Defining Polycentric Urban Areas Through Commuting Cohesion in France - Methods for Multilevel Analysis and Visualisation of Geographical Networks - page 185

number of workers every day while the majority of municipalities import very few
commuters. For this study, we return to the level of the entire French commuters'
network. We apply a recursive algorithm to identify the polycentric structure of the
urban areas. Finally, we present a large network evolution analysis.

12.2 Data Cleaning

The census data that is used to construct the commuters' network does not distin-
guish between the municipality of administrative residence and the municipality
of actual residence ( Talbot , 2001 ). Additionally, the respondent may not report a
second place of residence in addition to their primary place of residence. These
situations, as well as others, raise numerous problems in the visualization of the
graphs that are inferred using this data. Several examples from the data acquired in
the 1999 census illustrate the types of problems that arise from a lack of information
and include the following:

￿ A total of 45 people commute over 1,000 km every day, essentially the distance

between Corsica and the north of France.

￿ Over 400 people commute over 500 km every day.

To filter out these edges, which are most likely erroneous, most approaches filter
out the links with low weight or the links that are distant geographically ( Bonnefoy,
Pumain, & Rozenblat , 1996 ; Talbot , 2001 ). These methods, applied on a French
departmental or regional level, provide convincing results. However, the diversity
of situations at the national level limits the applicability of these methods. Also,
as with many graph problems in geography, we have the problem of selecting a
threshold. We need to choose a threshold that depends on the geographic distance
between the two municipalities or/and the number of commuters that make the trip
on a daily basis.
We choose to apply a gravity model to help distinguish between the edges
that represent practical daily commutes with those that, most likely, result from
missing census information ( Nijkamp , 1975 ; Pumain , 2001 ; Sen & Smith , 1995 ;
Shen , 1999 ). A gravity model stipulates that the attraction between two elements is
proportional to their mass P and inversely proportional to the distance d between
them.

k P i P j
d ij
Because we would like to prevent reasonable links from being filtered, we
replaced the weight of the municipalities of residence and employment with a
specific attribute of the edges, namely the portion of the migrants in the total
working population of the municipalities of residence and employment, as described
in the introduction.
The gravitational filtering of the graph makes the data appear to be more
reasonable. The excessively long commutes have disappeared, which were likely

T ij =