Connectivity of Air Transport Networks

CHAPTER 5

Connectivity of Air Transport Networks Contents Connectivity in air transport networks Traditional models of airport connectivity Unweighted measures of airport connectivity Weighted measures of airport connectivity Other betweenness-based measures of connectivity Connectivity and airline business models 5.6.1 Measuring spatial concentration 5.6.2 Measuring temporal concentration 5.6.3 The impact of codeshare in airline connectivity 5.7. Demand-based measures of connectivity References 5.1. 5.2. 5.3. 5.4. 5.5. 5.6.

117 118 120 124 130 134 135 139 144 146 147

5.1 Connectivity in air transport networks The aim of the air transport industry is to connect the world by transporting people and goods using the airport infrastructure. In that sense, an airport is a door that opens its catchment area to the rest of the world. Recent research states that the development of airport infrastructures follows regional economic growth, although this causality relationship can be reversed in peripheral regions [16]. This means that regions with low connectivity can enhance their competitiveness improving the connectivity of their airports. Therefore there is no surprise that academics and practitioners in transport science have made efforts to develop indices of measuring connectivity of airports [5]. In this chapter, we review how complex network science can help to measure connectivity of air transport networks. We consider a twodimensional classification of connectivity measures based on transport networks: • Local versus global connectivity: the first connectivity airport measures that come to mind are the number of direct connections, passenger transported, and so on. These are measures of local or direct connectivity. However, the development of hub-and-spoke operations have enhanced Air Route Networks Through Complex Networks Theory https://doi.org/10.1016/B978-0-12-812665-3.00012-8

Copyright © 2020 Elsevier Inc. All rights reserved.

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the value of global or indirect connectivity or hubbing, that is, the availability of indirect connections of an airport. • Weighted versus unweighted measures: In the chapter of analysis of airport networks, we have seen that direct connections can be considered unweighted or weighted. We consider that an unweighted direct connection between two airports exists if there is at least one direct connection between these airports in a time window. In weighted networks, we associate with each connection a measure of its intensity. The most common are the number of flights scheduled, available seats or available seats per kilometre. In the following section, we introduce some traditional approaches to measuring airport connectivity. Then we will use complex networks theory to assess connectivity introducing degree and betweenness as unweighted measures of local and global connectivities, respectively. The computation of edge betweenness can be used to evaluate route connectivity. We will see that these measures, especially betweenness, can be too affected by topological structure. The effect of connectivity can be corrected with weighted measures, like strength or weighted betweenness. These measures consider traffic intensity of the connections by using information included in air traffic data. An alternative way to overcome the effect of topology is to use alternative measures of node betweenness, weighted betweenness or betweenness computed with a cut-off value.

5.2 Traditional models of airport connectivity Connectivity is a key feature of a network infrastructure, so there is no surprise that transportation research scholars and managers are interested in developing measures of airport connectivity. There is a body of the literature, whose main interest is to assess airport competitiveness that has developed those measures. The most straightforward of airport connectivity measure is based on the connectivity matrix whose components dij are the numbers of steps required to reach airport j from airport i. Then the connectivity index CIi is defined as CIi =

1  |I |

dij ,

(5.1)

j ∈I

where I is the set of airports having direct or indirect connections with airport i.

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The connectivity index is a quite rough measure, as it does not consider quality attributes of each route from the passenger viewpoint. The NETSCAN model [21,6] assigns a number of connectivity units CNU to a connection, based on a quality index and the weekly frequency of flights. The quality index QUAL is equal to one for non-stop connections and zero for the connections with a perceived travel time longer than a maximum travel time. The computation of CNU is as follows: MAXT = (3 − 0.075NST) NST PTT = FLY + 3TRF PTT−NST QUAL = 1 − MAXT −NST CNU = QUAL × FREQ

(5.2) (5.3) (5.4) (5.5)

where the parameters are: • NST: non-stop travel time • FLY: flying time • TRF: transfer time • MAXT: maximum perceived travel time • PTT: perceived travel time • QUAL: quality index of the individual connection (equal to zero if PTT is longer than MAXT) • FREQ: frequency of flights • CNU: number of connectivity units As we can see from Eq. (5.5), connectivity units are equal to the route frequency (number of flights scheduled per week) weighted by a quality index. The maximum value of quality is for direct connections. For indirect connections, a measure of perceived travel time (PTT) is computed assigning different weights to flight time and transfer time. As passengers prefer to minimise transfer time, one hour of transfer time is made equivalent to three hours on flight. This weighting is somewhat arbitrary [21], as to our notice no study has been undertaken about passenger preferences regarding transfer and flight times on a behavioural basis: in fact, we can argue that these can be different for different groups of passengers, for example, leisure vs business passengers. If PTT is longer than a MAXT value, dependent on total flight time NST, the connection is considered too long, and its quality is set to zero. The connectivity of airports is assessed by adding the CNUs of all direct and indirect connections departing from it. Airports with many non-stop connections will then have high values of CNU.

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To analyse the temporal configurations of European airline networks, Burghouwt and de Wit [4] defined a weighted indirect connection index WI based on a transfer index TI and a routing index RI: WI =

2.4TI + RI . 3.4

(5.6)

The transfer index TI assesses the quality of the connection, based on similar principles as the NETSCAN model, whereas the routing index is based on the value of the routing factor. They define the routing factor as the quotient between the actual in-flight time (that is, without including transfer time) and the estimated in-flight time of a direct connection, based on great circle distance. A common approach to measuring routing factor is using distances instead of times, so it can be obtained as the quotient between the sum of distances of all connecting flights and the distance between origin and destination. A route with a high routing factor takes an excessive detour to reach its destination, so its appeal to passengers is low. The routing factor is a common indicator in connectivity studies to discard “back-tracking” routes. Complex networks theory can offer alternative measures of airport connectivity, modelling the air route network as an airport network. In the following sections, we present several measures of connectivity, based on weighted and unweighted airport networks.

5.3 Unweighted measures of airport connectivity We can use the concepts of node degree and betweenness taken from the complex networks literature to define indicators of node importance or centrality: • Degree: in an airport network, the node degree is equal to the number of different connections from an node (airport or metropolitan area) to other nodes. We usually suppose that each arriving connection has its departing counterpart, so we can use an undirected representation. Airports and metropolitan areas with high degree have a large number of connections with other network nodes, so they are considered well-connected nodes. • Betweenness: airports or metropolitan areas with high betweenness lie frequently in the middle of indirect connections, so it is likely that they act as hubs where airlines schedule connecting flights. Then we can say

