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number of edges to eliminate to disconnect the graph. In Chap.
6
,Lambert,
Bourqui and Auber presented geographically nested and socially nested network
dichotomies. The geographical organisation identified the intercontinental links that
dominated the air passenger traffic network. Globalisation facilitated the emergence
of clusters at the centre of the worldwide network, which emerged as essential links
between continents. Because the analysis was driven by the network topology, we
were able to detect which parts of the network remained in continental organisations
and which parts transcended them.
The present volume revealed how each node of a network participates and
contributes to the formation of clusters (Chap.
5
). Because a node can participate
in more than one cluster, the concepts of “participation” and “contribution” inspired
from factor analysis were used to evaluate how each node participated in specific
clusters and the extent to which participation in a specific cluster contributed to its
internal cohesion. This approach identified several issues:
The extent to which these procedures could be used to evaluate polycentric
structures, such as the commuters described in Chap.
12
;
The extent to which these measures might be described at multiple levels;
How to introduce fuzzy measures in cluster membership.
Various methods to define clusters were developed by the authors of this
volume: DAGMaps, strength clustering, Lambda-sets, and multistep methodologies.
Comparisons of different methods of clustering developed for air passenger traffic
(in Chap.
9
) and commuting (in Chap.
12
) did not identify a universal method
for detecting the communities comprising different patterns and indicated that
clustering is a strategic approach that must be adapted to each specific problem.
Detecting clusters simplified large and complex networks by abstracting cohesive
groups and aggregating these groups into higher-level entities to produce smaller,
simpler networks. Addressing the issues raised by clustering graphs, Gleyze
distinguished two concepts (Chap.
3
). The concept of “cohesion” corresponds to
the currently popular notion of modularity that is often embodied and measured by
edge density. However, other types of clusters that do not qualify as dense subgroups
might also be of interest, such as star-shape clusters with the central concept of
“reachability”. The same network may exhibit different patterns, depending on the
level or scale at which it is defined. This heterogeneity of patterns requires new
methods to detect the different levels of networks' organisation.
6
Interactions Between Levels
Examining interrelations between organisations at different geographical scales
contributes to the understanding of the equilibrium and disequilibrium of territories
(Chap.
2
). Many social phenomena developed at one level have their root in other
levels, and these levels interact. This interaction is illustrated by the subsidiarity
of firms, which is produced both by local processes in cities and by their global
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