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These different ways of comprehending the relationship between two nodes
finally influence the choice of the clustering criterion used to study a network. In
that respect, the geographical examples presented in this chapter often adapt the
clustering criterion to the context of the study.
Several criteria may be adapted and mixed to provide a relevant clustering
method. For example, MacKechnie and Mackaness ( 1999 ) propose to simplify a
cartographic representation of a network by sequential clustering of nodes that are
closest to each other (cf. Fig. 3.18 ).
In this geographical application, Mackechnie and Mackaness finally use a similar
criterion:
￿
with the definition of a n -clique,
￿
and with the hierarchical approach relating to cut-sets (except that components
are progressively gathered together instead of being separated).
Ultimately, they build a method that is relevant for identifying possible spatial
clusters according to the level of observation.
In addition, it is important to underline that these research directions are not
exhaustive. Actually, they depend on the notion of cohesion, but within some
contexts it may be relevant to consider other clustering criteria:
￿
the adhesion notion: adhesive structures are characterized by the convergence of
ties towards a “leader” node and are representative of local hierarchies within the
network;
￿
the similarity notion: the associated structures contain similar nodes considering
the relationships they maintain with the rest of the network ( Wasserman & Faust ,
1994 ).
Finally, if the study of a geographical network is strongly dependent on the
context, application of a clustering method requires the accurate identification and
interpretation of the topological criteria that affect this operation.
References
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mgm.fr/num7/index.html
Berge, C. (1973). Graphes (3rd ed., 1983, 400 p.). Paris, France: Gauthier-Villars.
Bollobás, B. (1998). Modern graph theory (394 p.). New York: Springer.
Gleyze, J.-F. (2005). La vulnérabilité structurelle des réseaux de transport (848 p.). Unpublished
doctoral dissertation, Université Paris VII, Paris, France.
Gleyze, J.-F. (2009, September 4-8). Friendship and neighbourhood in the eurovision song
contest. In Proceedings of ecqtg09, 17th European Colloquium on theoretical and quantitative
geography . Maynooth, Ireland.
Levine, J. (2009). Large networks (13 p.). Unpublished draft, Hanover, NH: Dartmouth University.
Retrieved July 21, 2009, from http://www.dartmouth.edu/~jlevine/NSF%20%205.pdf
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