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that these nodes are central nodes of the network, as they ensure their connectivity. The distinction between well-connected nodes and central nodes is related to the two dimensions of hubbing, traffic generation and connectivity, respectively [19]. We can assess if the degree and betweenness are related to traffic generation and connectivity using a sample of the world airport network including all flights registered in the OAG database scheduled on August 2018. In Table 5.1, we present a list of the twenty airports with highest degree and betweenness of the world airport network. Both listings are remarkably different: of the twenty airports with highest betweenness, only eleven appear in the listing of high degree. Among the well-connected airports with low degree, there stands out the Ted Stevens Anchorage (ANC), the main hub of the Alaskan network. In the top twenty list of highest betweenness, there also appear two Canadian airports serving the cities of Toronto and Vancouver, two Australian airports serving Sydney and Brisbane, and the international airports of Tokyo, Singapore and Hong Kong. Populations of Canada and Australia are geographically dispersed, so air transport plays an important role to assure connectivity between cities. The high value of betweenness of nodes acting as gateways of regions of the world airport network was detected by Guimerà and Amaral [10], who labelled this phenomenon as “anomalous centrality”. In Fig. 5.1, we have plotted the degree and betweenness of each node of the world airport network. We can see that the Anchorage (ANC) airport has the highest value of betweenness of the WAN and a relatively small degree. The presence of central nodes that are not well connected (i.e., nodes of high betweenness and low degree) has not been found in other complex networks, like the Internet or the power grid. To illustrate the presence of airports that act as gateways of isolated regions, we have analysed the Alaskan region with more detail. Fig. 5.2 presents the Alaskan airport network of flights arriving at and departing from Alaskan airports. This airport network has N = 202 nodes (active airports) and E = 281 edges (direct connections). Alaska is a low-density populated area with extreme climatological conditions, where air transport can be a choice to travel between Alaskan cities. The airport of highest degree in this network is Bethel (BET) with 29 connections, followed by Anchorage (ANC, 24 connections), Fairbanks (FAI, 21 connections) and Juneau (JNU, 19 connections).

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Table 5.1 Ranking of the twenty airports with highest degree and betweenness of the world airport network and metropolitan areas of each airport. Higest degree Higest betweenness

FRA

Frankfurt am Main Charles de Gaulle Atatürk Amsterdam Airport Schiphol Beijing Capital Munich Hartsfield Jackson Atlanta Chicago O’Hare Dallas Fort Worth Dubai

Frankfurt

ANC

Paris

FRA

Istanbul Amsterdam

DXB LAX

Beijing

CDG

Munich Atlanta

IST PEK

Chicago

ORD

Dallas-Fort Worth Dubai

NRT

Shanghai Pudong Adolfo Suárez Madrid–Barajas Barcelona

Shanghai

SIN

Madrid

YYZ

Barcelona

LHR

London Gatwick Brussels

London

BNE

Brussels

SYD

London

HKG

MAN

London Heathrow Manchester

Manchester

DFW

LAX SVO

Los Angeles Sheremetyevo

Los Angeles Moscow

YVR PVG

STN

London Stansted

London

GRU

CDG IST AMS PEK MUC ATL ORD DFW DXB PVG MAD BCN LGW BRU LHR

AMS

Ted Stevens Anchorage Frankfurt am Main Dubai Los Angeles

Anchorage

Charles de Gaulle Atatürk Beijing Capital Chicago O’Hare Narita

Paris

Amsterdam Airport Schiphol Singapore Changi Lester B. Pearson London Heathrow Brisbane

Amsterdam

Sydney Kingsford Smith Chek Lap Kok Dallas Fort Worth Vancouver Shanghai Pudong GuarulhosGovernador André Franco Montoro

Sydney

Frankfurt Dubai Los Angeles

Istanbul Beijing Chicago Tokyo

Singapore Toronto London Brisbane

Hong Kong Dallas-Fort Worth Vancouver Shanghai Sao Paulo

The relevance of Anchorage (ANC) and Fairbanks (FAI) airports comes from their role in connecting Alaska with the rest of the world. In Fig. 5.3,

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Figure 5.1 Connectedness (degree) versus centrality (betweenness) for the airports of the WAN. Airports with high strength or betweenness are presented with its IATA code.

Figure 5.2 The Alaskan airport network of flights arriving at and departing from an Alaskan airport.

we can see that ANC and FAI are the gateway to Alaska from the rest of the world when it comes to air transport. These airports lay in between the shortest paths between all Alaskan airports and the rest of the world, so they

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Figure 5.3 The Alaskan airport network of flights arriving at or departing from an Alaskan airport. Connections with Russian and Japanese airports, which also come through Ted Stevens Anchorage airport, have been omitted.

have a high betweenness. Fig. 5.3 also shows that most of the connections to Alaska come from airports of the United States (some connections with Russian and Japanese airports have not been pictured) and that there is only one direct connection between Alaskan and Canadian airports, as Alaska is a US territory. The Alaskan network is an example of the geographical and political forces that shape the world airport network. The Alaskan network illustrates that airports with high betweenness act as gateways of isolated subnetworks of the world airport network (e.g., Alaska or Canada), so this measure has a strong topological motivation [19]. Betweenness is not a good metric to detect large intercontinental hubs. The topological bias of betweenness can be corrected in two ways: • Introducing geographical (distance) and intensity of traffic parameters to compute betweenness. This leads us to consider the world airport network as a weighted network. • Computing betweenness with a cut-off value, that is, considering shortest paths of length below a threshold or cut-off value. This is particularly realistic in the world airport network, as travellers tend to avoid trips with many connections.

5.4 Weighted measures of airport connectivity Connections between nodes in complex networks can present significant differences of capacity and intensity. The world airport network presented

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in the previous sections treats all direct connections equally, irrespective of the volume of flights or passengers of each connection, although direct connections between airports can present large variability in intensity. This has been taken into account by extant research: in Barrat et al. [2], where measures of weighted networks were defined, the world airport network was one of the presented case studies. Depending on data availability, several measures can be used as proxies of intensity of a direct connection: • Frequency of flights: the number of flights scheduled between an origin and a destination in the time window considered to obtain the airport network. • Available seats: Seats for sale in the time window, which should not include seats reserved for the crew and seats not available for sale for technical or regulatory reasons. • Available seats per kilometre (ASKs): the number of available seats of a route, multiplied by kilometres flown. ASKs is the fundamental unit of production of a passenger airline. The values of these measures for undirected networks are obtained by adding the values for the connections taking as origin each of the two nodes of the connection. Each of these measures allows defining an edge weight wij measure, representing the intensity of the connection between airports i and j. Whereas the local connections of nodes are measured with node degree in unweighted networks, in weighted networks, we define the node strength as si =



wij .

(5.7)

j ∈N

The previous research, like Barrat et al. [2] or Du et al. [8], has considered the frequency of flights as edge weights when defining weighted airport networks. We must note, though, that the selection of the weighting variable may lead to quite different network representations. To illustrate, in Table 5.2, we present the top twenty airports by node strength for each of the three edge weights defined before. The content of the top ten lists of Table 5.2 is quite different from the degree and betweenness classifications presented in Table 5.1, and the three weight-based rankings present remarkable differences. In the first rows of the frequency ranking, there appear US and Asian airports, followed in lower places by the big European hubs. The seats ranking is also leaded by US and Asian airports, although European hubs rank higher in this listing.

