Scenarios for a post-COVID-19 world airline network

Jiachen Ye12 Peng Ji12lowast Marc Barthelemy34lowast1Institute of Science and Technology for Brain-Inspired Intelligence Fudan University Shanghai 200433 China

2Potsdam Institute for Climate Impact Research (PIK) 14473 Potsdam Germany3Institut de Physique Theacuteorique Universiteacute Paris Saclay CEA CNRS F-91191 Gif-sur-Yvette France

4Centre drsquoAnalyse et de Matheacutematique Sociales (CNRSEHESS) 54 Boulevard Raspail 75006 Paris France(Dated July 8 2020)

The airline industry was severely hit by the COVID-19 crisis with an average demand decrease ofabout 64 (IATA April 2020) which triggered already several bankruptcies of airline companies allover the world While the robustness of the world airline network (WAN) was mostly studied as anhomogeneous network we introduce a new tool for analyzing the impact of a company failure thelsquoairline company networkrsquo where two airlines are connected if they share at least one route segmentUsing this tool we observe that the failure of companies well connected with others has the largestimpact on the connectivity of the WAN We then explore how the global demand reduction affectsairlines differently and provide an analysis of different scenarios if its stays low and does not comeback to its pre-crisis level Using traffic data from the Official Aviation Guide (OAG) and simpleassumptions about customerrsquos airline choice strategies we find that the local effective demand canbe much lower than the average one especially for companies that are not monopolistic and sharetheir segments with larger companies Even if the average demand comes back to 60 of the totalcapacity we find that between 46 and 59 of the companies could experience a reduction of morethan 50 of their traffic depending on the type of competitive advantage that drives customerrsquosairline choice These results highlight how the complex competitive structure of the WAN weakensits robustness when facing such a large crisis

I INTRODUCTION

We see only the beginning of the socio-economic im-pact of the coronavirus pandemic (COVID-19) thatspread over the whole world in the first semester of 2020All sectors agriculture manufacturing industry and ofcourse the tertiary sector will be strongly affected bythis crisis [1] and our way of life could deeply changeIn particular the airline industry was severely hit withmany governments that enforced both domestic and in-ternational travel restrictions at various degrees Somecountries restricted the flights from severely affected ar-eas while others even cancelled almost all flights Thesetravel restrictions did delay or interrupt the further trans-mission of the COVID-19 [2] but also caused great dam-age to the world airline network (WAN) [3] the mostimportant travel network in todayrsquos world and one of thekey infrastructures of todayrsquos global economy

More precisely the COVID-19 outbreak caused a de-cline from 44 665 segments in the period 1-7 January2020 to 24 371 in the period 19-25 April 2020 (represent-ing a decrease of 454) thus impacting a large numberof companies In order to visualize this variation weaverage over a 7-day time window the capacity (givenby the number of seats for all flights) for each com-pany and plot the result on Fig 1 In particular weshow the capacity for the three biggest airline compa-nies in China (Air China China Southern Airlines andChina Eastern Airlines) and how their capacity dropped

lowastElectronic address pengjifudaneducnmarcbarthelemyiphtfr

around the beginning of February Many other airline

0101~01070205~0211

0311~03170415~0421

000025050075100125150175

Capa

city

(X10

6 )

American AirlinesAir FranceAir China LimitedChina Southern AirlinesDelta AirlinesLufthansa CargoChina Eastern AirlinesUnited Airlines Cargo

Figure 1 Evolution of the capacity of various airline compa-nies early 2020 We highlight several large companies Thecapacity of each company is averaged over every 7 days

companies also faced the decrease of capacity later withthe epidemic spreading over the whole world includingLufthansa Cargo at the end of February and Delta Air-lines American Airlines United Airlines Cargo and AirFrance during the middle of March

This is not the first time that the WAN suffered large-scale disruptions For example the eruption of the vol-cano Eyjafjallajokull in 2010 not only threatened thesafety of local residents but also seriously affected the airtraffic in Europe by causing the cancellation of 108 000flights disrupting the travel plans of 105 million passen-gers and costing the airline industry in excess of $17 bil-lion in lost revenue [4 5] There are however differenceswith these rare events which brought massive losses for

arX

iv2

007

0210

9v1

[ph

ysic

sso

c-ph

] 4

Jul

202

0

2

the air industry and the current crisis First it remainsunclear how long this pandemic will last Since effect ofhigh temperature and high humidity on COVID-19 seemsto be limited [6] most experts do not expect that the epi-demic will naturally come to an end in the summer 2020As a consequence governments may have to maintain thetravel restrictions which is definitely a strike to the wholeair industry Second it remains unclear how the demandwill resume back to normal if it does so An analysis ofthe Boston Consulting Group [7] proposed various sce-narios for the evolution of the air travel demand themost probable one being a gradual recovery stretchinginto 2021 (lsquoprolonged U-shapersquo) This is motivated bythe fact that international travel is discouraged and thatborders will slowly reopen leading to a slow return of theconsumer confidence The economic recession and thefailure of travel distributors will enhance this drop of airtravel demand This situation could thus last a whileand has already provoked the bankruptcies of more than20 airlines so far [8 9] such as Air Italy (Italy) Flybe(UK) which was the largest independent regional airlinein Europe Trans States Airlines (US) Compass Airlines(US) Virgin Australia (Australia) Avianca (Colombia)etc Other major airlines called for multibillion bailoutin order to survive [10]

There are of course different reasons why an airlinegoes bankrupt [11] but it ultimately boils down to thelack of cash to cover the airlinersquos liabilities An impor-tant ingredient is then the structure of the WAN and inparticular how the different airlines which compose itare superimposed and interact with each other Anothercrucial ingredient is how customers will choose an airlinerather than another one and it is in these extreme casesthat a competitive advantage will prove to be fundamen-tal In this work we will address two aspects Firstwe will analyze the robustness of the WAN against thebankruptcy of different airlines and which failures arethe most dangerous for its connectivity In this part wewill also study how the traffic can reorganize itself In asecond part we will consider how the global traffic de-mand reduction will affect different airlines and for thiswe will test various strategies of how customers choosetheir airline company For these studies we will use realtraffic data from the Official Aviation Guide (OAG) forthe WAN (see Material and Methods)

II THE EFFECT OF BANKRUPTCIES ON THEWORLD AIRLINE NETWORK

A Robustness and the lsquoairline company networkrsquo

Usually the WAN is defined as the network composedof nodes that are airports and links that represent directflights between two airports [12ndash14] An obvious fact butoften ignored in many studies about the WAN is thatit results in fact from the superimposition of routes be-longing to different airlines leading to the well-known

emergent hub-and-spoke structure [15] Each airline op-timizes its own profit and the WAN can thus be seenas the emerging network resulting from the choices of allthese operators Despite this important aspect the struc-ture and the robustness of the WAN have mostly beenstudied from a topological point of view with a focus onthe effect on the giant connected component of node orlink removal [16ndash18] However as noted above describ-ing the WAN as a simple topological network might beoversimplified and in order to reach realistic conclusionsit seems necessary to take into account other aspects ofthis network (for a review and research agenda aboutthe robustness of this network see [19]) In particularsome works studied this important airline aspect andconsidered the WAN as a multilayer network where eachlayer is a different airline company [14 20ndash22] We notethat in [22] the authors considered an interesting studyof re-scheduling of passengers after the failure of a givensegment

Here we will analyze the robustness of the WAN whenfacing airline bankruptcies This is different from theusual robustness study where nodeslinks are removedInstead the removal of an airline implies the removal ofpossibly many segments andor the decrease of capacityif the segment is shared with another company or thecomplete removal of the link if the airline was the onlyone operating on it We first construct the WAN basedon the data provided by the OAG for the period 1st Jan-uary - 25th April 2019 (see Material and Methods fordetails) In order to analyze the robustness of this multi-layer network from this point of view we then constructwhat we call here the lsquoairline company networkrsquo (ACN)where nodes represent airline companies (the number ofnodes is here m = 849) and two nodes in this networkare connected if the corresponding companies share atleast a segment Obviously two airline companies canshare more than one segment and it is natural to definethe weight of a link in the ACN as the segment overlapgiven by

Oij =

sum

`isinLicapLj

minNi(`) Nj(`)minNi Nj

i 6= j

0 i = j

(1)

where Li is the set of segments operated by company iNi(`) is the capacity of company i on segment ` (aver-aged over T = 116 days) and Ni =

sum`isinLi

Ni(`) is thetotal capacity of company i This segment overlap cap-tures the similarity between two airline companies andits distribution is shown in Fig S1 in the appendix Weobserve a wide range of this overlap and while most ofthe companies do not share segments with each othernearly 100 pairs of companies display an overlap equal to1 indicating that either one is included in the other orthat they are proposing exactly the same set of segmentsand are thus in direct competition

The study of this weighted ACN allows us to have abetter view of how the different airlines interact with each

3

other In particular it will help us to understand howrobust the WAN is when airlines are failing In generalwhen studying the robustness of the WAN different linkor node removal strategies are adopted [16 17] Remov-ing a link implies that all companies operating on thissegment stopped simultaneously which is unlikely to oc-cur in general except in cases of airport closures whichhappened for example during the eruption of the vol-cano Eyjafjallajokull Here we will consider the specificsituation where many airlines can fail The bankruptcyof an airline does not imply however that one or moresegments in the WAN will disappear but just that itscapacity will be reduced

Based on the segment overlap it is natural to definethe average segment overlap of a company with its lsquoneigh-boursrsquo as

Oi =1

|Ci|sumjisinCi

Oij (2)

where Ci = j | Oij gt 0 is the set of companies sharingat least one segment with company i and |Ci| representsthe number of corresponding companies A large averagesegment overlap indicates that the corresponding airlinecompany shares many segments with others and is thusin direct competition with them In contrast a smalloverlap indicates a company that operates alone on somesegments and does not suffer any competition there It isthen tempting to think that the average segment overlapcan serve as an indicator for identifying lsquocriticalrsquo compa-nies whose bankruptcy will induce the isolation of cer-tain airports and cities and cause a great damage to theconnectivity of the WAN

