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Fig. 12.1
Graph of
commuters for France in
1999 after data “cleaning”
average distances that were imputable to weekly commutes performed by working
people who travel home only for the week-end. The reasonable commutes are
preserved, as shown in (Fig.
12.1
).
After filtering, we apply a coloring that is proportional to a metric value. The
value is computed based on the structural properties of the graph. Frequently, we
use the strength metric (
Auber, Chiricota, Jourdan, & Melançon
,
2003
;
Guimerà,
Mossa, Turtschi, & Amaral
,
2005
) where the edges of low cohesion, or components
with less local participation, are given a pale color and the components with high
cohesion are given a darker color. These areas of the graph, defined as high cohesion
sub-systems, are what we consider to be urban areas.
Our approach differs from the classical approach, which is applied in many
countries (see, for example, the French Statistic Institute's definition), where it is
assumed that at least
n
% of the active population work in the central locality or
agglomeration area (Fig.
12.2
a). The classical approach assumes centrifuge flows
only occur from the peripheral municipalities to the city center, and it does not take
into account any polycentric communities that may arise. Thus, our visualization
method, applied to the network of commuters, provides a color to the nodes and
edges in such a way that the polycentric sub-systems pop out visually. These sub-
systems act like commuter satellites around a city center (Fig.
12.2
b). This network
approach is congruent with a polycentric model and allows for the cities to be
directly or indirectly linked to their center (Fig.
12.2
).
When the filtering stage is complete, we next work at the urban areas level.
We illustrate the polycentric structure of the French urban areas through several
examples and present the metrics to characterize this polycentrism.
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