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useful for finding local properties associated with a particular city. We had defined
some terms that will be used when creating these egocentric networks.
Given
commuter data
for year
D
i
(this data includes the number of commuters
between a pair of cities and the name and geographic position of each city), a
commuter network
G
i
(
U
i
,
V
i
)
is defined where
A node
U
i
is a city. Cities are mapped to their geographic coordinates. As a
consequence, the relative position of the nodes reproduces the geography.
An edge
V
i
connects two towns if they exchange commuters.
Given the set of commuter networks over all 4 years
(
G
1
,
G
2
,
G
3
,
G
4
)
, the union
of these graphs,
G
(
U
,
V
)
,isdefinedas
U
=
U
i
V
=
V
i
i
i
Therefore,
G
is also a network.
If
C
is the commuter data for 1 year,
C
where
t
i
is the town of
residence,
t
j
is the town of the workplace, and
n
is the number of commuters that
pass between the towns. Let us denote
linki j
as the weighted edge between
t
i
and
t
j
.
Path(
t
, length) is a ordered sequence of cities starting at
t
such that a link exists
between the adjacent towns in the sequence, and the sequence is a given length.
Given a city, a number of paths of the distance length exist in the commuter
data C for a given year. This data can be filtered where D = Filter(C) with ti in
Path(t,length) or tj in Path(t,length). Next, we format all 4 years of our data, using
the Tulip[7] framework, into a single file with all of the attributes available: the
number of commuters for each year on all edges (a weight of 0 is entered if the edge
did not exist for a given year); the geographic positions for each city; and the city
names. The city names will be used as an identifier, and, as such, we must ensure
that the names do not vary from census to census.
Building a visualization inside of the urban areas as delineated in the first stage
can be achieved using a series of Tulip plugins (
Auber
,
2003
). During this study, we
choose to work on the major cities of France such as Bordeaux or Lyon. To begin,
we work on the union of all 4 years between 1975 and 1999. Therefore, each edge
in this graph has a collection of four weights.
All of the nodes that lie on a path of length less than or equal to three are included.
A path length of at most three was chosen because the graph is densely connected.
All of the cities of distance three or smaller from the query city are included. We
could have used the weighted distance from the city center, but that remains for
future work. The nodes and the edges of this graph were stocked in a vector for
efficiency reasons. This city-centric view of the data can help the geographers to
reason about the polycentric structures around a given city.
The next step is to filter the data, at several scales, around the regional and
departmental levels surrounding the capitals. In the process of creating a graph on
demand by combining all of the edges, we considered that the value of the edge
could be positive (if this edge exists in 1 year of data) or negative (if there is no
=
Table
(
t
i
,
t
j
,
n
)
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