Classically when ignoring the structure in terms of air-line companies the most effective strategy to destroy theconnectivity of the WAN is to remove the most centralnodes (ie nodes with highest betweenness centralitysee [16 17]) or the links with the lowest traffic [18] Asalready mentioned above these results do not providemuch information about the impact of airline bankrupt-cies and the partial reduction in traffic capacity for cer-tain segments In order to test this influence we firstconsider the robustness of the WAN for four differentremoval strategies (i) random removal of airline com-panies (ii) removal of airline companies with the largestpassenger capacity Ni (iii) removal of airline companieswith the largest betweenness centrality computed in theweighted ACN (iv) removal of airline companies withthe largest average segment overlap Oi We note thatfor strategy (iii) the calculation of the betweenness cen-trality in the weighted ACN relies on the shortest pathbetween two nodes such that the sum of weights (herethe segment overlap Oij) is maximal among all connec-tive paths As most robustness analysis do we choosethe size of the giant component (ie the connected sub-graph with the largest number of nodes) as the measureof the connectivity of the WAN

We show in Fig 2 the size of the giant component ofthe WAN as a function of the fraction of the cumulative

0 20 40 60 80 100Fraction of Cumulative Capacity of Removed Companies

0500

100015002000250030003500

Size

of t

he G

iant

Com

pone

nt (W

AN)

RandomCapacityBetweenness CentralityAverage Segment OverlapMonopolistic Index

Figure 2 Size of the giant component of WAN as the func-tion of the fraction of the cumulative passenger capacity ofremoved companies Five different removal strategies of air-line companies are compared

passenger capacity of removed companies (which impliesthat the intervals along the x-axis between dots are notuniform due to the diversity of the companiesrsquo capaci-ties) For the strategy (ii) where we remove companiesaccording to their passenger capacity (from the largestto the smallest) the variation over the x-axis is large butthe impact on the WAN is small Sorting and removingcompanies according to their betweenness centrality inthe ACN is also not very effective Compared to thesecases removing airline companies in a random order hasactually a larger impact on the WAN structure Howeverwe observe that the last strategy (iv) is very effectiveremoving companies according to their integration withother companies seems to have the largest impact on theWANrsquos connectivity suggesting that crucial paths in theWAN are shared by the same set of companies Moregenerally this is a sign that in order to understand therobustness of the WAN and the impact of the failure ofan airline company we need to take into account its in-teraction with the other companies

This discussion shows that not all airlines are equiva-lent and that their bankruptcy can display a large varietyof consequences In particular the location of the airlinein the ACN or in other words how it is coupled to othercompanies seems to be a crucial ingredient for under-standing the impact of its bankruptcy This leads us toquantify how much a company has the monopoly over itsdifferent segments and we define the monopolistic indexas

Mi =1

|Li|sum`isinLi

Ni(`)summj=1Nj(`)

(3)

where |Li| is the total number of segments serviced bycompany i This index is equal or close to 1 if most thesegments of company i are dominated by i The distribu-tion of Mi shown in Fig 3 indicates that there is a largevariety of companies with various degree of monopolydemonstrating the large diversity of the airlines compa-nies The peak at M = 1 indicates that there are about

4

00 02 04 06 08 10Monopolistic Index

01020304050607080

Dist

ribut

ion

Figure 3 Distribution of monopolistic index

80 companies which are totally monopolistic all theirsegments are not shared with another company

The importance of this feature can be checked with ourrobustness test we remove companies according to theirmonopolistic index and obtain the result shown in Fig 2The rapid decrease of the WAN connectivity with thisstrategy confirms our conclusion about the importanceof airlines interactions for understanding the structure ofthe WAN and its robustness

B Rerouting after bankruptcy

An important process not considered in the robustnessanalysis above is the direct consequence on passengers ofan airline company bankruptcy These passengers haveto be rerouted and need to choose flights of other com-panies (when it is possible) putting extra stress on someflights In some cases even the bankruptcy of companiescan isolate some cities leaving no other choices for thepassengers to find another transportation mode In thissection we will simulate this process for various level ofdemand decrease starting from the real data in orderto understand the possible post-COVID-19 scenarios forthe WAN

We denote by α isin [0 1] the average demandload ra-tio for all flights We consider here the uniform case (seethe next section for other assumptions) where the actualnumber of passengers for airline company i on segment `is then αNi(`) where the capacity is Ni(`) If the com-pany i fails its αNi(`) passengers have to be reroutedfor each of its segment ` We assume here that passen-gers always choose the shortest path with less transfersas possible If for the segment ` there are other directflights provided by other companies some lucky passen-gers can take them (which will be possible with α lt 1)Once the flights of current shortest path are fully oc-cupied the rest of the passengers will be rerouted overthe second shortest path and so on If all the reroutedpassengers can reach their final destinations we com-pute the average number of additional transfers and theaverage additional distance as the lsquocostrsquo of the airlinersquos

0 20 40 60 80 100Demand

0203040506070809

Wei

ghte

d Av

erag

e Co

st o

f Tra

nsfe

r

Figure 4 Weighted average cost of transfers number due torerouting (with weight given by the capacity of companies)

bankruptcy For example if a passenger wanted to flyfrom city a to b at first now heshe has to transfer incity k In this case hisher number of additional trans-fers is 1 and the additional distance is (dak + dkb)minus dabwhere dab is the distance between city a and b In theless favorable case where some passengers cannot reachtheir destination which can happen if all flights are fullybooked the WAN fails and we compute the number ofthese stranded passengers

We test the bankruptcy of each airline company inthe database and use the rerouting process as describedabove We show in Fig S2 the weighted average costof additional transfers with weight equal to the capac-ity of companies not inducing stranded passengers (seeFig S2(a) for the additional distance) For a low globaldemand passengers can always be rerouted without toomany problems but with increasing α passengers needto make always more transfers and at the cost of a largerdistance We also consider the total number of passengersstranded due to the bankruptcies of airlines if they cannotbe successfully rerouted (Fig S2(b)) As an indicationwe fit the result with a power law function and obtain thelarge exponent value of 375 indicating a rapid increasewith α of the number of stranded passengers when αis of the order of 05 there is a significative number ofstranded passengers of about 25 millions

The existence of stranded passengers depends on a crit-ical point of demand for each airline company (denotedby αci for company i) above which its passengers can-not transfer successfully after its bankruptcy or in otherwords bankruptcy of company i leads to stranded pas-sengers only for α gt αci The distribution of this demandthreshold is shown in Fig S2(c) We observe a roughlyuniform distribution for all values of αci and a peak atαci = 0 which corresponds to the case of cities served bya single company When these companies go bankruptpassengers have no other means to reach their destina-tion (this is the case for approximately 300 companies)We also observe a peak around αci asymp 1 signaling the exis-tence of very robust situation for which their bankruptcyalmost never lead to stranded passengers

5

III THE EFFECT OF A LOWER DEMANDAND CUSTOMERrsquoS AIRLINE CHOICE

STRATEGIES

When the global demand decreases we have assumedso far that all segments and all companies are affected inthe same uniform manner This is however not true ingeneral and we have to test various customerrsquos strate-gies for choosing a company A reduction in the globaldemand can thus have different local consequences andlead to very low passenger traffic demand for some com-panies These are obviously the companies that will bethe most at risk and it is the focus of this part to identifythem

We first focus on one segment ` shared by multiplecompanies Before the crisis each company has its ca-pacity Ni(`) on this segment and the total number ofseats is N(`) =

sumiNi(`) We assume that the global

demand is still described by α isin [0 1] for all segments(for further studies we could assume some geographi-cal dependence) the actual number of passengers on thissegment is αN(`) The question is then how we removethe (1minusα)N(`) passengers on this segment ` or equiva-lently how the remaining αN(`) passengers choose theirairlines There are many factors influencing the decisionfor choosing a specific airlines including the frequencyreliability price etc (see for example the study [23])We decided here to focus on two main aspects the ca-pacity of an airline and its rank A large capacity usuallygoes together with a large frequency and reliability andfor the rank we use the rank list of worldrsquos top 100 Air-lines 2019 provided by Skytrax [24]

We thus consider the following 6 strategies so that allαN(`) passengers find their seats on the flights amongthese companies (i) The first lsquoUniformrsquo Strategy (UN)used as a reference Each company receives a number ofpassengers proportional to its capacity This random caseignores all competitive avantage but provides a bench-mark for assessing the effect of other strategies (ii) ThelsquoBiggest Firstrsquo Strategy (BF) Passengers are assumed toalways give preference to the company with the largestcapacity (and then to the second largest one etc) (iii)lsquoOne-Uniformrsquo Strategy (1UN) Passengers are assumedto choose first the company with the highest rank (pro-vided by [24]) If no companies on the rank list operateon this segment a random company will be chosen firstAfter flights of the first-choice company are fully occu-pied the other companies receive a number of passengersproportional to their capacities (iv) lsquoOne-Biggest Firstrsquo(1BF) Passengers are assumed to choose the companywith the highest rank first If no companies on the ranklist are available for this segment a random company willbe chosen After flights of the first-choice company arefull passengers give then their preference to the companywith the largest capacity (v) lsquoRank-Uniformrsquo (RUN)Passengers are assumed to choose companies accordingto the rank list If flights of companies on the list are oc-cupied the other companies receive a number of passen-

0 20 40 60 80 100Demand

0

20

40

60

80

100

Loca

l Effe

ctiv

e De

man

d0 20 40 60 80 100

Local Effective Demand0

20

40

60

80

100

Dist

ribut

ion

Demand 36Demand 60Demand 80

Figure 5 Local effective demand for the lsquoBiggest Firstrsquo strat-egy (a) Change of local effective demand for all companies(we highlight the curves for the 23 companies that have gonebroke) The vertical red dotted line represents the estimatedvalue of global demand α = 36 in April 2020 (b) Distribu-tion of local effective demand for α = 36 60 and 80

gers proportional to their capacities (vi) lsquoRank-BiggestFirstrsquo (RBF) Passengers are assumed to choose compa-nies according to the rank list If flights of companies onthe list are full passengers give then their preference tothe company with the largest capacity

