urban systems that innovations spread preferentially from
the largest cities, already a concentration of multiple networks, to the smallest
ones ( Batty , 2005 ; Pumain , 2006 ). At a micro level of individual behavior, these
processes are largely due to the search for security rather than maximization, in
a context of partial information in game theory ( Luce & Raiffa , 1957 , Chapter
3, Section 2). The “bounded rationality” concept mainly developed by Simon
( 1955 , 1972 , 1999 ) explains why, in a context of a random probability of meeting
opportunities, individuals choose the first satisfactory opportunity rather than the
best one. These trends lead to a strengthening of major cities, where opportunities
are more diversified and where interactions are maximized, decreasing transaction
costs ( Coase , 1937 ). This process allows some specific properties of centralities,
equivalence or structural equivalence for places or groups of places according to the
positions of located individuals.

￿ Centralities: inequalities between places in terms of their relative position in

networks are obviously dependent on accessibility or reachability into some set
of places in a certain context and at a certain period ( Bretagnolle, Pumain, &
Rozenblat , 1999 ). Many kinds of indexes allow close analysis of these central