sustainability

Article Study on Structural Characteristics of China’s Passenger Airline Network Based on Network Motifs Analysis

Ying Jin 1, Ye Wei 1,*, Chunliang Xiu 2, Wei Song 3 and Kaixian Yang 4

1 School of Geographical Sciences, Northeast Normal University, Changchun, Jilin 130024, China; [email protected] 2 College of Jang Ho Architecture, Northeastern University, Shenyang, Liaoning 110169, China; [email protected] 3 Department of Geography and Geosciences, University of Louisville, Louisville, KY 40292, USA; [email protected] 4 Department of Geography and Geoinformation Science, University of Illinois Urbana-Champaign, IL 61801, USA; [email protected] * Correspondence: [email protected]; Tel.: +86-177-9000-6582



Received: 24 March 2019; Accepted: 24 April 2019; Published: 28 April 2019


Abstract: The air passenger transport network system is an important agent of social and economic connections between cities. Studying on the airline network structure and providing optimization strategies can improve the airline industry sustainability evolution. As basic building blocks of broad networks, the concept of network motifs is cited in this paper to apply to the structural characteristic analysis of the passenger airline network. The ENUMERATE SUBGRAPHS (G, k) algorithm is used to identify the motifs and anti-motifs of the passenger airline network in China. A total of 37 airline companies are subjected to motif identification and exploring the structural and functional characteristics of the airline networks corresponding to different motifs. These 37 airline companies are classified according to the motif concentration curves into three development stages, which include mono-centric divergence companies at the low-level development stage, transitional companies at the intermediate development stage, and multi-centric and hierarchical companies at the advanced development stage. Finally, we found that adjusting the number of proper network motifs is useful to optimize the overall structure of airline networks, which is profitable for air transport sustainable development.

Keywords: passenger airline network; network motif; China

1. Introduction Passenger aviation plays a unique role in the global transportation system, facilitating the high-speed carriage of people over long distances. Efficient passenger airline networks are crucial for long-term air transport sustainable development. Based on the complex network theory, the air transportation system can be viewed as a spatial network where the nodes are airports and the edges are air routes or flights. In this theoretical framework, many studies on airline network were carried out using complex network models or methods and many valuable findings were revealed. A number of these studies focused on the overall structure of the airline network, like the small-world [1], the scale-free distribution [2], community structures [3], or hub-and-spoke organizational patterns [4]. Thus, this kind of study can be categorized as a structure-oriented perspective [5]. In other studies, scholars mainly raised questions from the perspective of nodes and their relationships, like the investigation of centrality measures [6], clustering [7], or assortativity [8], etc. This group of studies

Sustainability 2019, 11, 2484; doi:10.3390/su11092484 www.mdpi.com/journal/sustainability Sustainability 2019, 11, 2484 2 of 15 can be categorized as a node-oriented perspective. In spite of the many research findings from existing studies, more research on the air transport network form new perspectives are still needed. In this context, we try to apply a combined “structure-node” concept, namely network motifs, to analyze the microcosmic organization of the airline network, hoping to make some novel discoveries and provide new insights in understanding the air transportation system. The concept of a network motif was proposed by Shen-Orr et al. in their study on the transcriptional regulation network of Escherichia coli [9]. Network motifs are basic building blocks in networks. They are defined as the interconnection mode that has recurrence frequencies in the real network much higher than those in a randomized network. Shen-Orr et al. found that each network motif had a specific function in determining gene expression and motif structure can illustrate the entire transcriptional network of the organism. Furthermore, their team member Milo et al. found that network motifs ubiquitously exist in universal classes of the network such as biochemical, neurobiological, ecological, and engineering networks [10]. To be a high-order network connection mode, network motifs are crucial for understanding the basic structures that control and modulate many complex system behaviors [11]. Later, the network motif was widely applied to network function studies in different disciplines. For example, Reigl et al. found that there were some over-presented motifs that may perform stereotypical functions in the C. elegans nervous system [12]. Sporns and Kötter identified the characteristic network building blocks that are the structural and functional brain network motifs in neuroanatomical data [13]. Itzkovitz and Alon studied the network motifs that arise solely from geometric constraints [14]. Valverde and Solé analyzed a large set of software class diagrams to learn about the condition of network motifs in computational graphs [15]. Ohnishi et al. specified the network motifs of the inter-firm network to clarify production mechanisms and economic functions [16]. City network consists of the flows of population, commodities, information, and capital, and city network studies always embody transportation [17], economy [18,19] and the society [20], among which air transportation network is a common and important research focus. Research on the structure of air passenger transport network is helpful in understanding, and more importantly, optimizing the structures of the urban system and inter-city transportation system, as well as their sustainable development. The ENUMERATE SUBGRAPHS (G, k) (ESU) algorithm, a widely used method, was employed to identify the three-node and four-node motifs and anti-motifs of the passenger airline network in China including 37 Chinese airline companies. In addition to the topological characteristic, function, classification, concentration, and combination of motifs, the network organization mode and developing stages of the passenger airline networks were analyzed based on motifs and other ancillary information. Finally, a motif-based optimizing strategy was proposed.

2. Data and methods

2.1. Data Open big data have been used broadly in transport network analysis [21]. The data of China’s passenger airline network were compiled from the Ctrip.com, which is one of the largest travel websites in China [22–24]. The study area is limited to the mainland of China excluding Hong Kong, Macao, and Taiwan. All routes data we considered are from the scheduled domestic timetable for one week from July 2, 2015, to July 8, 2015. We used python to crawl the flight information including departure airport, arrival airport, departure city, arrival city and airline company from https://flights.ctrip.com/. In 2015, there were 37 airline companies in China. As there is only a few flights follow a “circle” pattern [3] and the purpose of this paper is analyzing the topological structure of the Chinese passenger airline network, the network was treated as unweighted and undirected. The nodes in the network represent airports, and links were created if any two airports are connected by a direct passenger flight. This network can be represented as an adjacency matrix (An n), × that aij = 1 if a flight link exists between a city-pair (i and j), otherwise, aij = 0. This method of network Sustainability 2019, 11, 2484 3 of 15

Sustainability 2019, 11, x FOR PEER REVIEW 3 of 18 establishment is similar to previous works [25–27]. If some flights shared the same flight code when Thethey flights were operating operated under through code-sharing strategic cooperation, agreements they but were not combinedflying the as actual one flight flights [28 were]. The not flights considered.operating If under there code-sharingare two airports agreements in the same but notcity flying (like theBeijing, actual Shanghai), flights were the not two considered. airports wereIf there combinedare two into airports one innode. the same Figure city 1 (like shows Beijing, the stru Shanghai),cture of the China’s two airports passenger were airline combined network into one that node . containsFigure 2061 shows nodes the and structure 2095 edges. of China’s The width passenger of edges airline differentiates network that the contains number 206of flights nodes andalong 2095 withedges. each link. The width of edges differentiates the number of flights along with each link.

Figure 1. China’s passenger airline network in 2015. Figure 1. China’s passenger airline network in 2015. 2.2. Methods 2.2. Methods 2.2.1. Motif Analysis 2.2.1. Motif Analysis Network motifs are basic interactive subgraphs whose frequencies in a real network are significantly higherNetwork than motifs those inare a randomizedbasic interactive network, subgraphs while those whose occurring frequencies less frequently in a real thannetwork randomized are significantlynetwork arehigher called than anti-motifs those in a [randomized9,10,13,29]. Networknetwork, motifwhile canthose be occurring a useful tool less tofrequently observe thethan local randomizedrelationship network pattern are in thecalled airline anti-motifs network [[9,10,13,29].30]. Network motif can be a useful tool to observe theThe local randomized relationship networks pattern have in the the airline same network single-node [30]. characteristics as real networks, which meansThe randomized that each node networks in a randomized have the networksame single has-node the same characteristics number of incoming as real networks, and outgoing which edges meansas the that corresponding each node in node a randomized has in a real network network. has the same number of incoming and outgoing edges asThe the relevantcorresponding statistical node characteristics has in a real usednetwork. to evaluate the motifs include [9,10]: The1. relevant Frequency statistical of motif characteristics used to evaluate the motifs include [9,10]: 1. ForFrequency a given of subgraph motif S with n nodes, the number of times it appears in the real network is n(S), andFor thea given total subgraph number of S timeswith n that nodes, all subgraphs the number with of times n nodes it appears appear in the real network is nN(S;) then,, andthe the appearance total number frequency of times ofthat the all subgraph subgraphsS is: with n nodes appear in the real network is N; then, the appearance frequency of the subgraph S is: n(S )n(S) Frequency= = (1) Frequency N (1) N If theIf thesubgraph subgraph S is Stheis motif the motif of the of network, the network, this thisfrequency frequency is called is called the frequency the frequency of the of motif, the motif, or theor themotif motif concentration. concentration. 2. 2.Value Value P ofP motifof motif ValueValue P refersP refers toto the the probability probability that that thethe numbernumber of of times times that that the the motif motifM appearsM appears in the inrandom the randomnetwork network is bigger is bigger than that than in that the realin the network. real network. A smaller Avalue smaller of Pvalueindicates of P greater indicates importance greater of importancethe motif of in the the motif network. in the When network. the probabilityWhen the probabilityP is lower thanP is lower a cuto thanff value a cutoff (in this value paper (in isthis 0.01), paperthe is occurrence 0.01), the timesoccurrence of subgraphs times of insubgraphs the network in the are network deemed toare be deemed significantly to be highersignificantly than in a higherrandomized than in a network,randomized and network, the subgraphs and the can su bebgraphs seen as can “network be seen motifs”as “network [10]. motifs” [10]. 3. 3.Value Value Z ofZ motifof motif Sustainability 2019, 11, 2484 4 of 15