Considering all the segments for each company i fora given strategy s and for a given value of α we de-note the actual number of passengers for company i byNsi (α) The local effective demand for company i (and

for strategy s) is then given by

Esi (α) =Nsi (α)

Ni (4)

Companies with a large value of the local effective de-mand will have enough passengers to function normallywhile those with a low local effective demand can beconsidered at risk of bankruptcy For the strategy oflsquoBiggest Firstrsquo we show the change of local effective de-mand for all companies (Fig 5(a)) and its distributionwhen α is equal to 36 (the estimated value of demandin April 2020 according to IATA [25]) 60 and 80 inFig 5(b) Even if most companies have a local effec-tive demand around 36 there are about 80 companieswithout any passengers For the 23 companies that went

6

0 20 40 60 80 100Demand

0

20

40

60

80

100Av

erag

e of

Loc

al E

ffect

ive

Dem

and

UNBF1UN1BFRUNRBF

0 20 40 60 80 100Demand

00

05

10

15

20

Rela

tive

Disp

ersio

n o

f Loc

al E

ffect

ive

Dem

and UN

BF1UN1BFRUNRBF

Figure 6 Comparison of local effective demand between 6different strategies (a) Average of local effective demand(b)Relative Dispersion of local effective demand The verticalgray dotted lines highlight α = 36 60 and 80

bankrupt so far their local effective demand was in therange [0 49] consistently with the idea that a com-pany with demand less than 50 is in financial danger

In order to compare quantitatively these differentstrategies we show the local effective demand averagedover all companies and its relative dispersion (equal tothe ratio of dispersion to average) in Fig 6(ab) Forthe uniform case where airlines are chosen completelyat random the local effective demand of each companyis as expected identically equal to α (EUN

i (α) equiv α)All other strategies produce important variations fromFig 6(a) we can roughly estimate that for a demand of36 certain companies can experience a local reductionof demand as low as about 30 or even less if we take intoaccount the dispersion which cannot be neglected (therelative dispersion is always of order 1 - see Fig 6(b))Even for a global demand of 60 all these strategies(except for the purely random case) predict that mostcompanies will experience a decrease of 50 or more oftheir traffic In order to highlight this local heterogeneityeffect we plot in Fig 7 the proportion of companies withlocal effective demand less than 50 (We choose here50 as this seems an already drastic reduction of thedemand that can be barely sustainable for most com-panies Results for other values of the local reduction

give similar results see Fig S4) Except for the uniformstrategy Fig 7 shows that for the current state of airtravel demand α = 36 more than 90 of companieswill see an actual number of passengers less than half oftheir capacity in the pre-crisis state Even if the globaldemand is back to 60 then between 46 and 59 ofthe companies will have an actual number of passengersless than half of their capacity in the pre-crisis state Inthe unlikely event that it will go back in a near futureto 80 we still see from 11 to 36 of companies withhalf of their regular traffic

IV DISCUSSION

The results in this paper are twofold First the impacton the WAN connectivity of an airline company failuredepends on its coupling with other companies If thecompany shares many segments with others its failurewill more strongly affect the WAN structure This showsthat the impact of a bankrupted airline cannot be dis-cussed independently from the other companies and thatit is necessary to take into account the whole structureof the coupling between companies - which is encodedin the ACN introduced here Next we showed that theglobal demand reduction can hide large heterogeneitiesin its impact at the airline level More precisely we havefound that depending on the customer choice strategythe local reduction of demand can be extremely differentfrom its average value in particular in the presence ofa competitive advantage This shows that more compa-nies than we can expect from a simple demand reductionargument could be strongly affected by this crisis Inthe reasonable scenario where the global demand is backto 60 of its total capacity our analysis suggests thatroughly half of the companies will see their traffic dividedby two These results need naturally to be enriched bymany other details about companies but we believe thatthey pave the way for constructing a robust tool allowingus to understand and predict the future of the WAN

V MATERIAL AND METHODS

A Data availability

The data that support the findings of this study werepurchased at OAG httpswwwoagcom

B Data

The Official Aviation Guide (OAG) one of the largestglobal travel data providers provides the detailed infor-mation of every scheduled flight including the operatingairline company origindestination airport aircraft typenumber of seats departure date etc

3

other In particular it will help us to understand howrobust the WAN is when airlines are failing In generalwhen studying the robustness of the WAN different linkor node removal strategies are adopted [16 17] Remov-ing a link implies that all companies operating on thissegment stopped simultaneously which is unlikely to oc-cur in general except in cases of airport closures whichhappened for example during the eruption of the vol-cano Eyjafjallajokull Here we will consider the specificsituation where many airlines can fail The bankruptcyof an airline does not imply however that one or moresegments in the WAN will disappear but just that itscapacity will be reduced

Based on the segment overlap it is natural to definethe average segment overlap of a company with its lsquoneigh-boursrsquo as

Oi =1

|Ci|sumjisinCi

Oij (2)

where Ci = j | Oij gt 0 is the set of companies sharingat least one segment with company i and |Ci| representsthe number of corresponding companies A large averagesegment overlap indicates that the corresponding airlinecompany shares many segments with others and is thusin direct competition with them In contrast a smalloverlap indicates a company that operates alone on somesegments and does not suffer any competition there It isthen tempting to think that the average segment overlapcan serve as an indicator for identifying lsquocriticalrsquo compa-nies whose bankruptcy will induce the isolation of cer-tain airports and cities and cause a great damage to theconnectivity of the WAN

Classically when ignoring the structure in terms of air-line companies the most effective strategy to destroy theconnectivity of the WAN is to remove the most centralnodes (ie nodes with highest betweenness centralitysee [16 17]) or the links with the lowest traffic [18] Asalready mentioned above these results do not providemuch information about the impact of airline bankrupt-cies and the partial reduction in traffic capacity for cer-tain segments In order to test this influence we firstconsider the robustness of the WAN for four differentremoval strategies (i) random removal of airline com-panies (ii) removal of airline companies with the largestpassenger capacity Ni (iii) removal of airline companieswith the largest betweenness centrality computed in theweighted ACN (iv) removal of airline companies withthe largest average segment overlap Oi We note thatfor strategy (iii) the calculation of the betweenness cen-trality in the weighted ACN relies on the shortest pathbetween two nodes such that the sum of weights (herethe segment overlap Oij) is maximal among all connec-tive paths As most robustness analysis do we choosethe size of the giant component (ie the connected sub-graph with the largest number of nodes) as the measureof the connectivity of the WAN

We show in Fig 2 the size of the giant component ofthe WAN as a function of the fraction of the cumulative

0 20 40 60 80 100Fraction of Cumulative Capacity of Removed Companies

0500

100015002000250030003500

Size

of t

he G

iant

Com

pone

nt (W

AN)

RandomCapacityBetweenness CentralityAverage Segment OverlapMonopolistic Index

Figure 2 Size of the giant component of WAN as the func-tion of the fraction of the cumulative passenger capacity ofremoved companies Five different removal strategies of air-line companies are compared

passenger capacity of removed companies (which impliesthat the intervals along the x-axis between dots are notuniform due to the diversity of the companiesrsquo capaci-ties) For the strategy (ii) where we remove companiesaccording to their passenger capacity (from the largestto the smallest) the variation over the x-axis is large butthe impact on the WAN is small Sorting and removingcompanies according to their betweenness centrality inthe ACN is also not very effective Compared to thesecases removing airline companies in a random order hasactually a larger impact on the WAN structure Howeverwe observe that the last strategy (iv) is very effectiveremoving companies according to their integration withother companies seems to have the largest impact on theWANrsquos connectivity suggesting that crucial paths in theWAN are shared by the same set of companies Moregenerally this is a sign that in order to understand therobustness of the WAN and the impact of the failure ofan airline company we need to take into account its in-teraction with the other companies

This discussion shows that not all airlines are equiva-lent and that their bankruptcy can display a large varietyof consequences In particular the location of the airlinein the ACN or in other words how it is coupled to othercompanies seems to be a crucial ingredient for under-standing the impact of its bankruptcy This leads us toquantify how much a company has the monopoly over itsdifferent segments and we define the monopolistic indexas

Mi =1

|Li|sum`isinLi

Ni(`)summj=1Nj(`)

(3)

where |Li| is the total number of segments serviced bycompany i This index is equal or close to 1 if most thesegments of company i are dominated by i The distribu-tion of Mi shown in Fig 3 indicates that there is a largevariety of companies with various degree of monopolydemonstrating the large diversity of the airlines compa-nies The peak at M = 1 indicates that there are about

4

00 02 04 06 08 10Monopolistic Index

01020304050607080

Dist

ribut

ion

Figure 3 Distribution of monopolistic index

80 companies which are totally monopolistic all theirsegments are not shared with another company

The importance of this feature can be checked with ourrobustness test we remove companies according to theirmonopolistic index and obtain the result shown in Fig 2The rapid decrease of the WAN connectivity with thisstrategy confirms our conclusion about the importanceof airlines interactions for understanding the structure ofthe WAN and its robustness

B Rerouting after bankruptcy

An important process not considered in the robustnessanalysis above is the direct consequence on passengers ofan airline company bankruptcy These passengers haveto be rerouted and need to choose flights of other com-panies (when it is possible) putting extra stress on someflights In some cases even the bankruptcy of companiescan isolate some cities leaving no other choices for thepassengers to find another transportation mode In thissection we will simulate this process for various level ofdemand decrease starting from the real data in orderto understand the possible post-COVID-19 scenarios forthe WAN

