Información pecuaria

Many complex systems can naturally be represented by one or more networks, as they can be perceived from different level of interpretation. On can think of the human brain to illustrate such affirmation. It is possible to represent the brain as a set of nodes (neurons) connected by link (synapses), but also as a set of brain regions interchanging information. Similarly, the air transport system can be viewed from different angles, and therefore represented by different networks. This property of complex network theory allows to tackle different problems, focusing on the relevant information of each one of them. Confronted with this vast menu of possibilities, it is important to determine which networks to investigate as a function of the problem under study.

The majority of studies done so far have been performed in networks where nodes are airports [ZL13a]. Indeed, important problems in air transport research are related with the mobility of passengers or the propagation of delay. In those cases, traffic oriented details (such as naviga-tion points, virtual space points through which the aircraft must pass) are irrelevant. A network where nodes (representing airports) linked whenever a direct flight between the two airports exists is far more adequate towards delay or mobility studies. A network connecting the nav-igation points of the airspace would unwieldy yield added knowledge about delay propagation

or passenger mobility. But even choosing airports to be the nodes of a network, several sources of information, like scheduling, types of flight or airlines, are disregarded by projection. To put that another way: airport networks can be naturally decomposed into many sub-networks by considering separately flights of the same airline or alliance, types of flight, etc. The differ-ence between considering a single or multiple network sub-types is important. For instance, two nodes (representing airports A and B) might be connected considering all airlines but dis-connected considering only a subset of airlines; this situation can arise provided A and B are connected through a indirect flight, composed of two direct flights of two different airlines. As such, looking at those differences might provide information about the strategy of different type of airlines (e.g. local airlines versus low-carrier). This multilayer properties of the air transport network have been extensively studied; for instance, [LC04, CZGG⁺13, CGGZ⁺13] investigated the interdependencies between sub-networks corresponding to different airlines. Multi-layer, or multiplex, networks are then defined as graphs composed of several layers, where different types of links (e.g. for each airline) might connect two nodes (airports).

An airport network, be it a single sub-network or a projection of various ones, has also a natural weighting scheme. Indeed, we said that two nodes are linked when the corresponding airports are connected through a flight. But the network in itself is a static representation of a dynamic process - that is - the information exchanged (here flights, but it might also be a more abstract notion like delays) within a given period is projected into the graph. Were we to consider a snapshot of the system, no information whatsoever about the traffic of passengers would be contained; it is precisely considering a larger time window that connections between airports occur, at different frequencies. The fact that the number of connections of two distinct pairs of airports might be distinct in the time period under study (e.g. there might be a larger flow of passenger, or a larger number of flights, between A and B than between B and C) might be specified into the graph by pondering the links, for example by using the frequency of connections or the volume of transported persons. Therefore the weighting scheme would be given by the number of flights, beyond themere binary connectivity. Note that graphs can be directional - that is, a link might go from A to B but not from B to A. That be told, in has been empirically observed that most airport networks are very close to be symmetric, i.e.

roughly the same number of flights (or passengers) exist from A to B than from B to A.

In practice, graphs in passenger-oriented networks (i.e. with airports as nodes) are seldom directional. However, in some cases it could be so; let us consider an example. Some flights cannot take off or land on time because of a delay in another flight: these are called reactionary delays. To investigate the aforesaid phenomenon, [CTZ13] used a directed graph in which a link is created between two airports whenever the Granger causality test (see Section 2.2.1) indicates that the delays suffered in one of them is caused by the delay in the other. Such approach narrows the representation to airports involved in reactionary delays; therefore the resulting topology yields knowledge about whether delays generated in certain airports propagate through all the system or remain confined within a relatively small region.

While we could stop here, as airport networks are the only type that will be used in this PhD Thesis, for the sake of completeness we here review some additional alternative ways of reconstructing air transport networks.

Crew networks Reactionary delays, i.e. delays caused by the delay of another flight, are partly due to the late arrival of passengers, or because of the crew itself [PMO13]. Thus, nodes can represent crews linked between them when sharing the same aircraft.

Sector networks The complex system conception of airspace leads naturally to its partition in hierarchical operational pieces - sectors - mainly for simplifying its management and optimise its capacity. Each sector is then managed by a pair of controllers, with flight plans tuned in order to not violate the maximum traffic load of each of them. The concept of network of sectors has recently been proposed in [GVC⁺14], where nodes are sectors, and links between two nodes are representative of a same flight passing through the two sectors during the considered time window. Community detection has been used on top of this network as an approach to improve airspace design.

Navigation points network Until technology will reach a maturity such to allow a safe free routing, aircraft have to travel through air routes defined by fixed navigation point. While more safe, this strategy implies the appearance to potential bottlenecks in central zones

of the airspace, where several aircraft converge. To improve our understanding of routing and airspace design, [GVC⁺14, KQJWBXB12] considered a new network where each navigation point as a node, linked when at least one flight goes directly from one node to the other in the considered time interval.