For a motif, the number of times it appears in the real network is Nreali , and the number of times it appears in the random network is Nrandi ; the mean of Nrandi is < Nrandi > and the standard deviation is

σrandi ; then, the value Z of the motif in the real network is:

Nreali < Nrandi > Zi = − (2) σrandi

Generally, the statistical significance of the motif is evaluated by calculating the value Z. In the case Z > 0, the subgraph is a motif; in the case Z < 0, the subgraph is an anti-motif. Value Z can be used to measure the importance of the motif. A higher value of Z indicates greater importance of the motif in the network. This paper identified motifs in China’s passenger airline network through the Rand-ESU algorithm using the analysis tool FANMOD [31,32]. The ENUMERATE SUBGRAPHS (G, k) (ESU) algorithm specifies that starting from a peak v in the input network, the peaks adjacent to certain peaks whose subscript is bigger than v and does not belong to VSubgraph are added into VExtention. According to the method of enumerating by virtue of the tree structure and sampling the subgraphs, a gradual extension of the subgraph from the subgraph with the scale of 1 ensures that each subgraph is searched for only once and no meaningless subgraphs are generated. In the process of enumerating subgraphs (ESU) through the Rand-ESU algorithm, judging whether to continue expanding a certain subgraph based on probability can greatly improve the efficiency of the algorithm and can also expand the search scale to 14 peaks, indicating that this is a highly effective method.

2.2.2. Network Analysis To assess the heterogeneity and hierarchy of network nodes in 37 airline company networks, average degree and Zipf index were employed to assist the analysis. 1. Average degree The degree of a node refers to the number of all connected edges of the node in the network, and the average degree refers to the average value of degrees of all nodes in the whole network. In this study, the average degree of each airline company indicates that the average value of all airports’ degrees in the company’s network. 2. Zipf law Zipf’s law is one of the little quantitative and reproducible regularities found in economics. Zipf index was used to describe city sizes in 1949, and the size distributions of cities are power laws τ with a specific exponent, meaning that the probability of attaining a certain size x is proportional to x− . The τ was thus called Zipf index [33]. Zipf’s law also holds in many other scientific fields [34]. In this article, the degrees of nodes of each airline company were ranked by size, and they all essentially followed a power law distribution under exponential regression. Their power exponents of them were seen as their Zipf index.

3. Characteristics of Motifs of China’s Passenger Airline Network

3.1. Motifs of China’s Passenger Airline Network In order to examine the micro functional structure of China’s passenger airline network, we scanned for all possible three-node and four-node undirected subgraphs. We got one three-node motif (3a), one three-node anti-motif (3b), three four-node motifs (4a, 4b and 4d), and three four-node anti-motifs (4c, 4e, and 4f) in the network. Table1 summarizes basic parameters of all motifs and anti-motifs including the subgraph shape, the frequency of the motifs appearing in the real network (Frequency [Original]), the average frequency of the subgraphs appearing in the random network (rMean-Freq [Random]), Z values of the motifs, and P values of the motifs. Sustainability 2019, 11, x FOR PEER REVIEW 5 of 18 Sustainability 2019, 11, x FOR PEER REVIEW 5 of 18 Sustainability 2019, 11, x FOR PEER REVIEW 5 of 18 SustainabilitySustainability 20192019,, 1111,, x 2484 FOR PEER REVIEW 5 5of of 18 15 Sustainability Table2019,, 11 1.,, xxStatistic FORFOR PEERPEER information REVIEWREVIEW of motifs/anti-motifs of China’s passenger airline network. 5 of 18 Table 1. Statistic information of motifs/anti-motifs of China’s passenger airline network. Table 1. Statistic information of motifs/anti-motifs of China’s passenger airline network. Table 1. Statistic informationFrequency of motifs/anti-motifs rMean-Freq of China’s passenger airline network. ID SubgraphTable 1. StatisticShape informationFrequency of motifs rMean-Freq/anti-motifs of Value China’s Z passenger Value airlineP Subgraph network. Type ID Subgraph Shape Frequency[Original] rMean-Freq[Random] Value Z Value P Subgraph Type ID Subgraph Shape Frequency[Original] rMean-Freq[Random] Value Z Value P Subgraph Type ID SubgraphSubgraph Shape Frequency[Original] rMean-Freq[Random] Value Z Value P SubgraphSubgraph Type 3aID [Original]17.260% [Random]12.314% Value10.079 Z Value0 P Motif 3a Shape [Original]17.260% [Random]12.314% 10.079 0 MotifType 3a 17.260% 12.314% 10.079 0 Motif 3a 17.260% 12.314% 10.079 0 Motif 3a 3a 17.260%17.260% 12.314%12.314% 10.079 10.079 0 0 Motif Motif 3b 82.740% 87.686% −10.079 1 Anti-motif 3b 82.740% 87.686% −10.079 1 Anti-motif 3b 82.740% 87.686% −10.079 1 Anti-motif 3b 3b 82.740%82.740% 87.686%87.686% −10.07910.079 1 1 Anti-motif Anti-motif 4a 27.949% 18.533% −7.953 0.001 Motif 4a 27.949% 18.533% 7.953 0.001 Motif 4a 27.949% 18.533% 7.953 0.001 Motif 4a 4a 27.949%27.949% 18.533%18.533% 7.953 7.953 0.001 0.001 Motif Motif 4b 8.358% 7.220% 6.100 0 Motif 4b 8.358% 7.220% 6.100 0 Motif 4b 8.358% 7.220% 6.100 0 Motif 4b 4b 8.358%8.358% 7.220%7.220% 6.100 6.100 0 0 Motif Motif 4b 8.358% 7.220% 6.100 0 Motif 4c 48.139% 52.695% -6.326 0.996 Anti-motif 4c 48.139% 52.695% -6.326 0.996 Anti-motif 4c 4c 48.139%48.139% 52.695%52.695% -6.3266.326 0.996 0.996 Anti-motif Anti-motif 4c 48.139% 52.695% -6.326− 0.996 Anti-motif 4d 2.650% 1.356% 11.474 0 Motif 4d 2.650% 1.356% 11.474 0 Motif 4d4d 2.650%2.650% 1.356%1.356% 11.474 11.474 0 0 Motif Motif 4d 2.650% 1.356% 11.474 0 Motif 4e 0.690% 3.527% −6.710 0.998 Anti-motif 4e 4e 0.690%0.690% 3.527%3.527% −6.7106.710 0.998 0.998 Anti-motif Anti-motif 4e 0.690% 3.527% −−6.710 0.998 Anti-motif 4e 0.690% 3.527% −6.710 0.998 Anti-motif 4f 4f 12.214%12.214% 16.670%16.670% −13.02113.021 1 1 Anti-motif Anti-motif 4f 12.214% 16.670% −−13.021 1 Anti-motif 4f 12.214% 16.670% −13.021 1 Anti-motif 4f 12.214% 16.670% −13.021 1 Anti-motif Considering the three-node subgraphs, motif 3a is a triangular structure formed by three Considering the three-node subgraphs, motif 3a is a triangular structure formed by three mutuallyConsideringConsidering connected thethe airports, three-nodethree-node while subgraphs, subgraphs, anti-motif motif motif3b 3ais ais3a V-shaped a triangularis a triangular structure structure structure formed formed byformed by the three connection by mutually three mutuallyConsidering connected the airports, three-node while subgraphs, anti-motif motif3b is a3a V-shaped isis aa triangulartriangular structure structurestructure formed byformedformed the connection byby threethree betweenmutuallyconnected oneconnected airports, airport while airports, and anti-motiftwo while disconnected anti-motif 3b is a V-shaped airports. 3b is a structure V-shaped 3a is a formedstructural structure by the buildingformed connection by block the between connectionof China’s one mutuallybetween oneconnected airport airports, and two while disconnected anti-motif airports. 3b isis aa V-shaped V-shaped3a is a structural structurestructure buildingformed by block the connectionof China’s betweenpassengerairport and one airline two airport disconnectednetwork and bytwo Milo’s airports.disconnected definition 3a is aairports. structural[10]. 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structural characteristic that one airport node is connected with multiple disconnected nodes to form Sucha star structures shape. Such have structures a higher appearancehave a higher frequency appearance in the frequency network, in but the theynetwork, cannot but be they the buildingcannot be blocksthe building of the motifs. blocks Motifs of the 4a, motifs. 4b, and Motifs 4d have 4a, a 4b common, and 4d characteristic have a common of further characteristic connection of based further on theconnection looped structure. based on At the the samelooped time, structure. each node At ofthe motifs same 4b time, and 4d each is connected node of withmotifs at least4b and another 4d is twoconnected nodes to with form at aleast mesh another topology two withnodes higher to form reliability a mesh topology and more with complex higher structure. reliability Moreover, and more motifscomplex 4a, 4b,structure. and 4d allMoreover, have more motifs connected 4a, 4b, edges and than4d all other have subgraphs more connected with the edges same numberthan other of nodes.subgraphs The airline with the network same di numberffers from of thenodes. railway The network airline network and other differs ground from transportation the railway networks network thatand require other physicallyground transportation constructed routes.networks The that air transportationrequire physically network constructed is serviced routes. by air routes,The air andtransportation it has higher network efficiency is dueserviced to its greaterby air routes, number and of potentialit has higher connections efficiency and due the flexibilityto its greater of establishingnumber of potential them. connections and the flexibility of establishing them.