We denote by α isin [0 1] the average demandload ra-tio for all flights We consider here the uniform case (seethe next section for other assumptions) where the actualnumber of passengers for airline company i on segment `is then αNi(`) where the capacity is Ni(`) If the com-pany i fails its αNi(`) passengers have to be reroutedfor each of its segment ` We assume here that passen-gers always choose the shortest path with less transfersas possible If for the segment ` there are other directflights provided by other companies some lucky passen-gers can take them (which will be possible with α lt 1)Once the flights of current shortest path are fully oc-cupied the rest of the passengers will be rerouted overthe second shortest path and so on If all the reroutedpassengers can reach their final destinations we com-pute the average number of additional transfers and theaverage additional distance as the lsquocostrsquo of the airlinersquos

0 20 40 60 80 100Demand

0203040506070809

Wei

ghte

d Av

erag

e Co

st o

f Tra

nsfe

r

Figure 4 Weighted average cost of transfers number due torerouting (with weight given by the capacity of companies)

bankruptcy For example if a passenger wanted to flyfrom city a to b at first now heshe has to transfer incity k In this case hisher number of additional trans-fers is 1 and the additional distance is (dak + dkb)minus dabwhere dab is the distance between city a and b In theless favorable case where some passengers cannot reachtheir destination which can happen if all flights are fullybooked the WAN fails and we compute the number ofthese stranded passengers

We test the bankruptcy of each airline company inthe database and use the rerouting process as describedabove We show in Fig S2 the weighted average costof additional transfers with weight equal to the capac-ity of companies not inducing stranded passengers (seeFig S2(a) for the additional distance) For a low globaldemand passengers can always be rerouted without toomany problems but with increasing α passengers needto make always more transfers and at the cost of a largerdistance We also consider the total number of passengersstranded due to the bankruptcies of airlines if they cannotbe successfully rerouted (Fig S2(b)) As an indicationwe fit the result with a power law function and obtain thelarge exponent value of 375 indicating a rapid increasewith α of the number of stranded passengers when αis of the order of 05 there is a significative number ofstranded passengers of about 25 millions

The existence of stranded passengers depends on a crit-ical point of demand for each airline company (denotedby αci for company i) above which its passengers can-not transfer successfully after its bankruptcy or in otherwords bankruptcy of company i leads to stranded pas-sengers only for α gt αci The distribution of this demandthreshold is shown in Fig S2(c) We observe a roughlyuniform distribution for all values of αci and a peak atαci = 0 which corresponds to the case of cities served bya single company When these companies go bankruptpassengers have no other means to reach their destina-tion (this is the case for approximately 300 companies)We also observe a peak around αci asymp 1 signaling the exis-tence of very robust situation for which their bankruptcyalmost never lead to stranded passengers

5

III THE EFFECT OF A LOWER DEMANDAND CUSTOMERrsquoS AIRLINE CHOICE

STRATEGIES

When the global demand decreases we have assumedso far that all segments and all companies are affected inthe same uniform manner This is however not true ingeneral and we have to test various customerrsquos strate-gies for choosing a company A reduction in the globaldemand can thus have different local consequences andlead to very low passenger traffic demand for some com-panies These are obviously the companies that will bethe most at risk and it is the focus of this part to identifythem

We first focus on one segment ` shared by multiplecompanies Before the crisis each company has its ca-pacity Ni(`) on this segment and the total number ofseats is N(`) =

sumiNi(`) We assume that the global

demand is still described by α isin [0 1] for all segments(for further studies we could assume some geographi-cal dependence) the actual number of passengers on thissegment is αN(`) The question is then how we removethe (1minusα)N(`) passengers on this segment ` or equiva-lently how the remaining αN(`) passengers choose theirairlines There are many factors influencing the decisionfor choosing a specific airlines including the frequencyreliability price etc (see for example the study [23])We decided here to focus on two main aspects the ca-pacity of an airline and its rank A large capacity usuallygoes together with a large frequency and reliability andfor the rank we use the rank list of worldrsquos top 100 Air-lines 2019 provided by Skytrax [24]

We thus consider the following 6 strategies so that allαN(`) passengers find their seats on the flights amongthese companies (i) The first lsquoUniformrsquo Strategy (UN)used as a reference Each company receives a number ofpassengers proportional to its capacity This random caseignores all competitive avantage but provides a bench-mark for assessing the effect of other strategies (ii) ThelsquoBiggest Firstrsquo Strategy (BF) Passengers are assumed toalways give preference to the company with the largestcapacity (and then to the second largest one etc) (iii)lsquoOne-Uniformrsquo Strategy (1UN) Passengers are assumedto choose first the company with the highest rank (pro-vided by [24]) If no companies on the rank list operateon this segment a random company will be chosen firstAfter flights of the first-choice company are fully occu-pied the other companies receive a number of passengersproportional to their capacities (iv) lsquoOne-Biggest Firstrsquo(1BF) Passengers are assumed to choose the companywith the highest rank first If no companies on the ranklist are available for this segment a random company willbe chosen After flights of the first-choice company arefull passengers give then their preference to the companywith the largest capacity (v) lsquoRank-Uniformrsquo (RUN)Passengers are assumed to choose companies accordingto the rank list If flights of companies on the list are oc-cupied the other companies receive a number of passen-

0 20 40 60 80 100Demand

0

20

40

60

80

100

Loca

l Effe

ctiv

e De

man

d0 20 40 60 80 100

Local Effective Demand0

20

40

60

80

100

Dist

ribut

ion

Demand 36Demand 60Demand 80

Figure 5 Local effective demand for the lsquoBiggest Firstrsquo strat-egy (a) Change of local effective demand for all companies(we highlight the curves for the 23 companies that have gonebroke) The vertical red dotted line represents the estimatedvalue of global demand α = 36 in April 2020 (b) Distribu-tion of local effective demand for α = 36 60 and 80

gers proportional to their capacities (vi) lsquoRank-BiggestFirstrsquo (RBF) Passengers are assumed to choose compa-nies according to the rank list If flights of companies onthe list are full passengers give then their preference tothe company with the largest capacity

Considering all the segments for each company i fora given strategy s and for a given value of α we de-note the actual number of passengers for company i byNsi (α) The local effective demand for company i (and

for strategy s) is then given by

Esi (α) =Nsi (α)

Ni (4)

Companies with a large value of the local effective de-mand will have enough passengers to function normallywhile those with a low local effective demand can beconsidered at risk of bankruptcy For the strategy oflsquoBiggest Firstrsquo we show the change of local effective de-mand for all companies (Fig 5(a)) and its distributionwhen α is equal to 36 (the estimated value of demandin April 2020 according to IATA [25]) 60 and 80 inFig 5(b) Even if most companies have a local effec-tive demand around 36 there are about 80 companieswithout any passengers For the 23 companies that went

6

0 20 40 60 80 100Demand

0

20

40

60

80

100Av

erag

e of

Loc

al E

ffect

ive

Dem

and

UNBF1UN1BFRUNRBF

0 20 40 60 80 100Demand

00

05

10

15

20

Rela

tive

Disp

ersio

n o

f Loc

al E

ffect

ive

Dem

and UN

BF1UN1BFRUNRBF

Figure 6 Comparison of local effective demand between 6different strategies (a) Average of local effective demand(b)Relative Dispersion of local effective demand The verticalgray dotted lines highlight α = 36 60 and 80

bankrupt so far their local effective demand was in therange [0 49] consistently with the idea that a com-pany with demand less than 50 is in financial danger

In order to compare quantitatively these differentstrategies we show the local effective demand averagedover all companies and its relative dispersion (equal tothe ratio of dispersion to average) in Fig 6(ab) Forthe uniform case where airlines are chosen completelyat random the local effective demand of each companyis as expected identically equal to α (EUN

i (α) equiv α)All other strategies produce important variations fromFig 6(a) we can roughly estimate that for a demand of36 certain companies can experience a local reductionof demand as low as about 30 or even less if we take intoaccount the dispersion which cannot be neglected (therelative dispersion is always of order 1 - see Fig 6(b))Even for a global demand of 60 all these strategies(except for the purely random case) predict that mostcompanies will experience a decrease of 50 or more oftheir traffic In order to highlight this local heterogeneityeffect we plot in Fig 7 the proportion of companies withlocal effective demand less than 50 (We choose here50 as this seems an already drastic reduction of thedemand that can be barely sustainable for most com-panies Results for other values of the local reduction

give similar results see Fig S4) Except for the uniformstrategy Fig 7 shows that for the current state of airtravel demand α = 36 more than 90 of companieswill see an actual number of passengers less than half oftheir capacity in the pre-crisis state Even if the globaldemand is back to 60 then between 46 and 59 ofthe companies will have an actual number of passengersless than half of their capacity in the pre-crisis state Inthe unlikely event that it will go back in a near futureto 80 we still see from 11 to 36 of companies withhalf of their regular traffic

IV DISCUSSION

The results in this paper are twofold First the impacton the WAN connectivity of an airline company failuredepends on its coupling with other companies If thecompany shares many segments with others its failurewill more strongly affect the WAN structure This showsthat the impact of a bankrupted airline cannot be dis-cussed independently from the other companies and thatit is necessary to take into account the whole structureof the coupling between companies - which is encodedin the ACN introduced here Next we showed that theglobal demand reduction can hide large heterogeneitiesin its impact at the airline level More precisely we havefound that depending on the customer choice strategythe local reduction of demand can be extremely differentfrom its average value in particular in the presence ofa competitive advantage This shows that more compa-nies than we can expect from a simple demand reductionargument could be strongly affected by this crisis Inthe reasonable scenario where the global demand is backto 60 of its total capacity our analysis suggests thatroughly half of the companies will see their traffic dividedby two These results need naturally to be enriched bymany other details about companies but we believe thatthey pave the way for constructing a robust tool allowingus to understand and predict the future of the WAN

V MATERIAL AND METHODS

A Data availability

The data that support the findings of this study werepurchased at OAG httpswwwoagcom

