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The objective of our approach is to emphasize these “new reticular territories”,
which are defined by an inter-connected overhead grid that divides the world into
various levels of road service through mandatory stops in some hubs. The star-like
form of the networks, a consequence of deregulation of the air industry, supports
the emergence of a system comprising multiple air platforms. The dynamic space
of the center-periphery type is reinforced in these networks. With the emergence of
secondary centers (Seoul, Fort Lauderdale) ( Amiel , 2005 ), the great centers have
often become more powerful (New York, London, Chicago, Paris).
9.2.3
“Small World” Form of the Air Network
Thus, the world air network has specific “small world” properties. It is necessary,
for example, to take 15 different flights to go from Mount Pleasant (in the Falkland
Islands) to Wasu (New Guinea): this is the largest short path in the world air network
( Guimerà et al. , 2005 ). We can now see how “small worlds” are created in this
network. In fact, a high degree of connectivity exists between selected airports
so that short paths can be found between airports, but there are also numerous
peripheral airports that are very far from the entire network.
In particular, the different continents of the world are especially “coherent” in
the sense that airport traffic can create some very strong intertwined systems of
exchanges compared to sparser inter-continental links.
9.3
Clustering Methods for Air Transport Network
The methodologies applied to the air traffic network can be classified into three
families:
(a) Q value methods maximizing internal densities within groups;
(b) methods based on the Betweenness centrality index;
(c) common neighbors methods, including Jaccard or strength methods.
These methods are described below in the context of non-weighted graphs
(classical cases) and in the context of weighted graphs that we have developed.
9.3.1
The Q Va l u e M e t h o d
=
The Q value method was developed by Newman ( 2004 ). Given a graph G
(
,
)
= {
,
,...,
}
V
E
,let C
C 1
C 2
C p
denote the partitioning of this graph into clusters
,
,...,
|
|,|
|
|
(
) |
C 1
C 2
C p .Alsolet
V
E
denote the number of nodes and edges in G ,
E
Ci
|
(
,∗ ) |
denote the number of edges with extremities in the cluster C i ,and
E
Ci
denote
the number of edges with at least one extremity in the cluster C i .
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