(a) (b)

FigureFigure 2. 2.Characteristic Characteristic curvecurve graph of motifs motifs or or anti-m anti-motifsotifs of of China’s China’s passenger passenger airline airline network. network. (a) (a) TheThe originaloriginal frequencyfrequency curvescurves of China’sChina’s passenger airline networ network.k. (b) (b) The The value value Z Z distribution distribution curves of China’s passenger airlinecurves network. of China’s passenger airline network.

TheThe network network subgraphs subgraphs are are a a part part of of the the overall overall network, network, and and the the n-node n-node subgraphs subgraphs are are formed formed byby (n-1) (n-1) nodes nodes connected connected in in a particulara particular combination combinatio [10n [10].]. According According to theto the structural structural characteristics characteristics of motifsof motifs and anti-motifsand anti-motifs of China’s of China’s passenger passenger airline network,airline network, motifs 4a, motifs 4b, and 4a, 4d 4b, contain and 4d the contain triangular the structuretriangular of structure motif 3a, whileof motif anti-motifs 3a, while 4c, anti-motifs 4e, and 4f 4c, contain 4e, and the 4f V-shaped contain structurethe V-shaped of anti-motif structure 3b, of whichanti-motif reflect 3b, the which combination reflect the relationship combination among relationship the motifs among andthe theanti-motifs. motifs and the anti-motifs. MotifsMotifs can can represent represent the the characteristics characteristics of functionalof functional structures structures of the of realthe real network. network. Motifs Motifs of the of airlinethe airline network network (subgraphs (subgraphs 3a, 4a, 4b,3a, and4a, 4d)4b, showand 4d) common show characteristicscommon characteristics of more stable of topologicalmore stable structurestopological and structures more complete and more connection, complete which connection, reflects the which stability reflects of the overallthe stability structure of ofthe China’s overall passengerstructure airlineof China’s network. passenger Thus, airline these motifs network. are advantageousThus, these motifs subgraph are structuresadvantageous of the subgraph airline network.structures Anti-motifs of the airline are not network. the main Anti-motifs structures ofare the not real the network main structures and cannot of represent the real the network structural and characteristicscannot represent of the the real structural network. characteristics Anti-motifs of (subgraphs the real network. 3b, 4c, 4e,Anti-motifs and 4f) of (subgraphs the airline network3b, 4c, 4e, showand characteristics4f) of the airline of lower network levels show of connection characterist andics weaker of lower interaction, levels of so connection they are generally and weaker the disadvantageousinteraction, so they subgraph are generally structure the of disadvanta the airlinegeous network. subgraph structure of the airline network.

3.2.3.2. Motifs Motifs of of Networks Networks of of the the Airline Airline Companies Companies BasedBased on on 37 China’s37 China’s airline airline companies companies in 2015, in the 2015, unweighted the unweighted and undirected and undirected China’s passenger China’s airlinepassenger network airline was network diagramed was diagramed into 37 airline into networks. 37 airline networks. The 37 networks The 37 werenetworks subjected were subjected to motif detectionto motif detection one by one one using by one the FANMODusing the FANMOD tool. tool. TableTable2 shows 2 shows all motifs all motifs and anti-motifs and anti-motifs of airline companies.of airline companies. The airline companies’ The airline abbreviations companies’ (IATAabbreviations codes) were (IATA listed codes) in were Table listed2. In in Table Table2, 2. if In a companyTable 2, if ownsa company some owns subgraphs some subgraphs as motifs, as themotifs, corresponding the corresponding subgraphs subgraphs are marked are marked a “√” undera “√” under it. If ait. company If a compan ownsy owns some some subgraphs subgraphs as anti-motifs,as anti-motifs, the the table table cells cells under under the the relevant relevant subgraphs subgraphs show show blank. blank. Considering Considering the the small small scale scale andand the the simple simple and and disordered disordered airline airline route route network network of of 9Air 9Air Co. Co. Ltd., Ltd., no no motif motif was was generated. generated. After After eliminatingeliminating 9Air 9Air Co. Co. Ltd., Ltd., 36 36 airline airline companies companies remained remained for for motif motif analysis. analysis. The degree distribution reveals important information about the heterogeneity of the nodes [37]. Hubs are located in the highest hierarchical level, with many more linkages than the regular spoke nodes [38]. According to previous studies, the hub of every airline company is identified according to the degree. In this article, when a node’s degree is higher than the sum of triple standard deviations of the degrees and the average degree in the network, it will be considered as a hub. At the same time, the degree distribution of the airports was used to fit the rank-size curve and Sustainability 2019, 11, 2484 7 of 15

TableTableTableTableTableTableTableTable 2. 2. 2.Statistics2. 2.Statistics 2. StatisticsStatistics2. Statistics2.Statistics Statistics Statistics of of ofofnetwork ofnetworkof networkofnetwork networkofnetwork network network motif motif motifmotif motifmotif motif motifconditions conditions conditionsconditions conditionsconditions conditions conditions of of ofofairlin ofairlinof airlinofairlin airlinofairlin airlin eairline companiese ecompanies e companiesecompanies e companiescompaniese companies companies in in ininChina’s inChina’sin China’sinChina’s China’sinChina’s China’s China’s passenger passenger passengerpassenger passengerpassenger passenger passenger airline airline airlineairline airlineairline airline airline network. network. network.network. network.network. network. network. Table 2. Statistics of network motif conditions of airline companies in China’s passenger airline network. MotifsMotifsMotifsMotifsMotifsMotifsMotifsMotifs or or or orAnti-Motifs ororAnti-Motifs or Anti-Motifs Anti-Motifs or Anti-MotifsAnti-Motifs Anti-Motifs Anti-Motifs AirlineAirlineAirlineAirlineAirlineAirlineAirlineAirline AverageAverageAverageAverageAverageAverageAverageAverage Motifs or Anti-Motifs IDIDIDID IDID ID ID EdgesEdgesEdgesEdgesEdgesEdgesEdgesEdges NodesNodesNodesNodesNodesNodesNodesNodes FoundationFoundationFoundationFoundationFoundationFoundationFoundationFoundation ZipfZipfZipfZipfZipfZipfZipf Zipf HubsHubsHubsHubsHubsHubsHubsHubs 3a 3a3a3a3a 3a 3a 3a 3a 3b3b3b3b3b 3b3b 3b 3b 4a4a4a4a 4a 4a 4a 4a 4b 4b4b4b 4b4b 4b 4b 4c4c 4c4c 4c4c 4c 4c 4c 4d4d4d4d 4d4d 4d 4d 4e4e4e4e 4e 4e 4e 4e 4f 4f 4f 4f 4f 4f 4f 4f 4f ID AirlineCompanyCompanyCompanyCompanyCompanyCompanyCompany CompanyCompany Edges Nodes Foundation AverageDegreeDegreeDegreeDegree DegreeDegreeDegreeDegree Zipf Hubs

