A Small World Perspective on Urban Systems - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 22

Fig. 2.3 Urban-area
delineation using transitivity
properties

2.4 Network Properties As Cities Systems Properties

The small-world property has a clear interpretation for territories in general and
for urban systems in particular. The short average distance between entities can
be seen as a consequence of redundant paths through different routes between city
networks, strengthening direct and/or indirect interaction. This mutual interaction is
mainly through “clusters”, which can form inside cities or towns and that are heavily
connected by groups at another level between cities.

2.4.1 Urban Systems As Small Worlds

Empirical evidence of these networks is founded on some basic properties rein-
forcing these strengths ( Monge & Contractor , 2003 ), which, in transposition, could
make sense for geographical network organizations:

￿ Transitivity: This elementary property was shown early by sociologists

( We i m a n n , 1980 ): If an individual A is linked to B, and B is linked to C,
then A is most likely linked to C.
In geographical perspectives, we can transpose this property to interaction and
interdependency effects. If a place A is closely related and interdependent on B,
and B is linked to C then A is interdependent on C. For example, commuter
exchanges between municipalities create these kinds of chain dependencies
(Fig. 2.3 ). If a factory employing several thousands of people in A suddenly
closes, it will affect the residential population of B that sends commuters to A,
but in consequence, it also will affect C sending commuters to B. Sometimes, this
transitive relation is materialized by real exchanges (like commuters), but even