B Data

The Official Aviation Guide (OAG) one of the largestglobal travel data providers provides the detailed infor-mation of every scheduled flight including the operatingairline company origindestination airport aircraft typenumber of seats departure date etc

4

00 02 04 06 08 10Monopolistic Index

01020304050607080

Dist

ribut

ion

Figure 3 Distribution of monopolistic index

80 companies which are totally monopolistic all theirsegments are not shared with another company

The importance of this feature can be checked with ourrobustness test we remove companies according to theirmonopolistic index and obtain the result shown in Fig 2The rapid decrease of the WAN connectivity with thisstrategy confirms our conclusion about the importanceof airlines interactions for understanding the structure ofthe WAN and its robustness

B Rerouting after bankruptcy

An important process not considered in the robustnessanalysis above is the direct consequence on passengers ofan airline company bankruptcy These passengers haveto be rerouted and need to choose flights of other com-panies (when it is possible) putting extra stress on someflights In some cases even the bankruptcy of companiescan isolate some cities leaving no other choices for thepassengers to find another transportation mode In thissection we will simulate this process for various level ofdemand decrease starting from the real data in orderto understand the possible post-COVID-19 scenarios forthe WAN

We denote by α isin [0 1] the average demandload ra-tio for all flights We consider here the uniform case (seethe next section for other assumptions) where the actualnumber of passengers for airline company i on segment `is then αNi(`) where the capacity is Ni(`) If the com-pany i fails its αNi(`) passengers have to be reroutedfor each of its segment ` We assume here that passen-gers always choose the shortest path with less transfersas possible If for the segment ` there are other directflights provided by other companies some lucky passen-gers can take them (which will be possible with α lt 1)Once the flights of current shortest path are fully oc-cupied the rest of the passengers will be rerouted overthe second shortest path and so on If all the reroutedpassengers can reach their final destinations we com-pute the average number of additional transfers and theaverage additional distance as the lsquocostrsquo of the airlinersquos

0 20 40 60 80 100Demand

0203040506070809

Wei

ghte

d Av

erag

e Co

st o

f Tra

nsfe

r

Figure 4 Weighted average cost of transfers number due torerouting (with weight given by the capacity of companies)

bankruptcy For example if a passenger wanted to flyfrom city a to b at first now heshe has to transfer incity k In this case hisher number of additional trans-fers is 1 and the additional distance is (dak + dkb)minus dabwhere dab is the distance between city a and b In theless favorable case where some passengers cannot reachtheir destination which can happen if all flights are fullybooked the WAN fails and we compute the number ofthese stranded passengers

We test the bankruptcy of each airline company inthe database and use the rerouting process as describedabove We show in Fig S2 the weighted average costof additional transfers with weight equal to the capac-ity of companies not inducing stranded passengers (seeFig S2(a) for the additional distance) For a low globaldemand passengers can always be rerouted without toomany problems but with increasing α passengers needto make always more transfers and at the cost of a largerdistance We also consider the total number of passengersstranded due to the bankruptcies of airlines if they cannotbe successfully rerouted (Fig S2(b)) As an indicationwe fit the result with a power law function and obtain thelarge exponent value of 375 indicating a rapid increasewith α of the number of stranded passengers when αis of the order of 05 there is a significative number ofstranded passengers of about 25 millions

The existence of stranded passengers depends on a crit-ical point of demand for each airline company (denotedby αci for company i) above which its passengers can-not transfer successfully after its bankruptcy or in otherwords bankruptcy of company i leads to stranded pas-sengers only for α gt αci The distribution of this demandthreshold is shown in Fig S2(c) We observe a roughlyuniform distribution for all values of αci and a peak atαci = 0 which corresponds to the case of cities served bya single company When these companies go bankruptpassengers have no other means to reach their destina-tion (this is the case for approximately 300 companies)We also observe a peak around αci asymp 1 signaling the exis-tence of very robust situation for which their bankruptcyalmost never lead to stranded passengers

5

III THE EFFECT OF A LOWER DEMANDAND CUSTOMERrsquoS AIRLINE CHOICE

STRATEGIES

When the global demand decreases we have assumedso far that all segments and all companies are affected inthe same uniform manner This is however not true ingeneral and we have to test various customerrsquos strate-gies for choosing a company A reduction in the globaldemand can thus have different local consequences andlead to very low passenger traffic demand for some com-panies These are obviously the companies that will bethe most at risk and it is the focus of this part to identifythem

We first focus on one segment ` shared by multiplecompanies Before the crisis each company has its ca-pacity Ni(`) on this segment and the total number ofseats is N(`) =

sumiNi(`) We assume that the global

demand is still described by α isin [0 1] for all segments(for further studies we could assume some geographi-cal dependence) the actual number of passengers on thissegment is αN(`) The question is then how we removethe (1minusα)N(`) passengers on this segment ` or equiva-lently how the remaining αN(`) passengers choose theirairlines There are many factors influencing the decisionfor choosing a specific airlines including the frequencyreliability price etc (see for example the study [23])We decided here to focus on two main aspects the ca-pacity of an airline and its rank A large capacity usuallygoes together with a large frequency and reliability andfor the rank we use the rank list of worldrsquos top 100 Air-lines 2019 provided by Skytrax [24]

We thus consider the following 6 strategies so that allαN(`) passengers find their seats on the flights amongthese companies (i) The first lsquoUniformrsquo Strategy (UN)used as a reference Each company receives a number ofpassengers proportional to its capacity This random caseignores all competitive avantage but provides a bench-mark for assessing the effect of other strategies (ii) ThelsquoBiggest Firstrsquo Strategy (BF) Passengers are assumed toalways give preference to the company with the largestcapacity (and then to the second largest one etc) (iii)lsquoOne-Uniformrsquo Strategy (1UN) Passengers are assumedto choose first the company with the highest rank (pro-vided by [24]) If no companies on the rank list operateon this segment a random company will be chosen firstAfter flights of the first-choice company are fully occu-pied the other companies receive a number of passengersproportional to their capacities (iv) lsquoOne-Biggest Firstrsquo(1BF) Passengers are assumed to choose the companywith the highest rank first If no companies on the ranklist are available for this segment a random company willbe chosen After flights of the first-choice company arefull passengers give then their preference to the companywith the largest capacity (v) lsquoRank-Uniformrsquo (RUN)Passengers are assumed to choose companies accordingto the rank list If flights of companies on the list are oc-cupied the other companies receive a number of passen-

0 20 40 60 80 100Demand

0

20

40

60

80

100

Loca

l Effe

ctiv

e De

man

d0 20 40 60 80 100

Local Effective Demand0

20

40

60

80

100

Dist

ribut

ion

Demand 36Demand 60Demand 80

Figure 5 Local effective demand for the lsquoBiggest Firstrsquo strat-egy (a) Change of local effective demand for all companies(we highlight the curves for the 23 companies that have gonebroke) The vertical red dotted line represents the estimatedvalue of global demand α = 36 in April 2020 (b) Distribu-tion of local effective demand for α = 36 60 and 80

gers proportional to their capacities (vi) lsquoRank-BiggestFirstrsquo (RBF) Passengers are assumed to choose compa-nies according to the rank list If flights of companies onthe list are full passengers give then their preference tothe company with the largest capacity

Considering all the segments for each company i fora given strategy s and for a given value of α we de-note the actual number of passengers for company i byNsi (α) The local effective demand for company i (and

for strategy s) is then given by

Esi (α) =Nsi (α)

Ni (4)

Companies with a large value of the local effective de-mand will have enough passengers to function normallywhile those with a low local effective demand can beconsidered at risk of bankruptcy For the strategy oflsquoBiggest Firstrsquo we show the change of local effective de-mand for all companies (Fig 5(a)) and its distributionwhen α is equal to 36 (the estimated value of demandin April 2020 according to IATA [25]) 60 and 80 inFig 5(b) Even if most companies have a local effec-tive demand around 36 there are about 80 companieswithout any passengers For the 23 companies that went

6

0 20 40 60 80 100Demand

0

20

40

60

80

100Av

erag

e of

Loc

al E

ffect

ive

Dem

and

UNBF1UN1BFRUNRBF

0 20 40 60 80 100Demand

00

05

10

15

20

Rela

tive

Disp

ersio

n o

f Loc

al E

ffect

ive

Dem

and UN

BF1UN1BFRUNRBF

Figure 6 Comparison of local effective demand between 6different strategies (a) Average of local effective demand(b)Relative Dispersion of local effective demand The verticalgray dotted lines highlight α = 36 60 and 80

bankrupt so far their local effective demand was in therange [0 49] consistently with the idea that a com-pany with demand less than 50 is in financial danger

In order to compare quantitatively these differentstrategies we show the local effective demand averagedover all companies and its relative dispersion (equal tothe ratio of dispersion to average) in Fig 6(ab) Forthe uniform case where airlines are chosen completelyat random the local effective demand of each companyis as expected identically equal to α (EUN

i (α) equiv α)All other strategies produce important variations fromFig 6(a) we can roughly estimate that for a demand of36 certain companies can experience a local reductionof demand as low as about 30 or even less if we take intoaccount the dispersion which cannot be neglected (therelative dispersion is always of order 1 - see Fig 6(b))Even for a global demand of 60 all these strategies(except for the purely random case) predict that mostcompanies will experience a decrease of 50 or more oftheir traffic In order to highlight this local heterogeneityeffect we plot in Fig 7 the proportion of companies withlocal effective demand less than 50 (We choose here50 as this seems an already drastic reduction of thedemand that can be barely sustainable for most com-panies Results for other values of the local reduction

give similar results see Fig S4) Except for the uniformstrategy Fig 7 shows that for the current state of airtravel demand α = 36 more than 90 of companieswill see an actual number of passengers less than half oftheir capacity in the pre-crisis state Even if the globaldemand is back to 60 then between 46 and 59 ofthe companies will have an actual number of passengersless than half of their capacity in the pre-crisis state Inthe unlikely event that it will go back in a near futureto 80 we still see from 11 to 36 of companies withhalf of their regular traffic