1 Air China (CA) 770 139 1988 11.159 1.259 3 √ √ √ √ 11 1 1 1 1 AirAirAirAirAir AirChina ChinaChina ChinaChina China (CA) (CA)(CA) (CA)(CA) (CA) 770 770 770 770 770 770 139 139 139 139 139 139 1988 1988 1988 1988 1988 1988 11.159 11.159 11.159 11.159 11.159 11.159 1.259 1.259 1.259 1.259 1.259 1.259 3 3 3 3 3 3 √√ √ √ √ √ √√ √ √ √ √ √√ √ √ √ √ √√ √ √ √ √ 21 Beijing1Air Capital ChinaAir China Airlines (CA) (CA) (JD) 770 770 176 139 59 139 2010 1988 1988 5.966 11.159 11.159 1.019 1.259 1.259 2 3 3 √√ √ √√ √ √ √ √ √ √ √ 3 Chengdu Airlines (EU) 72 42 2010 3.429 0.637 1 √ √ 4 ChinaBeijingBeijing EasternBeijingBeijingBeijingBeijingBeijingBeijing Capital Capital Airlines CapitalCapital CapitalCapital Capital Capital (MU) 951 178 1988 10.807 1.198 4 √ √ √ √ 22 2 2 2 2 2 2 176176176176176176 176 176 59595959 59 59 59 59 2010 2010 2010 2010 2010 2010 2010 2010 5.966 5.966 5.966 5.966 5.966 5.966 5.966 5.966 1.0191.0191.0191.0191.0191.0191.019 1.019 22 2 2 2 2 2 2 √√ √ √ √ √ √ √ √√ √ √ √ √ √ √ √√ √ √ √ √ √ √ √√ √ √ √ √ √ √ 5 ChinaAirlines ExpressAirlinesAirlinesAirlinesAirlinesAirlinesAirlinesAirlines Airlines(JD) (JD) (JD)(JD) (JD)(JD) (JD) (JD) (G5) 331 99 2006 6.755 0.999 3 √ √ √ √ 6 China Southern Airlines (CZ) 930 155 1995 12.078 1.245 4 √ √ √ √ 7 China UnitedChengduChengduChengduChengduChengduChengduChengduChengdu Airlines (KN) 64 54 1984 2.415 0.686 1 √ √ √ 833 3 3 Chongqing 3 3 3 3 Airlines (OQ)72727272 72 72 72 72 27 42424242 42 42 24 42 42 2007 2010 2010 2010 2010 2010 2010 2010 2010 2.250 3.429 3.429 3.429 3.429 3.429 3.429 3.429 3.429 0.690.6370.6370.6370.6370.6370.6370.637 0.637 1 11 1 1 1 1 1 1 √√ √ √ √ √ √ √ √ √√√ √ √ √ √ √ √ √ AirlinesAirlinesAirlinesAirlinesAirlinesAirlinesAirlinesAirlines (EU) (EU) (EU)(EU) (EU)(EU) (EU) (EU) 9 Colorful Guizhou Airlines (CY) 7 6 2015 2.333 0.677 0 √ √ 10 DonghaiChinaChinaChinaChinaChinaChinaChinaChina AirlinesEastern Eastern EasternEastern EasternEastern Eastern Eastern (DZ) 28 19 2002 2.947 0.848 1 √ √ 1144 4 4 4 4 4 Fuzhou4 Airlines (FU)951951951951951951 951 951 26 178178178178178178 22178 178 2014 1988 1988 1988 1988 1988 1988 1988 1988 2.364 10.807 10.807 10.807 10.807 10.807 10.807 10.807 10.807 0.7821.1981.1981.1981.1981.1981.1981.198 1.198 1 44 4 4 4 4 4 4 √√ √ √ √ √ √ √ √ √√√ √ √ √ √ √ √ √√ √ √ √ √ √ √ √ √√ √ √ √ √ √ √ AirlinesAirlinesAirlinesAirlines (MU)(MU) (MU) (MU) 12 GrandAirlinesAirlines ChinaAirlinesAirlines Airlines(MU) (MU) (MU) (MU) (CN) 17 20 2007 1.700 0.666 0 √ √ 13 GuangxiChinaChina BeibuChinaChinaChinaChinaChinaChina Express Gulf Express ExpressExpress ExpressExpress Express AirlinesExpress (GX) 52 32 2015 3.355 0.709 1 √ √ 1455 5 5 5 5 Hainan5 5 Airlines (HU)331331331331331331 331 331 371 99999999 99 99 91 99 99 1993 2006 2006 2006 2006 2006 2006 2006 2006 8.244 6.755 6.755 6.755 6.755 6.755 6.755 6.755 6.755 1.1690.9990.9990.9990.9990.9990.9990.999 0.999 1 33 3 3 3 3 3 3 √√√ √ √ √ √ √ √ √√√ √ √ √ √ √ √ √ √√ √ √ √ √ √ √ √√ √ √ √ √ √ √ 15 HebeiAirlinesAirlinesAirlinesAirlinesAirlinesAirlines AirlinesAirlines (G5) (G5) (G5)(G5) (G5) (NS)(G5) (G5) (G5) 253 58 2010 8.877 0.942 1 √ √ √ 16 HongtuChinaChina AirlinesChinaChinaChinaChinaChinaChina (A6) 8 7 2014 2.286 0.769 0 √ √ √ 17 Jiangxi Airlines (RY) 10 9 2014 2.222 0.866 0 √ √ √

1866 6 6 6 6 6 6 Southern JoySouthernSouthernSouthernSouthernSouthern AirSouthernSouthern (JR) 930930930930930930 930 930 107 155155155155155155 58155 155 2008 1995 1995 1995 1995 1995 1995 1995 1995 3.754 12.078 12.078 12.078 12.078 12.078 12.078 12.078 12.078 0.8551.2451.2451.2451.2451.2451.2451.245 1.245 1 44 4 4 4 4 4 4 √√√ √√ √ √ √ √ √√ √√ √ √ √ √ √ √ √ √ √ √ √ √ √ √√ √ √√ √ √ √ 19 JuneyaoAirlinesAirlinesAirlinesAirlinesAirlinesAirlinesAirlines Airlines (CZ) (CZ) (CZ)(CZ) (CZ)(CZ) (HO)(CZ) (CZ) 120 57 2005 4.286 0.89 1 √ √ √ √ 20 Kunming Airlines (KY) 270 65 2009 8.438 0.995 1 √ √ √ 21China LuckyChinaChinaChinaChinaChinaChinaChina United AirUnited UnitedUnited UnitedUnited (8L)United United 83 48 2004 3.532 0.72 1 √ √ √ 77 7 7 7 7 7 7 64646464 64 64 64 64 54545454 54 54 54 54 1984 1984 1984 1984 1984 1984 1984 1984 2.415 2.415 2.415 2.415 2.415 2.415 2.415 2.415 0.6860.6860.6860.6860.6860.6860.686 0.686 11 1 1 1 1 1 1 √√ √√ √ √ √ √ √√ √√ √ √ √ √ √ √ √ √ √ √ √ √ 22AirlinesAirlinesAirlinesAirlinesAirlines 9AirAirlinesAirlinesAirlines (AQ) (KN) (KN) (KN)(KN) (KN)(KN) (KN) (KN) 6 6 2014 2.000 - 0 ------23 Okay Airways (BK) 73 48 2005 3.042 0.802 2 √ √ √ 24 QingdaoChongqingChongqingChongqingChongqingChongqingChongqing AirlinesChongqingChongqing (QW) 25 18 2013 2.778 0.671 1 √ √ 88 8 8 8 8 8 8 27272727 27 27 27 27 24242424 24 24 24 24 2007 2007 2007 2007 2007 2007 2007 2007 2.250 2.250 2.250 2.250 2.250 2.250 2.250 2.250 0.690.690.690.690.690.69 0.69 0.69 11 1 1 1 1 1 1 √√ √√ √ √ √ √ √ √ √ √ √ √ √ √ √√ √√ √ √ √ √ 25 RuiliAirlinesAirlinesAirlinesAirlinesAirlinesAirlines AirlinesAirlines ( O( O(( OQ) (O (DR)(Q)O OQ)( Q)O (Q)Q)O Q) Q) 26 20 2014 2.600 0.675 1 √ √ √ 26 Shandong Airlines (SC) 565 131 1999 8.692 1.2 3 √ √ √ √ ColorfulColorfulColorfulColorful 27 ShanghaiColorfulColorful AirlinesColorfulColorful (FM) 110 67 1985 3.333 0.709 1 √ √ √ 2899 9 9 9 Shenzhen9 9 9 GuizhouGuizhouGuizhouGuizhouGuizhouGuizhou AirlinesGuizhouGuizhou (ZH) 77 7 7 7 7 7 7 533 66 6 6 116 6 6 6 6 1992 2015 2015 2015 2015 2015 2015 2015 2015 9.4342.3332.3332.3332.3332.3332.3332.333 2.333 1.2760.6770.6770.6770.6770.6770.6770.677 0.677 3 00 0 0 0 0 0 0 √ √√ √√ √ √ √ √ √ √ √ √ √ √ √ √ √ √ 29 Sichuan Airlines (3U) 313 98 1986 6.454 1.001 2 √ √ √ √ AirlinesAirlinesAirlinesAirlinesAirlinesAirlinesAirlinesAirlines (CY) (CY) (CY)(CY) (CY)(CY) (CY) (CY) 30 Spring Airlines (9C) 32 23 2004 2.909 0.574 1 √ √ 31 Tianjin Airlines (GS) 225 91 2009 5.000 0.943 3 √ √ √ √ 32 Tibet Airlines (TV) 80 48 2010 3.404 0.964 1 √ √ √ 33 Urumqi Air (UQ) 17 14 2014 2.429 0.893 1 √ √ √ SustainabilitySustainabilitySustainabilitySustainabilitySustainabilitySustainabilitySustainabilitySustainability 2019 2019 2019 2019 2019 2019, 201911, 2019,11 ,11 ,,11 ,x;,11 11,,x; , 11,x; doi:, x; ,11doi:x; x;,doi: doi: x;,doi: doi:x;FOR doi:FOR doi: FORFOR FOR FOR PEERFOR PEERFOR PEER PEER PEER PEER PEER REVIEWPEER REVIEW REVIEW REVIEW REVIEW REVIEW REVIEW REVIEW www. www. www. www. www. www. www.mdpi.com/journal www.mdpi.com/journalmdpi.com/journalmdpi.com/journalmdpi.com/journalmdpi.com/journalmdpi.com/journalmdpi.com/journal/sustainability/sustainability/sustainability/sustainability/sustainability/sustainability/sustainability/sustainability 34 Western Airlines (PN) 66 40 2006 3.300 0.836 1 √ √ √ 35 Xiamen Airlines (MF) 754 120 1984 12.672 1.277 1 √ √ √ 36 Yangtze River Airline (Y8) 4 5 2002 1.600 0.765 0 √ √ √ 37 Zhejiang Loong Airlines (GJ) 58 39 2011 2.974 0.743 1 √ √ √ Sustainability 2019, 11, 2484 8 of 15