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Table 5.2 Top twenty of airports of the world airport network according to different vales of strength. Frequency Seats ASKs

ORD

Chicago O’Hare

ATL

DXB

Hartsfield Jackson Atlanta Beijing Capital Dubai

PEK

PEK

DEN

Beijing Capital Hartsfield Jackson Atlanta Denver

LAX

Los Angeles

JFK

LAX

Los Angeles

HND

CDG

IST

Atatürk

ORD

PVG

Shanghai Pudong Amsterdam Airport Schiphol Charles de Gaulle Frankfurt am Main Guangzhou Baiyun Dallas Fort Worth John F Kennedy

LHR

Tokyo Haneda Chicago O’Hare London Heathrow Frankfurt am Main Charles de Gaulle Chek Lap Kok Shanghai Pudong SoekarnoHatta Atatürk

FRA

LHR

London Heathrow

AMS

ICN

Incheon

DFW

CTU

Chengdu Shuangliu George Bush Intercontinental Houston Munich Adolfo Suárez Madrid–Barajas

CAN

ATL

AMS CDG FRA CAN DFW JFK

IAH MUC MAD SFO

San Francisco

FRA CDG HKG PVG CGK IST

DXB

Dubai

LAX

Los Angeles

LHR

London Heathrow John F Kennedy Charles de Gaulle Beijing Capital Chek Lap Kok Singapore Changi

PEK HKG SIN

SFO ICN PVG AMS

Amsterdam Airport Schiphol Dallas Fort Worth Guangzhou Baiyun Singapore Changi

ORD

ICN JFK DEL

SIN

Frankfurt am Main San Francisco Incheon Shanghai Pudong Amsterdam Airport Schiphol Chicago O’Hare

DOH

Hamad

BKK

Suvarnabhumi

YYZ

Lester B. Pearson

Incheon John F Kennedy

NRT ATL

Indira Gandhi

MAD

Narita Hartsfield Jackson Atlanta Adolfo Suárez Madrid–Barajas

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The frequency and seats ranking are skewed towards short-haul flights, as this is the segment where more seats are offered. The ASKs ranking includes airports with an important long-haul market, like Dubai (which scored lower in samples of previous years), New York JFK, Charles de Gaulle in Paris or Singapore Changi. These airports are known for being hubs of long-haul flights, mainly operated by full-service carriers. These results suggest that the frequency of flights may not be an adequate indicator of the intensity of a connection and that seats emphasise short-haul markets whereas ASKs emphasises long-haul markets. The degree and node strength are the measures of local centrality for weighted and unweighted networks, respectively. It is also possible to define weighted versions of betweenness, the global measure of centrality, for weighted graphs. Instead of measuring shortest paths with number of edges, the weighted betweenness considers paths with minimal value of total edge weights. This formulation of betweenness was sketched by Barrat et al. [2] and applied to the world airport network by Dall’Asta et al. [7]. In a weighted network, we can assign to edges either values representing geographical distance (or time) or associated with the intensity of relationship. These two measures help to build a composite measure of effective distance between two nodes of an airport network. This measure is proportional to the geographical distance (which can be considered as a proxy for travel time) and inversely proportional to edge weight: the more frequent the flights, the easier the travelling between two destinations. Dall’Asta et al. [7] define the effective distance of an edge as the quotient between distance dij and weight wi . With data available from OAG, this effective distance can be operationalised as d

lij = wijij

=

ASKs . seats × freq

(5.8)

In Table 5.3, we list the top ten airports in decreasing order of betweenness and two variants of weighted betweenness, the first considering geographical factors only (weights equal to distance) and the last considering geographical and frequency of flight factors. We have added unweighted betweenness computed to allow comparison among betweenness measures. Results of Table 5.3 show that the weighted betweenness considering distance is even more influenced by topology than unweighted betweenness. Let us consider the first three airports of this ranking: Ted Stevens Anchorage (ANC) is the gateway to the Alaskan network, Keflavik (KEF), the international Reykjavik airport, makes salient the geographical position

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Table 5.3 Top twenty airports ranked by betweenness, weighted betweenness (distance) and weighted betweenness (effective distance, frequency of flights as weight). Unweighted Distance Effective distance

ANC

Ted Stevens Anchorage Frankfurt am Main Dubai Los Angeles

ANC

Charles de Gaulle Atatürk

DEL

Beijing Capital Chicago O’Hare Narita

ORD

Amsterdam Airport Schiphol Singapore Changi Lester B. Pearson London Heathrow Brisbane Sydney Kingsford Smith Chek Lap Kok

DFW YVR PVG

FRA DXB LAX CDG IST PEK ORD NRT AMS SIN YYZ LHR BNE SYD HKG

GRU

Ted Stevens Anchorage Keflavik

LHR LAX

London Heathrow Los Angeles

Yelizovo Helsinki Vantaa Indira Gandhi

JFK HNL

John F Kennedy Honolulu

SIN

Beijing Capital Chicago O’Hare Ürümqi Diwopu Pulkovo

NRT

Singapore Changi Narita

DXB

Dubai

HKG

Chek Lap Kok

ORD

FRA

Frankfurt am Main

BOM

Chicago O’Hare Chhatrapati Shivaji

POM

CDG

HNL

Port Moresby Jacksons Honolulu

SEA

Charles de Gaulle Seattle Tacoma

LAX

Los Angeles

TLV

Ben Gurion

IST YVR

Atatürk Vancouver

AMM TPE

Queen Alia Taiwan Taoyuan

UUS

YuzhnoSakhalinsk

AMS

Dallas Fort Worth

MSP

MEL

Vancouver Shanghai Pudong GuarulhosGovernador André Franco Montoro

DEN MNL

Minneapolis– St Paul International Denver Ninoy Aquino Incheon

Amsterdam Airport Schiphol Melbourne

RUH MIA

King Khaled Miami

BKK

Suvarnabhumi

KEF PKC HEL

PEK

URC LED

ICN

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Figure 5.4 Relationship between node strength and weighted betweenness with the inverse of edge weights for frequency of flights (left), available seats (centre) and ASKs (left). Airports with high strength or betweenness are presented with its IATA code.

of Iceland, close to North America and the North European countries, and Yelizovo (PKC) is the international airport of Kamchatka in the Russian Far East. The betweenness based on effective distance, though, leads to a top ten ranking with airports considered as intercontinental hubs. The weighted betweenness based on effective distance balances the tendency of unweighted betweenness to overestimate the role of airports that act as gateways to isolated regions, such as Alaska or Canada, whereas the distance-based betweenness tends to make topological bias more salient. In the previous section, we have looked for anomalous centrality comparing values of degree and betweenness for each node (see Fig. 5.1). We have performed an analogous analysis with each of the three measures of edge weight, comparing the node strength with weighted betweenness, taking as edge weight the inverse of original edge weights. The results can be seen in Fig. 5.4. Using the weighted version of the world airport network helps us to detect nodes with anomalous centrality more easily. The results of the analysis for frequency of flights and available seats (left and centre graphics of Fig. 5.4, respectively) show two types of airports with anomalous centrality: • Airports with high strength and low betweenness: the airports of this group have a high volume of regional traffic but have low centrality, as they have a limited (or less salient) role as connecting airports. Most of these airports are located in US like Chicago O’Hare (ORD) or Atlanta International (ATL). • Airports with high betweenness and moderate strength: the airports of this group have less traffic than the previous group but lie in the middle of many connecting routes. Most of these airports act as intercontinental hubs between US and Europe: London Heathrow (LHR), JFK Interna-

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tional and Los Angeles International (LAX). Dubai International (DXB) also appears in this group due to the business model of Emirates airline, profiting from its geographical position to offer intercontinental flights [17]. These two dimensions correspond to the dimensions of hubbing described by Rodríguez-Déniz et al. [19]; the first group contains airports that generate traffic, whereas the second includes airports that ensure global connectivity. As the second group concentrates most of the long-haul flights, the only salient airports in the graphic defined with ASKs (Fig. 5.4, right), the airports with high values of degree and betweenness have many intercontinental flights.