IV DISCUSSION

The results in this paper are twofold First the impacton the WAN connectivity of an airline company failuredepends on its coupling with other companies If thecompany shares many segments with others its failurewill more strongly affect the WAN structure This showsthat the impact of a bankrupted airline cannot be dis-cussed independently from the other companies and thatit is necessary to take into account the whole structureof the coupling between companies - which is encodedin the ACN introduced here Next we showed that theglobal demand reduction can hide large heterogeneitiesin its impact at the airline level More precisely we havefound that depending on the customer choice strategythe local reduction of demand can be extremely differentfrom its average value in particular in the presence ofa competitive advantage This shows that more compa-nies than we can expect from a simple demand reductionargument could be strongly affected by this crisis Inthe reasonable scenario where the global demand is backto 60 of its total capacity our analysis suggests thatroughly half of the companies will see their traffic dividedby two These results need naturally to be enriched bymany other details about companies but we believe thatthey pave the way for constructing a robust tool allowingus to understand and predict the future of the WAN

V MATERIAL AND METHODS

A Data availability

The data that support the findings of this study werepurchased at OAG httpswwwoagcom

B Data

The Official Aviation Guide (OAG) one of the largestglobal travel data providers provides the detailed infor-mation of every scheduled flight including the operatingairline company origindestination airport aircraft typenumber of seats departure date etc

5

III THE EFFECT OF A LOWER DEMANDAND CUSTOMERrsquoS AIRLINE CHOICE

STRATEGIES

When the global demand decreases we have assumedso far that all segments and all companies are affected inthe same uniform manner This is however not true ingeneral and we have to test various customerrsquos strate-gies for choosing a company A reduction in the globaldemand can thus have different local consequences andlead to very low passenger traffic demand for some com-panies These are obviously the companies that will bethe most at risk and it is the focus of this part to identifythem

We first focus on one segment ` shared by multiplecompanies Before the crisis each company has its ca-pacity Ni(`) on this segment and the total number ofseats is N(`) =

sumiNi(`) We assume that the global

demand is still described by α isin [0 1] for all segments(for further studies we could assume some geographi-cal dependence) the actual number of passengers on thissegment is αN(`) The question is then how we removethe (1minusα)N(`) passengers on this segment ` or equiva-lently how the remaining αN(`) passengers choose theirairlines There are many factors influencing the decisionfor choosing a specific airlines including the frequencyreliability price etc (see for example the study [23])We decided here to focus on two main aspects the ca-pacity of an airline and its rank A large capacity usuallygoes together with a large frequency and reliability andfor the rank we use the rank list of worldrsquos top 100 Air-lines 2019 provided by Skytrax [24]

We thus consider the following 6 strategies so that allαN(`) passengers find their seats on the flights amongthese companies (i) The first lsquoUniformrsquo Strategy (UN)used as a reference Each company receives a number ofpassengers proportional to its capacity This random caseignores all competitive avantage but provides a bench-mark for assessing the effect of other strategies (ii) ThelsquoBiggest Firstrsquo Strategy (BF) Passengers are assumed toalways give preference to the company with the largestcapacity (and then to the second largest one etc) (iii)lsquoOne-Uniformrsquo Strategy (1UN) Passengers are assumedto choose first the company with the highest rank (pro-vided by [24]) If no companies on the rank list operateon this segment a random company will be chosen firstAfter flights of the first-choice company are fully occu-pied the other companies receive a number of passengersproportional to their capacities (iv) lsquoOne-Biggest Firstrsquo(1BF) Passengers are assumed to choose the companywith the highest rank first If no companies on the ranklist are available for this segment a random company willbe chosen After flights of the first-choice company arefull passengers give then their preference to the companywith the largest capacity (v) lsquoRank-Uniformrsquo (RUN)Passengers are assumed to choose companies accordingto the rank list If flights of companies on the list are oc-cupied the other companies receive a number of passen-

0 20 40 60 80 100Demand

0

20

40

60

80

100

Loca

l Effe

ctiv

e De

man

d0 20 40 60 80 100

Local Effective Demand0

20

40

60

80

100

Dist

ribut

ion

Demand 36Demand 60Demand 80

Figure 5 Local effective demand for the lsquoBiggest Firstrsquo strat-egy (a) Change of local effective demand for all companies(we highlight the curves for the 23 companies that have gonebroke) The vertical red dotted line represents the estimatedvalue of global demand α = 36 in April 2020 (b) Distribu-tion of local effective demand for α = 36 60 and 80

gers proportional to their capacities (vi) lsquoRank-BiggestFirstrsquo (RBF) Passengers are assumed to choose compa-nies according to the rank list If flights of companies onthe list are full passengers give then their preference tothe company with the largest capacity

Considering all the segments for each company i fora given strategy s and for a given value of α we de-note the actual number of passengers for company i byNsi (α) The local effective demand for company i (and

for strategy s) is then given by

Esi (α) =Nsi (α)

Ni (4)

Companies with a large value of the local effective de-mand will have enough passengers to function normallywhile those with a low local effective demand can beconsidered at risk of bankruptcy For the strategy oflsquoBiggest Firstrsquo we show the change of local effective de-mand for all companies (Fig 5(a)) and its distributionwhen α is equal to 36 (the estimated value of demandin April 2020 according to IATA [25]) 60 and 80 inFig 5(b) Even if most companies have a local effec-tive demand around 36 there are about 80 companieswithout any passengers For the 23 companies that went

6

0 20 40 60 80 100Demand

0

20

40

60

80

100Av

erag

e of

Loc

al E

ffect

ive

Dem

and

UNBF1UN1BFRUNRBF

0 20 40 60 80 100Demand

00

05

10

15

20

Rela

tive

Disp

ersio

n o

f Loc

al E

ffect

ive

Dem

and UN

BF1UN1BFRUNRBF

Figure 6 Comparison of local effective demand between 6different strategies (a) Average of local effective demand(b)Relative Dispersion of local effective demand The verticalgray dotted lines highlight α = 36 60 and 80

bankrupt so far their local effective demand was in therange [0 49] consistently with the idea that a com-pany with demand less than 50 is in financial danger

In order to compare quantitatively these differentstrategies we show the local effective demand averagedover all companies and its relative dispersion (equal tothe ratio of dispersion to average) in Fig 6(ab) Forthe uniform case where airlines are chosen completelyat random the local effective demand of each companyis as expected identically equal to α (EUN

i (α) equiv α)All other strategies produce important variations fromFig 6(a) we can roughly estimate that for a demand of36 certain companies can experience a local reductionof demand as low as about 30 or even less if we take intoaccount the dispersion which cannot be neglected (therelative dispersion is always of order 1 - see Fig 6(b))Even for a global demand of 60 all these strategies(except for the purely random case) predict that mostcompanies will experience a decrease of 50 or more oftheir traffic In order to highlight this local heterogeneityeffect we plot in Fig 7 the proportion of companies withlocal effective demand less than 50 (We choose here50 as this seems an already drastic reduction of thedemand that can be barely sustainable for most com-panies Results for other values of the local reduction

give similar results see Fig S4) Except for the uniformstrategy Fig 7 shows that for the current state of airtravel demand α = 36 more than 90 of companieswill see an actual number of passengers less than half oftheir capacity in the pre-crisis state Even if the globaldemand is back to 60 then between 46 and 59 ofthe companies will have an actual number of passengersless than half of their capacity in the pre-crisis state Inthe unlikely event that it will go back in a near futureto 80 we still see from 11 to 36 of companies withhalf of their regular traffic

IV DISCUSSION

The results in this paper are twofold First the impacton the WAN connectivity of an airline company failuredepends on its coupling with other companies If thecompany shares many segments with others its failurewill more strongly affect the WAN structure This showsthat the impact of a bankrupted airline cannot be dis-cussed independently from the other companies and thatit is necessary to take into account the whole structureof the coupling between companies - which is encodedin the ACN introduced here Next we showed that theglobal demand reduction can hide large heterogeneitiesin its impact at the airline level More precisely we havefound that depending on the customer choice strategythe local reduction of demand can be extremely differentfrom its average value in particular in the presence ofa competitive advantage This shows that more compa-nies than we can expect from a simple demand reductionargument could be strongly affected by this crisis Inthe reasonable scenario where the global demand is backto 60 of its total capacity our analysis suggests thatroughly half of the companies will see their traffic dividedby two These results need naturally to be enriched bymany other details about companies but we believe thatthey pave the way for constructing a robust tool allowingus to understand and predict the future of the WAN

V MATERIAL AND METHODS

A Data availability

The data that support the findings of this study werepurchased at OAG httpswwwoagcom

B Data

The Official Aviation Guide (OAG) one of the largestglobal travel data providers provides the detailed infor-mation of every scheduled flight including the operatingairline company origindestination airport aircraft typenumber of seats departure date etc

6

0 20 40 60 80 100Demand

0

20

40

60

80

100Av

erag

e of

Loc

al E

ffect

ive

Dem

and

UNBF1UN1BFRUNRBF

0 20 40 60 80 100Demand

00

05

10

15

20

Rela

tive

Disp

ersio

n o

f Loc

al E

ffect

ive

Dem

and UN

BF1UN1BFRUNRBF

Figure 6 Comparison of local effective demand between 6different strategies (a) Average of local effective demand(b)Relative Dispersion of local effective demand The verticalgray dotted lines highlight α = 36 60 and 80

bankrupt so far their local effective demand was in therange [0 49] consistently with the idea that a com-pany with demand less than 50 is in financial danger