The degree distribution reveals important information about the heterogeneity of the nodes [37]. Hubs are located in the highest hierarchical level, with many more linkages than the regular spoke nodes [38]. According to previous studies, the hub of every airline company is identified according to the degree. In this article, when a node’s degree is higher than the sum of triple standard deviations of the degrees and the average degree in the network, it will be considered as a hub. At the same time, the degree distribution of the airports was used to fit the rank-size curve and calculate the Zipf index, which can help uncover levels of the hierarchy of node degrees [39]. For comparison, some basic information about airline networks and motif characteristics were summarized in Table2. As shown in Table2, 26 of the 36 airline companies have independent motifs 3a, and 10 companies have independent motifs 3b. Each airline company has only one of motifs 3a or 3b, indicating that these two motifs can respectively reflect the structural characteristics of different types of airline companies. More airline companies have the topologically stable, 3-node motifs 3a with the triangular structure. Motif 3a can manifest the common characteristics of networks of the majority of airline companies. From Table2 we can see that most companies with a large network scale, multi-hubs, and Zipf index higher than 1 have motif 3a. The number of airline companies with motifs 3b is small. These companies generally have a small network scale, a small number of routes, and small average degree and Zipf index (smaller than 0.9). Motifs 3b could represent the characteristic structure of small, immature airline companies. Thirty-one airline companies have motifs 4a, accounting for the vast majority, which fits with the characteristics of motifs of China’s passenger airline network. Motifs 4a can be viewed as a common characteristic motif of companies. Topologically, motifs 4a are combinations of motifs 3a and 3b, thereby having characteristics of both. A similar number of airline companies have motifs 4b, 4c, and 4d, respectively, approximately accounting for one third to one-fourth of the total number of airline companies. These three motifs manifest different class characteristics of airline companies. Most companies having motifs 4b and 4d are multi-hub networks with large scale, high network average degree, and Zipf index, and have been established for a long period of time. Thus, motifs 4b and 4d can represent the structural and functional characteristics of larger and mature airline networks. Most airline companies with motifs 4c have a small scale, low network average degree, and small Zipf index have been established for a short period of time, and have only one or no hub. An extremely small number of airline companies (2-3 companies) have motifs 4e and 4f. Motifs 4e and 4f are in looped structures and chain-shaped structures, and airline companies with these two kinds of motifs have a very small scale. This indicates that network motifs can reflect the structural and functional characteristics of the airline network. Table3 summarizes the structural characteristics of the motifs of China’s passenger airline network.

Table 3. Structural characteristics of motifs of China’s passenger airline network. TableTable 3. 3. StructuralStructural characteristics characteristics of motifs of ofChina’s motifs passenger of China’s airline network. passenger airline network. Structural Combination and Number of Motif StructuralStructural CombinationCombination and andNumber Upgrade of NumberDefinition of of the Motifs Motif Characteristics Upgrade Relations Airlines Definition of the MotifsDefinition of the Motifs CharacteristicsCharacteristics Upgrade RelationsRelations Airlines Airlines Minimum building Common motif; Triangular, ring Minimum building 26/36 Common motif; Triangular, ring block 26/36 Advantageous motif Common motif; Triangular,Triangular, ring ring block Minimum building block26/36 26Advantageous/36 motif 3a block Advantageous motif 3a Advantageous motif Characteristic motif of Minimum building Characteristic motif of Star, chain Minimum building 10/36 immature network; Star, chain block 10/36 immature network;Characteristic motif of immature Star, chainblock Minimum building blockdisadvanta 10/36 geous motif 3b disadvantageous motinetwork;f disadvantageous motif 3b disadvantageous motif Combination of 3a Common motif; Mesh Combination of 3a 31/36 Common motif; Common motif; MeshMesh and Combination 3b of 3a and31/36 3b 31Advantageous/36 motif 4a and 3b Advantageous motif 4a Advantageous motif Characteristic motif of Combination of 3a Characteristic motif of Mesh CombinationCombination of 3a of 3a12/36 mature network; Characteristic motif of mature MeshMesh Upgrade of 4a 12/36 12mature/36 network; 4b Upgrade ofUpgrade 4a of 4a advantageous motinetwork;f advantageous motif 4b advantageous motif Characteristic motif of small Characteristic motif of small Star Combination of 3b 13/36 Characteristic motif of small network StarStar Combination Combination of 3b of 3b 13/36 13/36network scale; Star Combination of 3b 13/36 network scale; scale; disadvantageous motif 4c disadvantageous motif 4c disadvantageous motif Characteristic motif of Combination of 3a Characteristic motif of Fully connected Combination of 3a 15/36 Fully connected Combination of 3a 15/36 mature network; 4d Fully connected Upgrade of 4a and 4b 15/36 mature network; 4d Upgrade of 4a and 4b advantageous motif 4d advantageous motif Quadrangle, Highly specific motif; Quadrangle, Combination of 3b 3/36 Highly specific motif; Ring Combination of 3b 3/36 disadvantageous motif 4e Ring disadvantageous motif 4e Ring disadvantageous motif Highly specific motif; Chain Combination of 3b 2/36 Highly specific motif; Chain Combination of 3b 2/36 disadvantageous motif 4f disadvantageous motif 4f

4. Classification of China’s Air Passenger Transport Companies Based on Motif Concentration 4. Classification of China’s Air Passenger Transport Companies Based on Motif Concentration Curve Curve When only the frequency of the motifs appearing in the real network is considered, the motif When only the frequency of the motifs appearing in the real network is considered, the motif concentration characteristic curve (Figure.3) of different airline companies can be drawn by concentration characteristic curve (Figure.3) of different airline companies can be drawn by connecting the frequency of different motifs of the same airline company. It can be seen that the connecting the frequency of different motifs of the same airline company. It can be seen that the curves of the companies with similar structural characteristics follow similar trends. Therefore, the curves of the companies with similar structural characteristics follow similar trends. Therefore, the airline companies can be classified according to the motif concentration curves. airline companies can be classified according to the motif concentration curves.

Figure 3. Motif concentration curves of airline companies. Figure 3. Motif concentration curves of airline companies.

According to Figure 3, China’s airline companies can be roughly classified into three types. According to Figure 3, China’s airline companies can be roughly classified into three types.

Sustainability 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/sustainability Sustainability 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/sustainability

Table 3. Structural characteristics of motifs of China’s passenger airline network.

