Topological Clustering for Geographical Networks - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 47

Fig. 3.16 Stations of the Parisian Metro network whose successive removal leads to the greatest
reduction in mean accessibility (From Gleyze ( 2005 ))
This method finally helps to hierarchically segment the graph into increasingly
cohesive subgroups.
The connectivity notion rarely appears in geographical studies as reticular
structures are often robust: actually, transportation, energy and communications
networks contain several redundant ties and are not considered to be systems that
could be gradually disconnected.
There is an exception to this fact: when analyzing risks, it may be relevant
to identify the most fragile points in the network. However, the edge density of
geographical networks is so high that it is not possible to identify clusters by succes-
sively damaging such points. In fact, these networks are almost never disconnected,
but some paths become so long that they could be considered as disconnected.
Nevertheless, Gleyze ( 2005 ) proposes to identify the node of a transportation
network whose removal would lead to the greatest decrease in the mean accessibility
inside the network. Then, he considers the network deprived of this node, identifies
the node in this network whose damage would exert the greatest effect on the mean
accessibility, removes this node, and so on.
Figure 3.16 shows the succession of the “most fragile” nodes of the Parisian
Metro network.