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Tabl e 8. 2
Topological characteristics of the world maritime network, 1996-2006
Direct links
Indirect links
Measure
Description
Calculation
1996
2006
1996
2006
e
Length
Number of edges
Sum
6,322
9,493
29,251
51,054
v
Population
Number of
vertices
Sum
975
1,240
975
1,240
k
Cyclomatic
number
Number of
independent
cycles
e
−
v
+
p
5,347
8,253
28,676
49,814
v
(
v
−
1
)
k
/
α
Alpha
Lattice degree
0.011
0.010
0.011
0.010
2
e
v
β
Beta
Degree of graph
complexity
6.484
7.655
30.001
41.172
v
(
v
−
1
)
γ
Gamma
Global
connectivity
e
/
0.013
0.012
0.061
0.066
2
v
(
v
−
1
)
C
Connectivity
degree
Observed vs.
optimal
connectivity
/
e
75.106
80.920
16.232
15.046
2
Source: calculated by the author based on LMIU and Joly (
1999
)
8.3.2
Topological Characteristics and Geographical Structure
The resulting graphs are characterized by a high complexity (Table
8.2
). The high
cyclomatic number, where p is the number of separated components, indicates a
high connexity of the graph. The higher the connexity, the more accessible is a node
from all other nodes. The connexity has increased between 1996 and 2006, and it is
always higher for indirect links because of a higher density of inter-port relations.
However, the lattice levels are relatively low, most likely due to the hierarchical
nature of the network. The global connectivity is also low, but it is higher for indirect
links, for the reasons cited above. In terms of complexity level, the high values for
non-planar graphs indicate a very complex pattern. Notably, the growth rate of the
number of ports connected is 27 %, but the maritime links grew 64 % over the same
period, resulting in a denser network. This is most likely an effect of the factors
cited by
De Langen et al.
(
2002
) on the current evolution of container networks. The
observed connectivity (c) has increased for direct links but has decreased for indirect
links, where it is significantly lower. All these facts indicate that the graph of indirect
links is denser and more complex due to the richness of inter-port relations, taking
into account the overall circulation of vessels instead of direct inter-port links, which
tend to break the continuum of shipping.
The structure of the graph can also be analyzed based on the relationship
between the number of ports and the number of connections (i.e., maritime degree).
The results presented in Fig.
8.1
indicate that the organization of liner networks
corresponds to a scale-free network that is defined by a power-law distribution.
A few ports dominate the network by their high number of connections, while
a majority of the other ports have only limited connections. Some exceptions in
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