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Fig. 12.9
Strength index around Marseille (
a
) and Lyon (
b
), year 1990
Fig. 12.10
Strength index around Marseille (
a
) and Lyon (
b
), year 1999
municipality to the cohesion of a subnetwork by measuring the city's representation
in the subnetwork or the number of links that it shares with the cluster.
The participation coefficient can be computed on a directed graph using the
incoming or outgoing degrees. The outgoing participation coefficient of a node v
can be defined by the following:
ω
(
v
,
w
)
p
+
(
∑
w
∈
N
G
(
v
)
v
)=
1
−
d
G
(
v
)
where
N
G
(
v
)
are the outgoing nodes from
v
,
ω
(
v
,
w
)
is the weight of the edge
(
v
,
w
)
,
and
d
G
(
is the sum of the weights for the outgoing edges of
v
. The incoming
participation coefficient is similarly defined. The outgoing participation coefficient
v
)
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