5.5 Other betweenness-based measures of connectivity When applied to airport networks, nodes betweenness detects airports that are gateways to isolated areas: as the shortest paths between the isolated airports and the rest of the world pass through these gateways, they have a high betweenness score. The largest of these disconnected area (at least measured by the number of unique connections) is Alaska, which explains that Ted Stevens Anchorage is the airport of highest betweenness along the years (see Table 5.1, Fig. 5.3 and Lordan et al. [13]). The prevalence of airports like International Anchorage in the ranking of betweenness comes from the fact that the shortest paths between airports of different isolated areas and the rest of the world pass through these local hubs. On the other hand, most of the longest paths of the world airport network connect airports of isolated areas. All the paths of length 11 in the August 2018 world airport network were between airports in Greenland (like the Ittoqqortoormiit Heliport OBY) and the Marshall Islands (like the Ujae Atoll Airport UJE). It is unlikely that connecting flights like this can take place in practice. The impact of isolated areas on betweenness can be mitigated computing betweenness considering shortest paths of values equal to or lesser than a cut-off value. In the context of air transport, this value is equal to the maximum number of connecting flights considered. Most of the connections in the world airport network take relatively few steps. For a sample of flights scheduled in August 2018, 72.08% of the connections can be made with four or less steps and 92.87% with five or less steps. In Table 5.4, we have listed the top ten airports of betweenness with cut-off values three and four, along with the ranking of betweenness considering all shortest paths (infinite cut-off).

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Table 5.4 Top twenty airports ranked by betweenness, and betweenness with cutoff values three and four. Unweighted Cut-off 3 Cut-off 4

ANC

IST

Atatürk

FRA

PEK

DXB IST

Atatürk

LAX

Los Angeles

CDG

CDG

CDG

Charles de Gaulle Atatürk

DXB

Beijing Capital Frankfurt am Main Charles de Gaulle Dubai

Frankfurt am Main Dubai

DXB

Ted Stevens Anchorage Frankfurt am Main Dubai

LAX

LAX

ORD

Beijing Capital Chicago O’Hare

Chicago O’Hare Los Angeles

Charles de Gaulle Beijing Capital Los Angeles

AMS

NRT

Narita

DFW

AMS

Amsterdam Airport Schiphol Singapore Changi

PVG

Lester B. Pearson London Heathrow Brisbane Sydney Kingsford Smith Chek Lap Kok

YYZ

Amsterdam Airport Schiphol Dallas Fort Worth Shanghai Pudong Hartsfield Jackson Atlanta Lester B. Pearson King Abdulaziz Sheremetyevo Indira Gandhi London Heathrow

Dallas Fort Worth Vancouver

SIN

Singapore Changi Incheon

HKG

Shanghai Pudong GuarulhosGovernador André Franco Montoro

ADD

Addis Ababa Bole OR Tambo

ICN

FRA

IST PEK

SIN YYZ LHR BNE SYD HKG DFW YVR PVG GRU

FRA

ORD

AMS

ATL

JED SVO DEL LHR

ICN

JNB

PEK

ORD

DFW ANC PVG YYZ SIN NRT LHR ATL

SYD

JED

Chicago O’Hare Amsterdam Airport Schiphol Dallas Fort Worth Ted Stevens Anchorage Shanghai Pudong Lester B. Pearson Singapore Changi Narita London Heathrow Hartsfield Jackson Atlanta Chek Lap Kok Sydney Kingsford Smith Incheon King Abdulaziz

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Air Route Networks Through Complex Networks Theory

The betweenness with cut-off rankings include airports that act as hubs in the US, European and Asian air transport networks. These values of betweenness can be considered more realistic in the context of air travel, as passengers rarely consider trips with more than four connecting flights. This cut-off value helps to reduce the effect of serving as hub of isolated areas: in fact, if we raise the cut-off value to five for this sample of the WAN, Anchorage International ranks high again. Betweenness with cut-off helps to mitigate topological effects that give high values of betweenness to Alaskan or Canadian airports. The traditional shortest path measures of connectivity are usually computed using the airport network representation. Weighted measures can account for differences of routes regarding frequency of flights or seats offered, so they provide a more accurate measure of connectivity. However, these measures do not consider travelling times or scheduling concerns. It is likely that many of the apparently existing connections in an airport network do not exist in practice, as passengers arriving from the first flight cannot connect with the next, as it has departed earlier or the connecting time is too short. It can also happen that a sequence of possibly connecting flights exists but that it can take more steps than in the airport network. Considering the effect of travel times and synced connections requires more sophisticated representations of the air transport network. The first approach is to consider the same airport network with edge weights equal to distances or travel times. This network can help to calculate lengths of indirect connections equal to the total time or distance, instead of the number of steps. They can also help to discard routes with a small number of steps but take too much time or distance (e.g., a route between two European airports with an intermediate step in an American airport). To consider only synced connections, we need a specific temporal representation of the air transport network. Malighetti et al. [14] developed a methodology to obtain measures based on the quickest path length. They applied it to the European air transport network, extending it to the US and Chinese networks in [18]. Using all existing schedules on a time window, they calculated the shortest travel time STTijt from airport i to j at a specific time t. This value depends on the real possibilities of connection existing at time t, so it is possible that it is not defined for some values of t if these possibilities were scheduled before t. Then we can compute the minimum travel time from every pair

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of airports as 



STTij = MIN STTijt . t

(5.9)

It can be also of interest to obtain the optimal departing time, the starting travel time that minimises the travel time, 



STij = t STTijt = STTij .

