Topological Clustering for Geographical Networks - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 43

Fig. 3.12 Clusters of countries swapping over-votes between each other in the Eurovision Song
Contest between 1993 and 2008 (From Gleyze ( 2009, September 4-8 )) (Note: all the over-votes
were taken into account in the cluster computation, but to make the figure more legible, only the
reciprocal over-votes are represented here (the edges correspond to reciprocal over-votes between
pairs of countries and the clusters are highlighted by bold lines ))

countries voter performers show an abnormal tendency to produce a high number of
votes. Then, he considers the country graph of such relations (called “over-votes”).
In this graph, the number of cliques (4) seems to be low compared with the quantity
and concentration of nodes (49) and over-votes (135). To detect larger structures,
Gleyze suggests lightening the exhaustiveness criterion. In that respect, he defines
a cluster as a set of nodes so that the over-vote density is not necessarily equal to
1, but must be higher than three quarters. In compensation, he demands that two
degree criteria be verified:

￿ each country of a cluster must give and receive at least one over-vote from another

country of the cluster,

￿ there must be at least one over-vote between each pair of countries in the cluster.

The Fig. 3.12 shows the country clusters highlighted by this method. While only
four cliques were identified at first, these degree criteria allow for the detection of
larger cohesive structures and their possible interactions.
Finally, the clustering methods based on the degree criterion guarantee the
redundancy of relations and thus strong cohesion among subgroup nodes. In the