Structural Combination and Number of Motif Definition of the Motifs Characteristics Upgrade Relations Airlines

Minimum building Common motif; Triangular, ring 26/36 block Advantageous motif 3a Characteristic motif of Table 3. Structural characteristicsMinimum of motifs building of China’s passenger airline network. Star,Table 3.chain Structural characteristics of motifs of China’s passenger airline10/36 network. immature network; Structural Combination andblock Number of Motif Structural Combination and Number of Definition of the Motifs 3bMotif Characteristics Upgrade Relations Airlines Definition of the Motifsdisadvanta geous motif Characteristics Upgrade Relations Airlines Minimum building Common motif; Triangular, ring MinimumCombination building of26/36 3a Common motif; Common motif; Triangular,Mesh ring block 26/36 31/36Advantageous motif 3a block Advantageous motif 3a block and 3b Advantageous motif Advantageous motif 4a 3a Characteristic motif of Minimum building Characteristic motif of Star, chain Minimum building 10/36 Characteristicimmature network; motif of Star, chain Minimumblock building 10/36 immature network; Characteristic motif of Star, chain block 10/36 disadvantaimmatureg network;eous moti f 3b Combinationblock of 3a disadvantageous motif 3b Mesh disadvanta12/36 geous motif mature network; CombinationUpgrade of 3a of 4a Common motif; Mesh Combination of 3a 31/36 Common motif; 4b Mesh Combinationand 3b of 3a 31/36 AdvantageousCommon motif; motif advantageous motif 4a Mesh and 3b 31/36 Advantageous motif Sustainability4a 2019, 11, 2484 and 3b Advantageous motifCharacteristic motif of small9 of 15 4a Characteristic motif of Combination of 3a Characteristic motif of MeshStar Combination Combination of 3a of12/36 3b Characteristic 13/36mature network; motif of network scale; Mesh CombinationUpgrade of of4a 3a 12/36 mature network; 4b Mesh Upgrade of 4a 12/36 advantamatureg network;eous moti f 4c 4b Upgrade of 4a advantageous motif disadvantageous motif 4b Table 3. Cont.Characteristicadvantageous motif moti of smallf Characteristic motif of smallCharacteristic motif of Star Combination of 3b 13/36 network scale; Star CombinationCombination of 3b of 13/36 3a network scale; 4c StarStructural CombinationCombination of 3b and Upgrade 13/36 Numberdisadvantanetwork of geous scale; moti f Motif 4c Fully connected disadvanta15/36 geous motifDefinition mature of thenetwork; Motifs 4c Characteristics UpgradeRelations of 4a and 4b AirlinesdisadvantaCharacteristicgeous motif moti off 4d Combination of 3a Characteristic motif of advantageous motif Fully connected Combination of 3a 15/36 Characteristicmature network; motif of Fully connected UpgradeCombination ofCombination 4a andof 3a 4b of 3a15/36 mature network; Characteristic motif of mature 4d FullyFully connected connected Upgrade of 4a and 4b 15/36 15mature/36 network; 4d Upgrade ofUpgrade 4a and 4b of 4a and 4b advantageous motinetwork;f advantageous motif 4d Quadrangle, advantageous motif Highly specific motif; Quadrangle, Combination of 3b Highly 3/36 specific motif; Quadrangle,Ring Combination of 3b 3/36 Highly specific motif; disadvantageousHighly specific motif; motif 4e Quadrangle,Quadrangle,Ring RingCombination Combination of 3b of 3b 3/36 disadvantageousHighly 3/36 specific motif; motif 4e Ring Combination of 3b 3/36 disadvantageous motif disadvantageous motif 4e Ring disadvantageous motif Highly specific motif; HighlyHighly specific specific motif; motif; ChainChain Combination Combination of 3b of 3b 2/36 Highly 2/36 specific motif; Chain Combination Combination of 3b of 2/363b disadvantageous 2/36 motif disadvantageous motif 4f disadvantageous motifdisadvantageous motif 4f 4f 4. Classification of China’s Air Passenger Transport Companies Based on Motif Concentration 4. Classification of China’s Air Passenger Transport Companies Based on Motif Concentration 4. Classification4.Curve Classification ofof China’s China’s Air AirPassenger Passenger Transport Transport Companies Based Companies on Motif Concentration Based on Motif 4. ClassificationCurve of China’s Air Passenger Transport Companies Based on Motif Concentration ConcentrationWhen only Curve the frequency of the motifs appearing in the real network is considered, the motif Curve When only the frequency of the motifs appearing in the real network is considered, the motif concentrationWhen only characteristic the frequency curve of the (Figure.3) motifs appearin of differentg in the airline real network companies is considered, can be drawn the motif by concentration characteristic curve (Figure.3) of different airline companies can be drawn by Whenconcentrationconnecting only the characteristicfrequency the frequency of differentcurve of(Figure.3) motifs the motifsof of the different same appearing airline airline company. companies in the It can realcan be networkbeseen drawn that theby is considered, the motif connectingWhen only the frequency the frequency of different of motifs the ofmotifs the same appearin airline company.g in the It can real be seennetwork that the is considered, the motif connectingcurves of the the companies frequency with of different similar structuralmotifs of chthearacteristics same airline follow company. simila Itr trends.can be Therefore,seen that the concentrationcurves of the characteristic companies with similar curve structural (Figure ch3)aracteristics of di fferent follow airline similar trends. companies Therefore, can the be drawn by connecting concentrationcurvesairline companiesof the companiescharacteristic can be classifiedwith similar accordingcurve structural (Figure.3)to thecharacteristics motif concentration of followdifferent simila curves.r trends. airline Therefore, companies the can be drawn by the frequencyairline companies of di canff erentbe classified motifs according of the to the same motif airlineconcentration company. curves. It can be seen that the curves of the connectingairline companies the frequency can be classified of differentaccording to themotifs motif concentrationof the same curves. airline company. It can be seen that the companies with similar structural characteristics follow similar trends. Therefore, the airline companies curves of the companies with similar structural characteristics follow similar trends. Therefore, the can be classified according to the motif concentration curves. airline companies can be classified according to the motif concentration curves.

Figure 3. Motif concentration curves of airline companies. Figure 3. Motif concentration curves of airline companies. According to Figure 3, China’s airline companies can be roughly classified into three types. According to Figure 3, China’s airline companies can be roughly classified into three types. Sustainability 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/sustainability Sustainability 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/sustainability Sustainability 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/sustainability

Figure 3. Motif concentration curves of airline companies. Figure 3. Motif concentration curves of airline companies. According to Figure3, China’s airline companies can be roughly classified into three types. TypeAccording I. The motifto Figure concentration 3, China’s curvesairline ofcompanies type I airline can companiesbe roughly areclassified shown into in Figure three4 types.. Most of these concentration curves have two obvious peaks at motifs 3b and 4c, one high value at motif 4a, Sustainability 2019, 11, x; doi: FOR PEER REVIEW www.mdpi.com/journal/sustainability zero at motifs 3a, 4b, and 4d, and a small number of specific values at motifs 4e and 4f. A total of 10 airline companies belong to type I. Most of these companies are young, have a small number of route edges (smaller than 30 for the majority), a small average network degree (smaller than 2.5 for the majority), obvious regionalization service of routes, and 1 or 0 hub. The structural characteristics of networks of type I companies are mono-centric divergence, with dominating star-shaped motifs 3b and 4c. The network characteristics of these airline companies indicate a low level of development. Type II. The characteristics of the motif concentration curves, shown in Figure5, are that most companies have two peaks at motifs 3a and 4a, as well as zero at motifs 3b, 4b, and 4d, while some companies have characteristic motifs 4c. The three-node motifs of type II airline companies are motifs 3a, which have more stable topological structures compared with the V-shaped three-node motifs of type I companies. Half of these airline companies operate as low-cost airlines, including Guangxi Beibu Gulf Airlines, Spring Airlines, Ruili Airlines, Lucky Air, Joy Air, and Tibet Airlines. Compared with type I companies, these type II companies have a richer network structural hierarchy, a larger scale, and a higher average network degree (2.5–5). However, structural performance is inferior to the airline network of type III companies. The structural characteristic of type II companies may be considered to be at the transitional development stage. Sustainability 2019, 11, x FOR PEER REVIEW 2 of 18

Type I. The motif concentration curves of type I airline companies are shown in Figure 4. Most of these concentration curves have two obvious peaks at motifs 3b and 4c, one high value at motif 4a, zero at motifs 3a, 4b, and 4d, and a small number of specific values at motifs 4e and 4f. A total of 10 airline companies belong to type I. Most of these companies are young, have a small number of route edges (smaller than 30 for the majority), a small average network degree (smaller than 2.5 for the majority), obvious regionalization service of routes, and 1 or 0 hub. The structural characteristics of networks of type I companies are mono-centric divergence, with dominating star-shaped motifs 3b and 4c. The network characteristics of these airline companies indicate a low level of development.

Sustainability 2019, 11, x FOR PEER REVIEW 2 of 18

Type I. The motif concentration curves of type I airline companies are shown in Figure 4. Most of these concentration curves have two obvious peaks at motifs 3b and 4c, one high value at motif 4a, zero at motifs 3a, 4b, and 4d, and a small number of specific values at motifs 4e and 4f. A total of 10 airline companies belong to type I. Most of these companies are young, have a small number of route edges (smaller than 30 for the majority), a small average network degree (smaller than 2.5 for the majority), obvious regionalization service of routes, and 1 or 0 hub. The structural characteristics of Sustainabilitynetworks 2019of type, 11, 2484 I companies are mono-centric divergence, with dominating star-shaped motifs10 of 153b and 4c. The network characteristics of these airline companies indicate a low level of development. Figure 4. Motif concentration curves of type I airline companies.