(5.10)

To compute the betweenness, we need to retain the number of quickest paths and the intermediary airports. If there are more than one connection with minimum travel time, then only those with the fewest steps are retained. With these quickest paths, Malighetti et al. [14] compute several pathbased metrics of connectivity: • The connectivity index CI, a measure of local connectivity. • The betweenness of each airport, computed using all quickest paths passing through the airport. • The essential betweenness, computed using the unavoidable quickest paths passing through the airport. The essential betweenness measure ends up being too dependent of network topology, similarly to unweighted betweenness (see results of Table 5.1 for the world airport network): in Malighetti et al. [14], the maximum value of essential betweenness in the European airport network is for Stockholm Arlanda airport, the gateway of a network of regional flights in Sweden. Computing quickest path-based measures requires the air transport network to be modelled as a temporal network, as all schedules in the time window have to be considered. The airport network is much simpler to model, as there is an edge for every available direct connection. In the temporal network, there is a node for each arrival or departure, and edges include not only existing flights, but also possibilities of connection available at each airport. Reported computations of quickest path measures have considered regional networks and time windows of 24 hours [14,18]. Once the temporal network is built, the quickest paths are computed using specific algorithms [15]. The construction of the temporal network needs additional considerations to eliminate unpractical or unreasonable possibilities of connection: • When we consider scheduling concerns, the real possibilities of connection are fewer than those present in the airport network. In other cases,

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some connections may be unpractical, as they take too much steps or make an excessive detour. This can be sorted out by eliminating routes with large values of routing factor (see Section 5.2). A usual, the rule of thumb is excluding paths with routing factor above 1.5 (see Table 5.9). • Other routes to exclude are those including close airports. For instance, it is possible that a route involves passing through London Heathrow and Stansted. These routes can be improved using alternative modes of transportation (e.g., going by road or rail to one of the airports). For this reason, Malighetti et al. [14] exclude routes passing through airports closer than 100 kilometres. Quickest path measures present a more precise view of real possibilities of connection at the cost of a more complex and computationally demanding representation available for regional networks and narrow time windows.

5.6 Connectivity and airline business models Basic properties of airline networks do not show differences between airlines adopting different route configurations (see Table 4.10 of Chapter 4). According to Alderighi et al. [1] and Lordan [12], differences between huband-spoke and point-ot-point network configurations can be explained as differences of spatial and temporal concentration. A route network with high spatial concentration is organised around a few airports: this is the case of the hub-and-spoke configuration, where traffic is organised around the hub. Airlines adopting a point-to-point route configuration have no explicit hubs, but tend to concentrate their routes around one or more operational bases. So, for different reasons, we can expect high spatial concentration in the route networks of low-cost and full-service airlines. In a route configuration with high temporal concentration, flights will be organised to facilitate connections. This is the case of hub-and-spoke networks, where flights are scheduled in a wave-system around the hub [4]. Airlines adopting pointto-point network configurations prefer schedule routes to optimise aircraft and labour productivity, so we would expect lower values of temporal concentration. Then full-service networks will have higher levels of temporal concentration than full-cost. However, we have to acknowledge that the full-service and full-cost business models are not the only ones adopted by airlines: Klophaus et al. [11] identify several hybrid business models, and some Arabian Gulf carriers, like Emirates, have a specific business model

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Table 5.5 A list of airlines adopting different business models, including hybrid [11] and Arabian Gulf [17]. Business model Airline

Low-cost carriers

Ryanair Volotea Southwest Airlines

Hybrid airlines

Vueling Airlines Transavia Norwegian

Full-service

American Airlines Lufthansa China Eastern Airlines

Arabian Gulf

Emirates

[17]. In the next section, we illustrate the methodology developed by [1] to evaluate spatial and temporal concentration to the airlines of Table 5.5.

5.6.1 Measuring spatial concentration An airline has a high spatial concentration if most of its operations depart from or arrive at one or a few airports. The network with maximum spatial concentration is the star network. In a star network of N nodes, the central node is connected with the other N − 1 nodes, and no connection exists between peripheral nodes (see Fig. 5.5). Spatial concentration is evaluated with the unweighted undirected airline airport network, where each node is an airport or metropolitan area, and edges represent direct connections between the nodes operated by the airline. Alderighi et al. [1] suggest evaluating the spatial concentration using the graph centrality indexes defined by [9] for social networks, as centrality in social networks is analogous to spatial concentration in transportation networks. These measures are relative to the maximum possible value of centrality for a graph of the same size, so they will be equal to one for a star graph. The degree-based graph centrality is defined as   1 kMAX − ki , kG = 2 N − 3N + 2 i=1 N

(5.11)

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Figure 5.5 A star graph, the network with maximum degree and betweenness graph centrality. The centre H of a star of N has maximum values of degree and betweenness for a network of size N.

where kMAX is the maximum value of degree in the network. The betweenness-based graph centrality is obtained as bG =

N  

1 N3

− 4N 2

+ 5N − 2



bMAX − bi .

(5.12)

i=1

Another measure of heterogeneity is the Gini index. This measure was developed by Conrado Gini to measure inequalities of income, but it can be used to measure inequality of any distribution. It is proportional to the area between the line of perfect equality and the Lorenz curve. If we consider heterogeneity of frequency of offered flights, then the Lorenz curve for the proportion x is equal to the fraction of flights offered from the x bottom airports, ranked by the considered measure. A Gini index equal to zero represents perfect homogeneity, and a value equal to one maximum represents heterogeneity. A practical way of computing the Gini index is as a half of the mean absolute differences, normalised by the mean of the considered measure:  1    xi − xj  . 2 2N x¯ i=1 j=1 N

G=

N

(5.13)

Whereas kG and bG are defined for unweighted networks, the Gini index can be computed for node strength measures, like the frequency of flights and available seats.

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Figure 5.6 The left plot presents the values of graph centralities bG (black) and kG (grey) for the selected airlines. The right plot presents the Gini indices calculated from available seats (black) and frequency of flights (grey) for the same airline list.

For the airlines listed in Table 5.5, we have computed the following indices of spatial concentration: • Degree-based graph centrality kG . • Betweenness-based graph centrality bG . • Gini index of node strength with edge weights equal to frequency of flights. • Gini index of node strength with edge weights equal to available seats. The values of the four indices of spatial concentration are shown in Fig. 5.6: • The Spearman correlations between the two graph centralities and the two Gini indices are 0.855 and 0.976, respectively, much higher than the Spearman correlations across centralities and Gini indices. Although the sample size is low, we can argue that graph centralities and Gini indices measure two different facets of spatial concentration corresponding to the unweighted and weighted airport network. • The lowest values of spatial concentration correspond to airlines adopting the low-cost business model: Ryanair, Volotea and Southwest Airlines. In Fig. 5.7, we present the route maps of Volotea and Southwest Airlines, which can be regarded as typical examples of point-to-point network configurations. These route maps provide additional evidence of low spatial concentration. • The route networks of airlines adopting hybrid business models present high values of spatial concentration. Vueling and Transavia are subsidiaries of larger airline companies or holdings (IAG and KLM, respectively). The route maps of Fig. 5.8 show that their airport networks are centred on hubs complementary to other companies of the same holding: Vueling on Barcelona-El Prat and Transavia on Amsterdam

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Figure 5.7 Route maps of Volotea (left) and Southwest Airlines (right). Both networks present relatively low indices of spatial concentration, the result of a point-to-point network configuration.

