Topological Clustering for Geographical Networks - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 41

Fig. 3.10 A large social network and its simplification by a clustering method based on a
reachability criterion (From Levine ( 2009 ))
Levine ( 2009 ) uses this principle to simplify a large social network with nodes
that are widely spread out over the territory. According to the fact that n -cliques
may overlap each other, this author proposes to cluster distinct sets of nodes that he
selects inside the different cells of a grid (cf. Fig. 3.10 ).
In this application, the reachability is used to gather nodes that are close to each
other, but some open-ended questions remain, such as the reachability of nodes
inside clusters (although they are included in a cell, two nodes of the same cluster
may be very far from each other if the shortest path between them passes through
other cells) or the relevance of the grid in the clustering process.
From a mathematical viewpoint, the reachability criterion does not necessarily
involve a high edge density inside the n -clique: actually, n -cliques may show star-
shaped structures as in Fig. 3.9 .