In order to compare quantitatively these differentstrategies we show the local effective demand averagedover all companies and its relative dispersion (equal tothe ratio of dispersion to average) in Fig 6(ab) Forthe uniform case where airlines are chosen completelyat random the local effective demand of each companyis as expected identically equal to α (EUN

i (α) equiv α)All other strategies produce important variations fromFig 6(a) we can roughly estimate that for a demand of36 certain companies can experience a local reductionof demand as low as about 30 or even less if we take intoaccount the dispersion which cannot be neglected (therelative dispersion is always of order 1 - see Fig 6(b))Even for a global demand of 60 all these strategies(except for the purely random case) predict that mostcompanies will experience a decrease of 50 or more oftheir traffic In order to highlight this local heterogeneityeffect we plot in Fig 7 the proportion of companies withlocal effective demand less than 50 (We choose here50 as this seems an already drastic reduction of thedemand that can be barely sustainable for most com-panies Results for other values of the local reduction

give similar results see Fig S4) Except for the uniformstrategy Fig 7 shows that for the current state of airtravel demand α = 36 more than 90 of companieswill see an actual number of passengers less than half oftheir capacity in the pre-crisis state Even if the globaldemand is back to 60 then between 46 and 59 ofthe companies will have an actual number of passengersless than half of their capacity in the pre-crisis state Inthe unlikely event that it will go back in a near futureto 80 we still see from 11 to 36 of companies withhalf of their regular traffic

IV DISCUSSION

The results in this paper are twofold First the impacton the WAN connectivity of an airline company failuredepends on its coupling with other companies If thecompany shares many segments with others its failurewill more strongly affect the WAN structure This showsthat the impact of a bankrupted airline cannot be dis-cussed independently from the other companies and thatit is necessary to take into account the whole structureof the coupling between companies - which is encodedin the ACN introduced here Next we showed that theglobal demand reduction can hide large heterogeneitiesin its impact at the airline level More precisely we havefound that depending on the customer choice strategythe local reduction of demand can be extremely differentfrom its average value in particular in the presence ofa competitive advantage This shows that more compa-nies than we can expect from a simple demand reductionargument could be strongly affected by this crisis Inthe reasonable scenario where the global demand is backto 60 of its total capacity our analysis suggests thatroughly half of the companies will see their traffic dividedby two These results need naturally to be enriched bymany other details about companies but we believe thatthey pave the way for constructing a robust tool allowingus to understand and predict the future of the WAN

V MATERIAL AND METHODS

A Data availability

The data that support the findings of this study werepurchased at OAG httpswwwoagcom

B Data

The Official Aviation Guide (OAG) one of the largestglobal travel data providers provides the detailed infor-mation of every scheduled flight including the operatingairline company origindestination airport aircraft typenumber of seats departure date etc

7

0 20 40 60 80 100Demand

0

20

40

60

80

100Pr

opor

tion

of C

ompa

nies

(Ei lt

05

)

UNBF1UN1BFRUNRBF

Figure 7 Proportion of companies with local effective demandless than 50 The vertical gray dotted lines highlight α =36 60 and 80

We focus on the nonstop flights during the periodfrom 1st January to 25th April 2020 for understanding

the variation of global air traffic caused by COVID-19and the corresponding period 1st January ndash 26th April2019 for constructing the world airline network (WAN) inlsquonormal statersquo In the WAN nodes represent cities andlinks denote existence of direct flights Considering allthe flights during 1st January to 26th April 2019 thereare n = 3 713 cities serving as originsdestinations andn` = 51 306 different segments connecting these citiesAs the comparison there are 3 752 cities and 49 215 seg-ments during the period 1st January to 25th April 2020We define the weight of link as the everyday capacity(number of seats) of flights between cities ie

wij =1

T

Tsumt=1

Nij(t) +Nji(t)

2 (5)

where Nij(t) is the total capacity of flights from city i tocity j on day t and T = 116 is the length of time range

[1] Maria Nicola Zaid Alsafi Catrin Sohrabi Ahmed Ker-wan Ahmed Al-Jabir Christos Iosifidis Maliha Aghaand Riaz Agha The socio-economic implications of thecoronavirus pandemic (covid-19) A review Interna-tional Journal of Surgery (London England) 781852020

[2] Matteo Chinazzi Jessica T Davis Marco Ajelli CorradoGioannini Maria Litvinova Stefano Merler Ana Pas-tore y Piontti Kunpeng Mu Luca Rossi Kaiyuan Sunet al The effect of travel restrictions on the spread ofthe 2019 novel coronavirus (covid-19) outbreak Science368(6489)395ndash400 2020

[3] Toyotaro Suzumura Hiroki Kanezashi Mishal DholakiaEuma Ishii Sergio Alvarez Napagao Raquel Peacuterez-Arnal and Dario Garcia-Gasulla The impact of covid-19 on flight networks arXiv preprint arXiv2006029502020

[4] Lucy Budd Steven Griggs David Howarth and StephenIson A fiasco of volcanic proportions eyjafjallajoumlkulland the closure of european airspace Mobilities 6(1)31ndash40 2011

[5] Peter Brooker Fear in a handful of dust aviation andthe icelandic volcano Significance 7(3)112ndash115 2010

[6] Jingyuan Wang Ke Tang Kai Feng and Weifeng LvHigh temperature and high humidity reduce the trans-mission of covid-19 Available at SSRN 3551767 2020

[7] Boston Consulting Group The post-covid-19flight plan for airlines (accessed 2020-06-29)httpswwwbcgcomfr-frpublications2020post-covid-airline-industry-strategyaspx

[8] Miquel Ros The 2020 airline bankruptcy list is open (ac-cessed 2020-06-29) httpsallplanetvblog2020117airlines-that-stopped-flying-in-2020

[9] David Slotnik Some of the worldrsquos airlines couldgo bankrupt because of the covid-19 crisis ac-cording to an aviation consultancy (accessed 2020-05-12) httpswwwbusinessinsiderfrus

coronavirus-airlines-that-failed-bankrupt-covid19-pandemic-2020-32020

[10] Rupert Jones Uk airlines call for multibillion bailoutto survive covid-19 crisis (accessed 2020-03-15)httpswwwtheguardiancomworld2020mar15uk-airlines-call-for-multibillion-bailout-to-survive-covid-19-crisis2020

[11] Karol Ciesluk What causes an airline to go bankrupt(accessed 2020-04-26) httpssimpleflyingcomairline-bankruptcy 2020

[12] Alain Barrat Marc Barthelemy Romualdo Pastor-Satorras and Alessandro Vespignani The architecture ofcomplex weighted networks Proceedings of the nationalacademy of sciences 101(11)3747ndash3752 2004

[13] Roger Guimera Stefano Mossa Adrian Turtschi andLA Nunes Amaral The worldwide air transportation net-work Anomalous centrality community structure andcitiesrsquo global roles Proceedings of the National Academyof Sciences 102(22)7794ndash7799 2005

[14] Massimiliano Zanin and Fabrizio Lillo Modelling the airtransport with complex networks A short review TheEuropean Physical Journal Special Topics 215(1)5ndash212013

[15] Deborah L Bryan and Morton E Orsquokelly Hub-and-spokenetworks in air transportation an analytical reviewJournal of regional science 39(2)275ndash295 1999

[16] Luca DallrsquoAsta Alain Barrat Marc Barthelemy andAlessandro Vespignani Vulnerability of weighted net-works Journal of Statistical Mechanics Theory and Ex-periment 2006(04)P04006 2006

[17] Oriol Lordan Jose M Sallan Pep Simo and DavidGonzalez-Prieto Robustness of the air transport net-work Transportation Research Part E Logistics andTransportation Review 68155ndash163 2014

[18] Trivik Verma Nuno AM Arauacutejo and Hans J HerrmannRevealing the structure of the world airline network Sci-entific reports 4(1)1ndash6 2014

8

[19] Oriol Lordan Jose M Sallan and Pep Simo Study ofthe topology and robustness of airline route networksfrom the complex network approach a survey and re-search agenda Journal of Transport Geography 37112ndash120 2014

[20] Stefano Boccaletti Ginestra Bianconi Regino CriadoCharo I Del Genio Jesuacutes Goacutemez-Gardenes Miguel Ro-mance Irene Sendina-Nadal Zhen Wang and Massim-iliano Zanin The structure and dynamics of multilayernetworks Physics Reports 544(1)1ndash122 2014

[21] Mikko Kivelauml Alex Arenas Marc Barthelemy James PGleeson Yamir Moreno and Mason A Porter Multilayernetworks Journal of complex networks 2(3)203ndash2712014

[22] Alessio Cardillo Massimiliano Zanin Jesuacutes Goacutemez-Gardenes Miguel Romance Alejandro J Garciacutea del Amo

and Stefano Boccaletti Modeling the multi-layer na-ture of the european air transport network Resilienceand passengers re-scheduling under random failures TheEuropean Physical Journal Special Topics 215(1)23ndash332013

[23] Sara Dolnicar Klaus Grabler Bettina Gruumln and AnnaKulnig Key drivers of airline loyalty Tourism Manage-ment 32(5)1020ndash1026 2011

[24] Worldrsquos top 100 airlines 2019 (accessed20200629) httpwwwworldairlineawardscomworlds-top-100-airlines-2019

[25] After april passenger demand trough first signals ofuptick (accessed 2020-06-29) httpswwwiataorgenpressroompr2020-06-03-01

Appendix A Segment overlap distribution

For the airline company network (ACN) we define the segment overlap between companies as

Oij =

sum

`isinLicapLj

minNi(`) Nj(`)minNi Nj

i 6= j

0 i = j

(S1)

where Li is the set of segments operated by company i Ni(`) is the capacity of company i on segment ` (averagedover T = 116 days) and Ni =

sum`isinLi

Ni(`) is the total capacity of company i This quantity captures the similarityof segments operated by two different companies The segment overlap Oij equal to 1 implies that either the set ofsegments of one company is included in the set of the other one or that they operate on exactly the same segmentsA value equal to 0 means that the corresponding companies operate over completely different sets of segments

The distribution of segment overlap is shown in Fig S1 and displays a wide range of values distributed in [0 1]We also observe that while the majority of the companies do not share any segments with each other (the highestpeak with segment overlap equal to 0) nearly 100 pairs of companies have an overlap equal to 1 meaning that theyoperate over the same set of segments (or the set of segments of a company is included in the set of the other one)indicating that these companies are in direct competition