Figure 5.8 Route maps of Vueling (left) and Transavia (right). Although these airlines are sometimes presented as low-cost, their route networks present a high spatial concentration around Barcelona-El Prat (BCN for Vueling, Amsterdam Schipol (AMS), Eindhoven (EIN) and Rotterdam the Hague (RTM) for Transavia.

Schipol, Eindhoven and Rotterdam the Hague. Norwegian, the other hybrid airline, has lower values of spatial concentration. • The three full-service airlines of the list have intermediate values of spatial concentration, measured by either graph centrality or Gini indices. Their airport networks are far from being a star network, so airlines have no pure hub-and-spoke configuration. Lufthansa has a two-hub route network based on Frankfurt (FRA) and Munich (MUC) airports, whereas American Airlines and China Eastern have a multi-hub structure, as shown in Fig. 5.9. As they take advantage of Sixth Freedom to schedule connecting flights between different countries, all their hubs are located in their home country.

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Figure 5.9 Route maps of American Airlines (left) and China Eastern (right). These companies operate intercontinental flights, but we have presented only their US and China nodes, respectively. These airlines operate a multi-hub network structure, all hubs being in their home country.

• Emirates Airlines has a almost pure hub-and-spoke structure centred

in Dubai (DBX) airport. For this reason, it has the highest values of Freeman indices. As there is no predominant spoke airport, the Gini index of Emirates has an intermediate value. As a generic conclusion, it seems that degree and betweenness graph centrality does a better job in discriminating airlines by spatial concentration, although it is based on unweighted airline airport networks, as Gini indices show less variability. These results are similar to those obtained by [1] when measuring spatial concentration. The results of spatial concentration analysis show a nuanced relationship between airline business model and spatial concentration: low-cost airlines have airport networks with low spatial concentration, whereas Emirates and subsidiaries of full-service carriers are more spatially concentrated. Full-service carriers tend to adopt a multi-hub structure, which allows them to offer connecting flights in several airports of its hometown. The number of hubs for these companies seems to be proportional to hometown extension: whereas Lufthansa has only two hubs, from Fig. 5.9 we can see that American Airlines has six hubs and China Eastern four.

5.6.2 Measuring temporal concentration In the spatial concentration analysis of different airline business models, we have detected airports with high centrality. The role of these airports in airline operations can be quite different, depending on the business model adopted:

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• Full-service carriers adopt a (multi-)hub-and-spoke network configura-

tion. This means that their central airports act as hubs. In these hubs, these companies offer connecting flights that allow them to reach spoke airports through indirect connections. • Low-cost airlines adopt a point-to-point configuration, which allows them to optimise the efficiency of aircraft and crew. For these airlines, central airports act as technical bases, where they centralise their maintenance operations. These bases can be also located in sources of high demand of air travel. The difference between hubs and technical bases lies in temporal concentration. Hub-and-spoke configurations require flights to be scheduled to facilitate passenger transfer, so they adopt a wave-system, scheduling their flights with several connection waves along the day. A connection wave is a set of incoming and outcoming flights, so all incoming flights can connect with all outgoing flights [4]. Companies operating with connection waves have a high number of potential indirect connections, that is, all possible connecting flights available with a specific routing schedule. A high number of potential indirect connections reveals a high temporal concentration of airline routing network. The number of potential indirect connections can be very high, as they can occur in different moments of time: for some routes, it is possible to find more than one connecting flight on the same day. So we need to filter possible indirect connections to retain only those attractive for travellers. The attractiveness of an indirect connection for an air traveller depends on the factors described in Table 5.6. To these factors we must add that any connection needs a minimum connection time to allow enough time for transfer of passengers and baggage from one plane to another. The specific values for these factors depend on traveller’s preferences and fares paid for the connecting flight. As researchers do not usually have access to fares of airline tickets, and even these can be different for the same route because of revenue management practices, they need to adopt a set of criteria to retain relevant indirect connections. The choices we are adopted for the evaluation of indirect connections are summarised in Table 5.7. Some of the criteria adopted in Table 5.7 are somewhat subjective and are often justified by previous research choices and ad hoc evidence. To our knowledge, there is little research on passenger’s preferences about connecting times or routing factor. To justify their choices on transfer times, Alderighi et al. [1] refer to the values of Table 5.8. We have maintained their choice of retaining connections with transfer times between 50 and

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Table 5.6 Factors affecting the attractiveness of an indirect connection. Factor Description

Routing factor

Time perception Fares Loyalty programs Hub

Ratio of total distance covered by all flights on an indirect connection to the distance between origin and destination. Connections with a high routing factor are not be attractive for air travellers. Passengers perceive transfer time as being longer than in-flight time. Lower fares may compensate for longer transfer and in-flight times. Flying with a specific airline may be attractive because the air traveller participates in its loyalty programme. Hub amenities can drive passengers to choose a connection through that hub.

Source: Veldhuis [21].

Table 5.7 Criteria adopted to compute indirect connections for the selected airlines. Factor Description

Flights Number of connections Connecting times Routing factor

All scheduled flights for each of the ten airlines of the sample in the second week of August 2018. No more than one connection for distance between origin and destination of less than 4,800 km, two or more connections for distances equal to or larger than 4,800 km. Minimum connecting time 50 min, maximum connecting time 120 min. Connections with routing factor less than or equal to 1.5.

Table 5.8 Connection quality thresholds (maximum waiting time in minutes) as defined by Bootsma [3]. Connection Excellent Good Poor

Europe–Europe Europe–intercontinental Intercontinental–intercontinental

90 120 120

120 180 240

180 300 720

Source: [1].

120 minutes, as a maximum connection time of 120 minutes is acceptable for all types of flights. As for the routing factor, in Table 5.9, we have presented some examples for long-haul and short-haul indirect connections, some of them experienced by authors. The Manchester–London connection through Amster-

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Table 5.9 Some values of routing factors (RF) for connecting flights. Distances in kilometres. Connection Step 1 Step 2 Direct RF

Manchester–Amsterdam–London Barcelona–Prague–Rhodes Barcelona–Amsterdam–Lima Barcelona–Istanbul–Almaty Barcelona–Frankfurt–Almaty

