Abstract
Studying geographical networks is made difficult by their size and complexity. Graph theory and its developments in sociology provide formal tools to simplify a graph by identifying cohesive subgroups inside the graph. This set of tools is based on clustering criteria, which use the extent of ties within subgroups, the node reachability, the node degree, the balance between inter- and intra-group ties and the subgroup connectivity. Graph theory also provides extensions that help to model the edge directions and the edge values and then take attributes specific to the geographical context into account. Finally, this set of methods provides a formal framework to simplify a network based on relevant topological criteria and develop new clustering rules for geographical networks in view of the context of the study.
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Notes
- 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).
- 2.
As defined, a n-clique may have a diameter greater than n because the shortest paths between its nodes may pass through the outer edges of the n-clique. Nevertheless, there are variants of this clustering method that control the subgroup diameter. Subgroups extracted by such methods are called “n-clans” and “n-clubs” (for further information, see Moody & White, 2003; Wasserman & Faust 1994).
- 3.
Subgroups with a similar criterion can also be built by considering the minimum number of adjacencies (rather than the maximum number of “non-adjacencies”), which we define as the k-core. A k-core is then a maximal subgroup of n nodes where each node is adjacent to at least k other nodes (Moody & White, 2003; Wasserman & Faust, 1994).
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Gleyze, JF. (2013). Topological Clustering for Geographical Networks. In: Rozenblat, C., Melançon, G. (eds) Methods for Multilevel Analysis and Visualisation of Geographical Networks. Methodos Series, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6677-8_3
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