00 02 04 06 08 10Segment Overlap

101

102

103

104

105

Dist

ribut

ion

Figure S1 Segment overlap distribution for all companies (shown in linlog)

Appendix B Rerouting after bankruptcy

For a given value of the demand α isin [0 1] we compute the effect of rerouting the passengers In particular weestimate the additional distance experienced by all the rerouted passengers (the difference of distance between new

9

and original routes) and count the number of stranded passengersFor companies whose bankruptcy does not induce stranded passengers we observe that passengers have to take

always more transfers and have to travel over longer distance with the increase of α Fig S2(a) shows the additionaldistance travelers take in order to reach their destination When α gt 70 passengers have to travel more than atotal of 1000 kilometers when transferring (results averaged over companies not inducing stranded passengers withweight given by the capacity)

For companies whose bankruptcy leads to stranded passengers the total number of stranded passengers (denotedby Ns) is shown in Fig S2(b) When α is of order of 05 there is a significative number of passengers stranded ofabout 25 million The exponent τ = 375 of the power law function fitting (Ns prop ατ ) indicates the rapid growth ofthe number of stranded passengers with α

In Fig S2(c) we show the distribution of the critical demand threshold (for each company) above which thereis a non zero number of stranded passengers The two peaks of the demand threshold in Fig S2(c) correspond totwo extremal types of airline companies Companies with αci asymp 0 dominate the segments for at least one city andits bankruptcy will cause the isolation of the corresponding cities while companies with αci asymp 1 have only a fewpassengers and their passengers will never experience difficulties to be rerouted after their bankruptcy

0 20 40 60 80 100Demand

500750

1000125015001750200022502500

Wei

ghte

d Av

erag

e Co

st o

f Dist

ance Unit km

0 20 40 60 80 100Demand

00

05

10

15

20

25

Num

ber o

f Stra

nded

Pas

seng

ers (

X107 )

SimulationFitting

0 20 40 60 80 100Demand Threshold

0

50

100

150

200

250

300

Dist

ribut

ion

Figure S2 Observations on passenger rerouting after airline company bankruptcy (a) Weighted average cost of additionaldistance with weight given by the capacity (b) Total number Ns of stranded passengers as a function of α (the solid lineindicates a power law fit of the form Ns prop ατ where the exponent is here τ = 375) (c) Distribution of demand threshold

Appendix C Local Effective Demand

The local effective demand Esi (α) is defined as

Esi (α) =Nsi (α)

Ni (S1)

where Nsi (α) represents the actual number of passengers for company i when passengers follow the airline choice

strategy s Small values of this quantity allow us to identify companies at risk of bankruptcyWe first show in Fig S3 for the strategy of lsquoBiggest Firstrsquo the distribution of the capacity of the airlines companies

with local effective demand less than 50 (computed for the global demand α = 36 which is the estimated value

10

of real demand in April 2020 by IATA) We see that even if most companies meeting this condition have a smallcapacity there are however a few large ones

For each strategy we compare the proportion of companies with local effective demand less than a value equal todifferent thresholds 20 50 or 80 (Fig S4) We observe a similar behavior for all these different thresholds Inaddition for a given threshold there is a critical point for α below which the proportion of companies is above 50In other words for α less than this critical point the proportion of companies with local effective demand less thanthe threshold is larger than 50 while for α larger than the critical point the proportion of companies with localeffective demand less than the threshold is less than 50 We show the value of the critical point of demand as afunction of the demand threshold and for different strategies in Fig S5 We observe that this critical point is alwayslarger than the threshold meaning that in general the local effective demand is always smaller than the global one

000 025 050 075 100 125 150 175Capacity (X106) of Airline Companies (Eilt50)

0100200300400500600700

Dist

ribut

ion

Figure S3 Distribution of capacity of companies with local effective demand less than 50 when α = 36 the estimated valueof real demand in April 2020

11

0 20 40 60 80 100Demand

0

20

40

60

80

100Pr

opor

tion

of C

ompa

nies

Strategy UN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy BF

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy 1UN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy 1BF

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy RUN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy RBF

Eilt20Eilt50Eilt80

Figure S4 Proportion of companies with local effective demand less than different threshold For each strategy three thresholdsare compared 02 05 and 08 (a) lsquoUniformrsquo strategy (b) lsquoBiggest Firstrsquo strategy (c) lsquoOne-Uniformrsquo strategy (d) lsquoOne-BiggestFirstrsquo strategy (e) lsquoRank-Uniformrsquo strategy (f) lsquoRank-Biggest Firstrsquo strategy The gray dotted lines highlight α = 36 60and 80

12

0 20 40 60 80 100Local Effective Demand Threshold

0

20

40

60

80

100

Criti

cal D

eman

d

UNBF1UN1BFRUNRBF

Figure S5 Comparison of critical demand as the function of local effective demand threshold between different strategies

• I Introduction
• II The effect of bankruptcies on the world airline network
• • A Robustness and the `airline company network
  • B Rerouting after bankruptcy
  • • III The effect of a lower demand and customers airline choice strategies
    • IV Discussion
    • V Material and methods
    • • A Data availability
      • B Data
      • • References
        • A Segment overlap distribution
        • B Rerouting after bankruptcy
        • C Local Effective Demand

10

of real demand in April 2020 by IATA) We see that even if most companies meeting this condition have a smallcapacity there are however a few large ones

For each strategy we compare the proportion of companies with local effective demand less than a value equal todifferent thresholds 20 50 or 80 (Fig S4) We observe a similar behavior for all these different thresholds Inaddition for a given threshold there is a critical point for α below which the proportion of companies is above 50In other words for α less than this critical point the proportion of companies with local effective demand less thanthe threshold is larger than 50 while for α larger than the critical point the proportion of companies with localeffective demand less than the threshold is less than 50 We show the value of the critical point of demand as afunction of the demand threshold and for different strategies in Fig S5 We observe that this critical point is alwayslarger than the threshold meaning that in general the local effective demand is always smaller than the global one

000 025 050 075 100 125 150 175Capacity (X106) of Airline Companies (Eilt50)

0100200300400500600700

Dist

ribut

ion

Figure S3 Distribution of capacity of companies with local effective demand less than 50 when α = 36 the estimated valueof real demand in April 2020

11

0 20 40 60 80 100Demand

0

20

40

60

80

100Pr

opor

tion

of C

ompa

nies

Strategy UN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy BF

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy 1UN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy 1BF

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy RUN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy RBF

Eilt20Eilt50Eilt80

Figure S4 Proportion of companies with local effective demand less than different threshold For each strategy three thresholdsare compared 02 05 and 08 (a) lsquoUniformrsquo strategy (b) lsquoBiggest Firstrsquo strategy (c) lsquoOne-Uniformrsquo strategy (d) lsquoOne-BiggestFirstrsquo strategy (e) lsquoRank-Uniformrsquo strategy (f) lsquoRank-Biggest Firstrsquo strategy The gray dotted lines highlight α = 36 60and 80

12

0 20 40 60 80 100Local Effective Demand Threshold

0

20

40

60

80

100

Criti

cal D

eman

d

UNBF1UN1BFRUNRBF

Figure S5 Comparison of critical demand as the function of local effective demand threshold between different strategies

• I Introduction
• II The effect of bankruptcies on the world airline network
• • A Robustness and the `airline company network
  • B Rerouting after bankruptcy
  • • III The effect of a lower demand and customers airline choice strategies
    • IV Discussion
    • V Material and methods
    • • A Data availability
      • B Data
      • • References
        • A Segment overlap distribution
        • B Rerouting after bankruptcy
        • C Local Effective Demand

11

0 20 40 60 80 100Demand

0

20

40

60

80

100Pr

opor

tion

of C

ompa

nies

Strategy UN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy BF

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy 1UN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy 1BF

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy RUN

Eilt20Eilt50Eilt80

0 20 40 60 80 100Demand

0

20

40

60

80

100

Prop

ortio

n of

Com

pani

es

Strategy RBF

Eilt20Eilt50Eilt80

Figure S4 Proportion of companies with local effective demand less than different threshold For each strategy three thresholdsare compared 02 05 and 08 (a) lsquoUniformrsquo strategy (b) lsquoBiggest Firstrsquo strategy (c) lsquoOne-Uniformrsquo strategy (d) lsquoOne-BiggestFirstrsquo strategy (e) lsquoRank-Uniformrsquo strategy (f) lsquoRank-Biggest Firstrsquo strategy The gray dotted lines highlight α = 36 60and 80

12

0 20 40 60 80 100Local Effective Demand Threshold

0

20

40

60

80

100

Criti

cal D

eman

d

UNBF1UN1BFRUNRBF

Figure S5 Comparison of critical demand as the function of local effective demand threshold between different strategies

• I Introduction
• II The effect of bankruptcies on the world airline network
• • A Robustness and the `airline company network
  • B Rerouting after bankruptcy
  • • III The effect of a lower demand and customers airline choice strategies
    • IV Discussion
    • V Material and methods
    • • A Data availability
      • B Data
      • • References
        • A Segment overlap distribution
        • B Rerouting after bankruptcy
        • C Local Effective Demand

12

0 20 40 60 80 100Local Effective Demand Threshold

0

20

40

60

80

100

Criti

cal D

eman

d

UNBF1UN1BFRUNRBF

Figure S5 Comparison of critical demand as the function of local effective demand threshold between different strategies

• I Introduction
• II The effect of bankruptcies on the world airline network
• • A Robustness and the `airline company network
  • B Rerouting after bankruptcy
  • • III The effect of a lower demand and customers airline choice strategies
    • IV Discussion
    • V Material and methods
    • • A Data availability
      • B Data
      • • References
        • A Segment overlap distribution
        • B Rerouting after bankruptcy
        • C Local Effective Demand