484 1358 1241 2229 1093

367 1883 10512 3927 5087

241 2311 9997 5962 5962

3.53 1.40 1.17 1.03 1.38

dam is a typical example of back-tracking flight, so it has a very high routing factor: this is a kind of connection discarded when filtering by routing factor. We can appreciate that Istanbul is more competitive than Frankfurt to connect Barcelona to Almaty (main city of Kazakhstan) because of its geographical position. The Barcelona–Amsterdam–Lima connection may seem a relevant detour, but the distance from Lima to European cities makes it acceptable. These values lead us to think that travellers will accept indirect connections with routing factors below 1.5. In our analysis, we have allowed no more than two connections for each trip, one connection for short-haul routes and two connections for long-haul routes. Then the outcome of indirect connections assessment will be the following values for each airline: • s0 : the number of unique direct connections offered by the airline. • s1 : the number of unique pairs origin-destination that can be reached with one or more stops (i.e., two flights or steps). • s2 : the unique pairs origin-destination that can be reached with at least two stops (i.e., two flights or steps). • N: the number of airports where departs or arrives at least one flight scheduled by the airline. The collection of paths between airports reachable in one, two or three steps can be seen as a refinement of the airline networks defined in the Section 4.5 of Chapter 4: the value of N defined here is also the number of nodes of the airport network, and the direct connections defined here are analogous to the edges of the airport network, so the values of s0 defined here and the number of edges of the airport network E reported in Table 4.10 of Chapter 4 are also analogous. An airline will have high values of temporal concentration if we can obtain many connecting flights from their airline schedule. Alderighi et al. [1] measures temporal concentration as the ratio of indirect connections to to-

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Table 5.10 Number of unique direct routes s0 , routes that have to be taken in at least one (s1 ) or two (s2 ) steps, ratio R1 of indirect to total connections, and total destinations reached N for operated routes the selected airlines. s0 s1 s2 R1 N Airline

Lufthansa American Airlines Emirates Vueling Norwegian Southwest Airlines China Eastern Airlines Ryanair Transavia Volotea

311 1051 155 332 245 716 741 1684 120 278

6922 21291 902 1426 752 2255 1631 2211 144 68

1689 5418 340 3 91 33 720 5 0 0

0.965 0.962 0.889 0.811 0.775 0.762 0.760 0.568 0.545 0.197

204 349 145 130 113 99 228 211 86 79

tal connections. In terms of the values defined here, if we consider a pure hub-and-spoke system of N nodes, then we have: • N (N − 1) /2 total connections of which • N − 1 direct connections and • (N − 1) (N − 2) /2 indirect connections For companies operating a hub-and-spoke network configuration, the number of direct connections with respect to total connections will be very small, as potential indirect connections grow with the square of number of airports covered. For airlines operating point-to-point, the quantity of indirect connections should be smaller, as their flights are not synced to make them possible. It is important to note that here we obtain all potential indirect connections, being offered by the airline or not: full-service carriers may not offer some indirect connections, and low-cost carriers do not sell any. Then we can measure temporal concentration with the ratio R1 =

s1 + s2 . s0 + s1 + s2

(5.14)

For airlines with high temporal concentration, the ratio R1 is closer to one and is closer to zero for low temporal concentration. The results of the indirect connectivity analysis are presented in Table 5.10. The airlines with highest values of temporal concentration are Lufthansa and American Airlines: most of the 96% of routes offered by these airlines are through indirect connectivity. Emirates and Vueling rank close to the full-service carriers, as most of their operations pass through their

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Table 5.11 Number of unique direct routes s0 , routes that have to be taken in at least one (s1 ) or two (s2 ) steps, ratio R1 of indirect to total connections, and total destinations reached N for marketed routes the selected airlines. s0 s1 s2 R1 N Airline

American Airlines Lufthansa Emirates China Eastern Airlines Vueling Norwegian Southwest Airlines Ryanair Transavia Volotea

1505 1055 682 1226 346 245 716 1684 120 278

24650 12099 2809 3340 1548 752 2255 2211 144 68

26534 19763 3550 3985 10 91 33 5 0 0

0.971 0.968 0.903 0.857 0.818 0.775 0.762 0.568 0.545 0.197

572 490 445 390 132 113 99 211 86 79

hub: Dubai International for Emirates and Barcelona-El Prat for Vueling. Transavia, the other company with an hybrid business model, has much lower temporal concentration, as its operations are spread through three hubs. As for temporal concentration, Volotea is the only company to behave like a pure low-cost. Ryanair, Norwegian and Southwest Airlines offer relatively high values of indirect connectivity; in fact, Vueling, Norwegian and Southwest Airlines sell tickets with connecting flights.

5.6.3 The impact of codeshare in airline connectivity The measures of spatial and temporal concentrations for the selected airlines have been calculated with the flights operated by the airline. Airlines can extend their network engaging in codeshare agreements with other airlines. In a codeshare agreement, two or more airlines market the same flight, each with their own airline flight code: in addition to the operating carrier, one or more marketing carriers selling the same flight with their own flight code. Codeshare agreements allow marketing airlines to extend their route network, and operating airlines can improve their load factor (ratio of sold seats to available seats). The temporal concentration analysis of the previous section was performed with operating flights only. To assess the effect of codesharing, we have repeated the analysis with the flights marketed in each airline. The results of the analysis are presented in Table 5.11, which has the same structure as Table 5.10.

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Figure 5.10 Comparison of unique direct routes s0 , routes that have to be taken in at least one (s1 ) or two (s2 ) steps without codeshare (left) and with codeshare (right) for the selected airlines.

The effects of codeshare are very uneven across airlines, as not all airlines engage in codeshare agreements. In Fig. 5.10, we have compared the indirect connectivity of each airline without and with codeshare. We can appreciate significant differences in connectivity for American Airlines and Lufthansa, belonging to Oneworld and Star Alliance, and in minor scale for China Eastern, member of SkyTeam, and for Emirates. For these airlines, the largest increase of indirect connections is for those that have to be made in at least two steps. This can be explained considering the available freedoms of the air: whereas it is possible for an airline to connect two foreign airports in a one-step connecting flight stopping in its local hub, to provide a two-step connecting flight the airline needs to sell tickets together with another airline, preferably with a hub located in another region of the world. This is one of the reasons for the formation of airline alliances. It must be noted, though, that an airline does not need to belong to an alliance to engage in codeshare, as the Emirates case illustrates, and that airlines can establish codeshare agreements with airlines not belonging to their alliances. Codeshare agreements have also a significant impact on network size and spatial concentration of the airport network, as can be seen in Fig. 5.11. Emirates and airlines following the full-service business model extend considerably their network when engaging in codeshare with other airlines following similar business models. As a result, spatial concentration is slightly reduced for these airlines, except for China Eastern. A comparison of the airport network without and with codeshare for China Eastern shows that in the codeshare network, airports like Paris Charles de Gaulle (CDG) Los Angeles (LAX) and New York JFK have high values of betweenness, and that the betweenness of Shanghai Pudong (PVG) and Kunming (MKG) air-

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Figure 5.11 Number of destinations reached (left) and betweenness-based graph centrality bG (right) for the selected airlines without codeshare (noc) and with codeshare (cod).

ports also increases significantly. This suggests that the role of China Eastern in SkyTeam is to facilitate Chinese routes to other alliance members, like Air France and Delta.

