Topological Clustering for Geographical Networks - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 37

The clustering tools stemming from graph theory help to highlight the similarities
between the individuals of a social graph, taking into account the relationships they
maintain based on several criteria.
The different clustering methods presented in this chapter are based on the
research work of Wasserman and Faust ( 1994 ) and Moody and White ( 2003 ), and
we discuss those works from a geographical perspective.

3.3.1 The Cohesion Concept

The following clustering methods are based on the concept of “cohesion” between
the “members”, i.e., individuals, of the same subgroup.
The Petit Robert French dictionary defines cohesion as:

￿ the strength that brings together the parts of a material substance;

￿ the feature of a set whose parts are united, matched.

This definition is very close to the meaning of cohesion in graph theory as applied
to sociology, as it defines subgroups of individuals who are strongly united by the
relationships between them.
It is quite important to distinguish the cohesion concept from the adhesion
concept related to structures centered on a node. Such structures are characterized
by the convergence of many ties towards a “leader”, node and therefore are strongly
dependent on the status of this node. For this reason, “adhesive” structures are
fragile because they can easily be affected by acting on this node.
On the contrary, “cohesive” structures are characterized by many independent
ties that unite their members. 1

Groups with stronger cohesion are more difficult to

split.
Finally, the group cohesion is affected by the arrangement of ties within the
group. Groups with stronger inner ties exhibit a better ability to hold together.

3.3.2 Qualitative Elements to Identify Cohesive Structures

The structure of a group is best held together when all its members are linked in
pairs. Such a structure corresponds to the “clique” notion of graph theory, but is
rarely observed because the lack of a single tie is enough to “downgrade” this
structure. However, the criterion of edge “exhaustiveness” specific to cliques can
be relaxed and lead to more convincing clustering methods that remain operational.

1 The contrast between cohesive and adhesive structures appears in the etymology of these words.
On the one hand, the words cohesion, colleague, and companion refer to notions of equality or
numerous connections; on the other hand, the words adhesion, adversary, and administrator refer
to notions of centrality or reference Moody & White ( 2003 ).