Structure and efficiency of the world-wide airport network Roger Guimer

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Structure and efficiencyof the
world-wideairport network Roger
GuimeràDepartment of Chemical Engineering
Northwestern UniversityStefano Mossa, Adrian
Turtschi, and Luís A. N. Amaral Pavia,
September 11, 2003
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The behavior of the airport network has a huge
economic impact
Cost of delays in 1989 in Europe 5 billion!!!
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The airport network is the support for the
propagation of some diseases
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Network designed (optimized) with economic
criteria

• Unlike other networks that are self-organized the
  airport network is designed so that its
  performance is optimal.

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The data
3883 cities and 531,574 direct flights
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The degree distribution follows a truncated power
law
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The betweenness measures the centrality of cities
The betweenness bi of node i is the number of
minimum paths between pairs of nodes to which i
belongs.
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The betweenness distribution also follows a
truncated power law
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Modeling the world-wide airport network
1-p
j
i
p
j
i
Dorogovtsev Mendes, Europhys. Lett. 52 (2000)
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Degree and betweenness distributions of model
networks are correct (with p0.65)
Does it mean that the model is reproducing ALL
the properties of the airport network?
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Most connected cities are NOT the most central
Most connected cities
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Most central cities are important
Most central cities
SARS virus outbreak
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Unlike the real network, in model networks most
connected cities are the most central
World-wide
North America
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Distance constraints in the modeling of the
airport network
1-p
j
i
p
j
i
Yook et. al., PNAS 99 (2002) Barthelemy,
cond-mat/0212086
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Distance constraints are only responsible of a
small part of the fluctuations
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Why the connectivity distribution has exponent -1?
Star-like network
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Communication model
k

• At each time step, a group of people needs to
  travel form city i to city to some other city k
  with probability r.
• Once a plane arrives to a city, it has to wait
  until all the planes that arrived before have
  departed.

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Which are the optimal networks?
Lower traffic
Higher traffic
Phys. Rev. Lett. 89 (2002)
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Conclusions

• Studying the airport network is important
  because
• Its behavior has an enormous economical impact.
• Is the support for the propagation of certain
  diseases.
• Is designed and redesigned for optimal
  performance.
• The airport network is a scale-free network in
  which the most connected cities are NOT, in
  general, the most central.
• Optimization considerations help to understand
  the structure and evolution of the network.

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Acknowledgements

• A. Arenas, A. Barrat, M. Barthélémy, A.
  Díaz-Guilera, R. Pastor-Satorras, and A.
  Vespignani.

More information http//amaral.northwestern.edu/
http//amaral.northwestern.edu/roger/
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Exponential distance constraint
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Average load of the network

• pijk Probability that a group of passengers at
  city i with destination k choose j as the next
  stop

• Betweenness of node j, Bj
• Total load