Type II. The characteristics of the motif concentration curves, shown in Figure 5, are that most companies have two peaks at motifs 3a and 4a, as well as zero at motifs 3b, 4b, and 4d, while some companies have characteristic motifs 4c. The three-node motifs of type II airline companies are motifs 3a, which have more stable topological structures compared with the V-shaped three-node motifs of type I companies. Half of these airline companies operate as low-cost airlines, including Guangxi Beibu Gulf Airlines, Spring Airlines, Ruili Airlines, Lucky Air, Joy Air, and Tibet Airlines. Compared with type I companies, these type II companies have a richer network structural hierarchy, a larger scale, and a higher average network degree (2.5–5). However, structural performance is inferior to the airline network of type III companies. The struct ural characteristic of Figure 4. Motif concentration curves of type I airline companies. type II companies may beFigure considered 4. Motif to concentration be at the transitional curves of type development I airline companies. stage.

Type II. The characteristics of the motif concentration curves, shown in Figure 5, are that most companies have two peaks at motifs 3a and 4a, as well as zero at motifs 3b, 4b, and 4d, while some companies have characteristic motifs 4c. The three-node motifs of type II airline companies are motifs 3a, which have more stable topological structures compared with the V-shaped three-node motifs of type I companies. Half of these airline companies operate as low-cost airlines, including Guangxi Beibu Gulf Airlines, Spring Airlines, Ruili Airlines, Lucky Air, Joy Air, and Tibet Airlines. Compared with type I companies, these type II companies have a richer network structural hierarchy, a larger scale, and a higher average network degree (2.5–5). However, structural performance is inferior to the airline network of type III companies. The structural characteristic of type II companies may be considered to be at the transitional development stage. Figure 5. Motif concentration curves of type II airline companies. Figure5. Motif concentration curves of type II airline companies. TypeType III. III. The The motif motif concentration concentration curves curves of thes of thesee airline airline companies companies show show a low a low peak peak (Figure (Figure 6). 6). TheThe peaks peaks appear appear at motifs at motifs 3a 3aand and 4a; 4a;motifs motifs 4b 4band and 4d 4dstill still have have certain certain values; values; zero zero appear appear at 3b, at 3b,4c, 4c, 4e,4e, and and 4f. 4f.The The net-shaped net-shaped motifs motifs 4b 4band and 4d 4dare are characteristic characteristic motifs motifs of mature of mature networks, networks, with with more more complexcomplex and and reliable reliable topological structure.structure. Type Type II andII and III airlineIII airline companies companies have thehave same the three-node same three-nodemotifs, but motifs, their four-nodebut their four-node motif curves motif are dicurvesfferent, are which different, verifies which that theverifies network that classification the network can classificationbe refined bycan motif be refined curves ofby high-level motif curves networks of high-level [40]. The networks majority of[40]. type The III airlinemajority companies of type III have a large number of route edges (bigger than or far bigger than 120 for each), multi-hubs in the network, airlineSustainability companies 2019 have, 11, x FORa large PEER number REVIEW of route edges (bigger than or far bigger than 120 for each),3 of 18 multi-hubshigh Zipf in index the network, (bigger than high 0.9), Zipf high index network (bigger degree than (bigger 0.9), high than network 5), and adegree long history (bigger of than operation. 5), Thus,and thesea long companies history of are operation. most mature, Thus, including these companies China’s threeare most flagship mature, airlines—Air including China, China’s China three Southern,flagship andairlines China―Air Eastern. China, Their China service Southern, networks and and China markets Eastern. reach Their out to service the entire networks mainland and Figure5. Motif concentration curves of type II airline companies. ofmarkets China. reach out to the entire mainland of China. Type III. The motif concentration curves of these airline companies show a low peak (Figure 6). The peaks appear at motifs 3a and 4a; motifs 4b and 4d still have certain values; zero appear at 3b, 4c, 4e, and 4f. The net-shaped motifs 4b and 4d are characteristic motifs of mature networks, with more complex and reliable topological structure. Type II and III airline companies have the same three-node motifs, but their four-node motif curves are different, which verifies that the network classification can be refined by motif curves of high-level networks [40]. The majority of type III airline companies have a large number of route edges (bigger than or far bigger than 120 for each), multi-hubs in the network, high Zipf index (bigger than 0.9), high network degree (bigger than 5),

Figure 6. Motif concentration curves of type III airline companies. Figure 6. Motif concentration curves of type III airline companies. After combining the concentration curves of these three types of airline companies, it can be seen that inAfter the development combining the process concentration of the airline curves networks of thes frome three low types to high of and airline becoming companies, more mature,it can be seen that in the development process of the airline networks from low to high and becoming more mature, the three-node V-shaped motifs 3b disappear gradually and are replaced by the triangular motif 3a. As to the four-node motifs, the star-shaped motif 4c diminishes gradually and finally disappears as the net-shaped motifs 4b and 4d appear. This transforming relationship displays certain conservation rule (Similar findings were reported in Reference [40]), i.e., low-level airline networks tend to have motifs 3b and 4c, while mature airline networks tend to have motifs 3a, 4b, and 4d. When one kind of network motif disappears, another kind of motif with the same number of nodes would appear in its place. There is a correspondence between the trends of the motif concentration curves and the structural characteristics and the development stages of airline networks. Type I motif curves correspond to single-centric divergent airline companies at a low stage of development, type II motif curves correspond to transitional airline companies at the intermediate development stage, while type III motif curves correspond to multi-centric and hierarchical airline companies at the mature development stage. The motifs with a higher level of connection correspond to mature airline companies.

5. Optimization Mechanism of China’s Passenger Airline Network Based on Motif Analysis Airline networks at different development stages have different types of motifs. Thus from a developing or evolving perspective, transforming the types of disadvantageous motifs in and adjusting the topology of some airline’s networks by increasing the number of advantageous motifs can be considered. Network motifs can provide an optimized strategy for the development of airline companies, no matter the companies with a large or small scale. This could help optimize network structures and improve the sustainability of the airline networks and the airline industry. Airline companies at the low development stage of network structure tend to have motifs 3b and 4c. These two kinds of motifs are corresponding to “point-to-point” and “Single-hub-and-spoke” structural pattern of the airline network (Figure 7). Very few airline companies have motifs 4e and 4f, the structure of which is similar to the linear structure of the airline network. Study proves that the network that combines the point-to-point structure and the “Single-hub-and-spoke” is the most cost-effective [41], and this kind of network generally corresponds to airline networks with a small scale. When operation cost and variable cost are low enough, the “point-to-point” networks can provide more services [42]. “Linear” networks are actually derivatives of the “point-to-point” networks, and they are generally applicable to the small-scale air transport market, especially branch lines. While linear networks improve passenger load of airplanes, addition of passengers is conducted midway, leading to the lack of stability and difficulty in forming economies of scale [43]. These small-scale and low-cost companies could Sustainability 2019, 11, 2484 11 of 15 the three-node V-shaped motifs 3b disappear gradually and are replaced by the triangular motif 3a. As to the four-node motifs, the star-shaped motif 4c diminishes gradually and finally disappears as the net-shaped motifs 4b and 4d appear. This transforming relationship displays certain conservation rule (Similar findings were reported in Reference [40]), i.e., low-level airline networks tend to have motifs 3b and 4c, while mature airline networks tend to have motifs 3a, 4b, and 4d. When one kind of network motif disappears, another kind of motif with the same number of nodes would appear in its place. There is a correspondence between the trends of the motif concentration curves and the structural characteristics and the development stages of airline networks. Type I motif curves correspond to single-centric divergent airline companies at a low stage of development, type II motif curves correspond to transitional airline companies at the intermediate development stage, while type III motif curves correspond to multi-centric and hierarchical airline companies at the mature development stage. The motifs with a higher level of connection correspond to mature airline companies.