5.7 Demand-based measures of connectivity The measures of connectivity described in this chapter are supply-based, as they are computed from information of flights schedules offered by airlines. Data available from Marketing Information Data Tapes (MDTI) allows us to gather information about demand, that is, tickets bought by passengers. MIDT data come from bookings made from Global Distribution Systems by travel agents such as Sabre or Amadeus. They include no information of tickets bought directly to airlines through their websites. MDTI data includes detailed information of each ticket, including origin and destination. This means that we can gather information about specific markets, that is, pairs of origin and destination. Demand-based data can draw a significantly different picture that supply-based data. For airlines using a hub-and-spoke distribution model, flights connecting peripheral airports with hubs are transporting passengers attracted by different markets. Rodríguez-Déniz et al. [20] define a market-based measure of betweenness based on shortest paths, where the contribution of each market is weighted by the proportion of passengers it covers: 

Qjk σjk (i) , Q σjk j,k∈N ,j=k=i

(5.15)

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where σjk and σjk (i) are the numbers of shortest paths between j and k and the number of these paths that go through i, respectively, Qjk is the demand   of passengers of market j, k , and Q is the total demand, respectively. The same authors define in Rodríguez-Déniz et al. [19] a measure of flow betweenness centrality based exclusively on demand data. They translate the concept of flow betweenness to the context of air transport demand, defining the passenger flow between j and k as the variable Qjk in Eq. (5.15). Then their measure of flow betweenness is 

Qjk (i) . Qjk j,k∈N ,j=k=i

(5.16)

Passenger-oriented metrics offer a perspective of airport centrality different from supply-based measures. Some of these measures, like that defined in Eq. (5.16), are completely independent from topological data. The drawback of those measures is the difficulty of gathering data: it is likely that MDTI offers skewed or incomplete information of ticket sales of low-cost carriers, as many of their tickets sales take place in their websites.

References [1] M. Alderighi, A. Cento, P. Nijkamp, P. Rietveld, Assessment of new hub-and-spoke and point-to-point airline network configurations, Transport Reviews 27 (5) (Sep. 2007) 529–549, https://doi.org/10.1080/01441640701322552. [2] A. Barrat, M. Barthélemy, R. Pastor-Satorras, A. Vespignani, The architecture of complex weighted networks, Proceedings of the National Academy of Sciences of the United States of America 101 (11) (Mar. 2004) 3747–3752, http:// www.pubmedcentral.nih.gov/articlerender.fcgi?artid=374315&tool=pmcentrez& rendertype=abstract. [3] P. Bootsma, Airline Flight Schedule Development – Analysis and Design Tools for European Hinterland Hubs, PhD thesis, Universiteit Twente, 1997. [4] G. Burghouwt, J. de Wit, Temporal configurations of European airline networks, Journal of Air Transport Management 11 (3) (May 2005) 185–198, http://linkinghub. elsevier.com/retrieve/pii/S0969699704000559. [5] G. Burghouwt, R. Redondi, Connectivity in air transport networks: an assessment of models and applications, Journal of Transport Economics and Policy 47 (1) (Nov. 2013) 35–53, https://www.jstor.org/stable/24396351%0A. [6] G. Burghouwt, J. Veldhuis, The competitive position of hub airports in the transatlantic market, Journal of Air Transport 1 (11) (2006) 106–130. [7] L. Dall’Asta, A. Barrat, M. Barthélemy, A. Vespignani, Vulnerability of weighted networks, Journal of Statistical Mechanics: Theory and Experiment 04 (Apr. 2006) P04006, http://iopscience.iop.org/1742-5468/2006/04/ P04006, http://stacks.iop.org/1742-5468/2006/i=04/a=P04006?key=crossref. 019695efb3ce58317554f2604375bff9.

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[8] W.-B. Du, X.-L. Zhou, O. Lordan, Z. Wang, C. Zhao, Y.-B. Zhu, Analysis of the Chinese airline network as multi-layer networks, Transportation Research Part E: Logistics and Transportation Review 89 (2016) 108–116, http://www.sciencedirect.com/ science/article/pii/S1366554515300521. [9] L. Freeman, Centrality in social networks conceptual clarification, Social Networks 1 (1979) 215–239, http://www.sciencedirect.com/science/article/pii/ 0378873378900217. [10] R. Guimerà, L.A.N. Amaral, Modeling the world-wide airport network, The European Physical Journal B – Condensed Matter 38 (2) (Mar. 2004) 381–385, https:// doi.org/10.1140/epjb/e2004-00131-0. [11] R. Klophaus, R. Conrady, F. Fichert, Low cost carriers going hybrid: evidence from Europe, Journal of Air Transport Management 23 (2012) 54–58, http://linkinghub. elsevier.com/retrieve/pii/S0969699712000166. [12] O. Lordan, Study of the full-service and low-cost carriers network configuration, Journal of Industrial Engineering and Management 7 (5) (Oct. 2014) 1112–1123, http:// www.jiem.org/index.php/jiem/article/view/1191. [13] O. Lordan, J.M. Sallan, P. Simo, D. Gonzalez-Prieto, Robustness of the air transport network, Transportation Research Part E: Logistics and Transportation Review 68 (Aug. 2014) 155–163, http://linkinghub.elsevier.com/retrieve/pii/ S1366554514000805. [14] P. Malighetti, S. Paleari, R. Redondi, Connectivity of the European airport network: “self-help hubbing” and business implications, Journal of Air Transport Management 14 (2) (Mar. 2008) 53–65, http://linkinghub.elsevier.com/retrieve/pii/ S0969699707000981. [15] E. Miller-Hooks, S. Stock Patterson, On solving quickest time problems in timedependent, dynamic networks, Journal of Mathematical Modelling and Algorithms 3 (1) (2004) 39–71, https://doi.org/10.1023/B:JMMA.0000026708.57419.6d. [16] K. Mukkala, H. Tervo, Air transportation and regional growth: Which way does the causality run?, Environment and Planning A 45 (6) (2013) 1508–1520. [17] J.F. O’Connell, The rise of the Arabian Gulf carriers: an insight into the business model of Emirates airline, Journal of Air Transport Management 17 (6) (Nov. 2011) 339–346, https://doi.org/10.1016/j.jairtraman.2011.02.003, https:// linkinghub.elsevier.com/retrieve/pii/S0969699711000160. [18] S. Paleari, R. Redondi, P. Malighetti, A comparative study of airport connectivity in China, Europe and US: Which network provides the best service to passengers?, Transportation Research Part E: Logistics and Transportation Review 46 (2) (2010) 198–210, https://doi.org/10.1016/j.tre.2009.08.003. [19] H. Rodríguez-Déniz, P. Suau-Sanchez, A. Voltes-Dorta, Classifying airports according to their hub dimensions: an application to the US domestic network, Journal of Transport Geography 33 (Dec. 2013) 188–195, https://linkinghub.elsevier.com/retrieve/ pii/S0966692313002093. [20] H. Rodríguez-Déniz, P. Suau-Sanchez, A. Voltes-Dorta, Using SAS® to measure airport connectivity: an analysis of airport centrality in the US network with SAS-IML® studio, in: Proceedings of the SAS Global Forum, 2013, p. 152. [21] J. Veldhuis, The competitive position of airline networks, Journal of Air Transport Management 3 (4) (Oct. 1997) 181–188, http://linkinghub.elsevier.com/retrieve/pii/ S0969699797861698.