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Finally, the clustering methods based on cut-sets cannot be directly applied to
geographical issues because of the high edge-density of geographical networks.
However, a criterion based on network weakness may indicate the components
that are likely to segment the network in the same way as cut-sets. For that reason,
this criterion has to be considered as a segmentation method instead of a clustering
method.
3.5
Conclusion
Graph theory provides clustering methods that help to simplify networks into
cohesive subgroups, i.e., into subgroups in which nodes are close to each other and
are difficult to disconnect. These methods depend on criteria whose implementation
may lead to splits of various sizes and natures. This review is not exhaustive;
nevertheless, it is representative of the main topological criteria that are commonly
used to build cohesive subgroups (cf. Fig. 3.17 ).
These clustering methods fit with three main ways to comprehend the relation-
ship between two nodes of a graph:
￿
according to the exhaustiveness and degree criteria, the relationship is assessed
in view of the presence or absence of an edge between these nodes;
￿
according to the reachability criterion, the relationship is assessed in view of the
connection quality, i.e., the length of the best path linking these nodes;
￿
finally, according to the inter-/intra-group and connectivity criteria, the rela-
tionship is assessed in view of the robustness of the connection, i.e., of the
Fig. 3.17
Main topological clustering criteria
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