5. Optimization Mechanism of China’s Passenger Airline Network Based on Motif Analysis Airline networks at different development stages have different types of motifs. Thus from a developing or evolving perspective, transforming the types of disadvantageous motifs in and adjusting the topology of some airline’s networks by increasing the number of advantageous motifs can be considered. Network motifs can provide an optimized strategy for the development of airline companies, no matter the companies with a large or small scale. This could help optimize network structures and improve the sustainability of the airline networks and the airline industry. Airline companies at the low development stage of network structure tend to have motifs 3b and 4c. These two kinds of motifs are corresponding to “point-to-point” and “Single-hub-and-spoke” structural pattern of the airline network (Figure7). Very few airline companies have motifs 4e and 4f, the structure of which is similar to the linear structure of the airline network. Study proves that the network that combines the point-to-point structure and the “Single-hub-and-spoke” is the most cost-effective [41], and this kind of network generally corresponds to airline networks with a small scale. When operation cost and variable cost are low enough, the “point-to-point” networks can provide more services [42]. “Linear” networks are actually derivatives of the “point-to-point” networks, and they are generally applicable to the small-scale air transport market, especially branch lines. While linear networksSustainability improve 2019, 11 passenger, x FOR PEER load REVIEW of airplanes, addition of passengers is conducted midway, leading4 of 18 to the lack of stability and difficulty in forming economies of scale [43]. These small-scale and low-cost companiesincrease the could connectivity increase the between connectivity network between branch network lines and branch the number lines and of the motifs number 3a, 4a, of motifs4b, and 3a, 4d 4a,to 4b, enrich and the 4d tonetwork enrich thehierarchy. network hierarchy.

Figure 7. Comparison between motifs and structural patterns of airline networks. Figure 7. Comparison between motifs and structural patterns of airline networks. In contrast, airline companies with highly developed networks have characteristic motifs with a higherIn connectioncontrast, airline level companies of connections, with highly such as develo motifsped 3a networks and 4a in have type charac II companiesteristic motifs and motifs with a 4bhigher and 4d connection in type III level companies. of connections, In real-world such as operation, motifs 3a airline and 4a companies in type II companies generally adopt and motifs mixed 4b airlineand 4d networks. in type ForIII example,companies. airline In real-world companies op operateeration, direct airline flights companie in non-hubs generally cities based adopt on mixed the hub-and-spokeairline networks. network. For example, The multi-hub-and-spoke airline companies networkoperate direct is the dominantflights in non- patternhub of cities hub-and-spoke based on the hub-and-spoke network. The multi-hub-and-spoke network is the dominant pattern of hub-and-spoke airline networks, under which several hub airports are connected to form the main line, and the hub airports and non-hub airports are connected to form branch lines [43]. Motifs 3a and 4a are similar to non-hub connection based on the hub-and-spoke pattern, and motifs 4b and 4d can be viewed as the further connection of the branch line or the multi-hub-and-spoke pattern. The addition of motifs 3a, 4a, 4b, 4d, and other more sufficiently connected motifs can increase the maturity of the airline networks and improve the network hierarchy (e.g., a system containing national hubs, and regional hubs) complexity, and stability. Of course, all of these complex developmental strategies are subject to airlines’ assessment of their specific focuses on different regions and different sets of routes in the national air passenger market. The variations between airlines, which are caused by a number of variables such as geography, historical ties, airline merging, competition, etc., also influence what strategies are adopted by the airlines and where and what types of hubs are located in their networks.

6. Conclusions and Discussions

6.1. Conclusions In this paper, the motifs and anti-motifs of China’s passenger airline network were identified by using ENUMERATE SUBGRAPHS (G, k) (ESU) algorithm and the FANMOD tool. Additionally, 37 Chinese air passenger transport companies were classified according to the motif concentration curves, to explore the structure and evolution of China’s passenger airline network. Finally, some strategies of the passenger airline network ware proposed for airlines to develop and optimize their networks. Major research findings are as follows: (1) From observation and comparative analysis of the development characteristics and motifs structure of airline companies, we found that different motifs could reflect various structural and functional characteristics of the airline networks. And network motifs of Chinese passenger airlines can be grouped into common motifs, motifs with mature network characteristics, and motifs with immature network characteristics. (2) There is a conservation relationship between the airline network motifs with the same number of nodes. In other words, the disappearance of a kind of motif is accompanied by the appearance of another kind of motifs, such as conservation between motifs 3a and 3b, between 4b and 4d, and between 4c, 4e, and 4f. However, the contents of the motif will change significantly with the growth of airline networks. Thus, the development stages of different air companies can be Sustainability 2019, 11, 2484 12 of 15 airline networks, under which several hub airports are connected to form the main line, and the hub airports and non-hub airports are connected to form branch lines [43]. Motifs 3a and 4a are similar to non-hub connection based on the hub-and-spoke pattern, and motifs 4b and 4d can be viewed as the further connection of the branch line or the multi-hub-and-spoke pattern. The addition of motifs 3a, 4a, 4b, 4d, and other more sufficiently connected motifs can increase the maturity of the airline networks and improve the network hierarchy (e.g., a system containing national hubs, and regional hubs) complexity, and stability. Of course, all of these complex developmental strategies are subject to airlines’ assessment of their specific focuses on different regions and different sets of routes in the national air passenger market. The variations between airlines, which are caused by a number of variables such as geography, historical ties, airline merging, competition, etc., also influence what strategies are adopted by the airlines and where and what types of hubs are located in their networks.

6. Conclusions and Discussions

6.1. Conclusions In this paper, the motifs and anti-motifs of China’s passenger airline network were identified by using ENUMERATE SUBGRAPHS (G, k) (ESU) algorithm and the FANMOD tool. Additionally, 37 Chinese air passenger transport companies were classified according to the motif concentration curves, to explore the structure and evolution of China’s passenger airline network. Finally, some strategies of the passenger airline network ware proposed for airlines to develop and optimize their networks. Major research findings are as follows: (1) From observation and comparative analysis of the development characteristics and motifs structure of airline companies, we found that different motifs could reflect various structural and functional characteristics of the airline networks. And network motifs of Chinese passenger airlines can be grouped into common motifs, motifs with mature network characteristics, and motifs with immature network characteristics. (2) There is a conservation relationship between the airline network motifs with the same number of nodes. In other words, the disappearance of a kind of motif is accompanied by the appearance of another kind of motifs, such as conservation between motifs 3a and 3b, between 4b and 4d, and between 4c, 4e, and 4f. However, the contents of the motif will change significantly with the growth of airline networks. Thus, the development stages of different air companies can be determined based on their motif concentration curves. Accordingly, 37 China’s airline companies in 2015 were divided into 3 types (stages): Mono-centric divergence companies at the low-level development stage, transitional companies at the intermediate development stage, and multi-centric and hierarchical companies at the advanced development stage. (3) The overall structure of airline networks could be optimized by raising the structural competency of advantageous motifs and reforming those structure types of disadvantageous motifs.

6.2. Discussions Different from previous network analysis methods, motif analysis neither emphasizes the overall structural organization nor focuses on the role of nodes, but rather consider the microcosmic organization structure. It is not only a synthesis of but also a supplement to the previous perspectives. This study demonstrated that the network motif is applicable and effective in the analysis of airline networks. New insights, such as determining the network organization mode and airline network development stages are provided by this research, which can serve as a reference for the optimization of the airline network. With the development of airline networks, the concentration of network motifs may vary significantly. Because of the conservation between motifs with same number nodes, the development stage of the air passenger transport companies can be divided effectively and scientifically based on the types of motifs (motif concentration curves). Compared with only considering the number of routes Sustainability 2019, 11, 2484 13 of 15 or the scale of airline companies, this method is more effective in evaluating and differentiating the development stages of airline networks. The organization modes like “hub-and-spoke” or “point-to-point” have received widespread attention, which is also considered as competitive strategies. However, there is no pure organizational mode in practice. Airline companies often adopt a mixed strategy. This is especially true for those transitional airline networks. Motif analysis could be helpful in carrying out a quantitative analysis of the network organization modes. Motifs can be regarded as a microstructural element, and the macrostructure of the airline networks like “hub-and-spoke” mode is reflected by the content of its feature motifs. Adjusting the structural patterns of the networks based on motif analysis is more stereoscopic compared with node-based network pattern adjustment. Adjusting the content of different network motifs and increasing the network hierarchy and complexity can serve as a new way for optimizing the structure patterns of airline networks and promoting the sustainable development of the aviation industry. In short, motif analysis provides us with a new analytical tool in the understanding of the passenger airline network. In passenger airline network, some nodes (like hubs) play key roles due to their important geographical location, economic development level, and other reasons. Apparently, the motifs containing these nodes are supposed to be more prominent. But they are not given specific consideration in this paper, which will be explored in future research. In addition, this paper only discussed the topological characteristics of the networks. Now that the passenger airline network is kind of geo-embedded network, more attention will be paid to the geographical properties, such as ground transportation, economy, and population in future studies. Additionally, we might want to explore how to define and identify the geographical motifs.

Author Contributions: Conceptualization, Y.W.; methodology, Y.W.; data curation, Y.J.; writing—original draft preparation, Y.J.; writing—review and editing, W.S.; visualization, K.Y.; supervision, C.X.; funding acquisition, C.X. Funding: This research was funded by National Natural Science Foundation (NSF) of China, grant number: No. 41871162; No.41630749. Conflicts of Interest: The authors declare no conflict of interest.

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