A Small World Perspective on Urban Systems - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 28

the overall dynamics of a network. The significance of these entropy indexes could
be interpreted as usual for entropy as signifying the degree of information contained
in each group or information for each node ( Lin , 1999 ; Shannon , 1948 ). With greater
information included inside a node or group, the node or group's resilience and
capability to renew are greater. Therefore, maximum entropy corresponds to a great
variety of links for each node (balanced participation in many groups) or, at the
level of clusters, various contributions of the nodes forming each group (and not
only one in the case of star patterns). This variety contains a high disorder and could
be interpreted as the system's high capability to maintain and renew itself ( Bailey ,
1990 ; Burt , 2005 ). This pattern illustrates for a particular node the “strength of weak
ties” introduced by ( Granovetter , 1973 ), in which a node has more opportunity for
a large number of weak links by relying on differentiated clusters formed by larger
links. In those clusters, the vicinities of economic links can develop processes of
agglomeration economies or network economies. However, weak links between
clusters are a source of diversity, which also produces a savings network, which
allows cities both to operate and renew themselves.
It is the coupling between strong and weak links that allows the reproduction of
the urban system and its transformations ( Guimerà et al. , 2005 ; Uzzi , 1997 ). We
could identify such types of clusters between cities in different kinds of networks
(e.g., transport, communication, migrations, multinational companies, etc.), and we
could specify for each city the intensity of its membership in a cluster and assess
to what extent these clusters correspond to territorial logic (of continents, countries
or urban areas) or the logic of economic specialization (cities specialized in the
same fields).
Besides diversity, specialization and “closure” are common patterns in networks,
according to the general form of “scale-free” laws (see above). The slope index
of the “scale-free function” can also constitute a norm used to measure high
concentrations ( Batty , 2005 ; Pumain, Paulus, Vacchiani-Marcuzzo, & Lobo , 2006 ).
Then, the scale-free measures of the contributions inside each group could be
adopted, but difficulty remains in defining these groups and their relative positions.

2.5 Conclusion

It is essential that our knowledge of all of the properties of these networks of cities be
deepened through a multi-level perspective. Identifying, qualifying and measuring
each level could better facilitate globalization because, at each level, there are many
processes that allow the emergence of urban properties in which “the whole becomes
not only more than but very different from the sum of its parts” ( Anderson , 1972 )
(as cited in Lane, 2006 ).
These methods facilitate the definition and qualification of new properties of
spatial resources based on networks, and new spatial groupings then lead to very
new approaches in geography. We have to test the contributions of these methods to
empirical studies and underline the new questions they bring out.