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Fig. 12.2
Delineations of
urban areas. (
a
) Classical
delineation. (
b
)Network
delineation
12.3
Characterization of Polycentrism in the French
Urban Areas
A polycentric urban area organizes itself around several political, social and
financial centers. The commuters' flows illustrate the existence of one or several
employment sub-centers, which are seen as points of attraction. Consequently,
the commuters' networks can help to illustrate polycentric structure by clarifying
how the municipalities contribute to the urban area's polycentrism. In this section,
we explain our methodology for defining and visualizing polycentrism through
commuting cohesions.
A previous study (
Rozenblat & Tissandier
,
2007
) shows the local polycentric
structures but could not take the geographic positions of the cities into account. We
fill this gap using the geographic coordinates of municipalities and, to deepen this
study, we also choose to realize an evolving network analysis. The aim is, finally, to
characterize the polycentric structure of French urban areas but also to underline the
formation of sub-centers. So, this work is essentially a dynamic graph visualization
problem. Therefore, at the urban area level and using a combined 4 years of census
data, we visualize the formation of a polycentric structure by using the cohesions of
the cities or by using the weighted connections in terms of the number of commuters
between the municipalities.
12.3.1
Metrics Calculated
To illustrate our method, we provide many example networks around cities such
as Lyon, Marseille, Lille, Bordeaux and Toulouse. Paris is not presented in this
section because the network of commuters around it is very dense. We were not
able to render images that were readable using our visualization system, which
demonstrates a limitation of our approach.
12.3.1.1
Betweenness Centrality
There are many centrality indices that are based on the set of the shortest paths
in a graph. The shortest path betweenness centrality can be viewed as a metric
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