Topological Characteristics and Vulnerability Analysis of ...

Research ArticleTopological Characteristics and Vulnerability Analysis ofRural Traffic Network

Xia Zhu Weidong Song and Lin Gao

Cartography and Geographic Information Engineering Liaoning Technical University Fuxin 12300 China

Correspondence should be addressed to Xia Zhu 1034149829qqcom

Received 12 December 2018 Revised 14 February 2019 Accepted 6 March 2019 Published 9 April 2019

Guest Editor Lei Zhang

Copyright copy 2019 Xia Zhu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Rural traffic network (RTN) as a complex network plays a significant role in the field of resisting natural disasters and emergenciesIn this paper we analyze the vulnerability of RTN via three traffic networkmodels (ie No-power TrafficNetworkModel (NTNM)DistanceWeightTrafficNetworkModel (DWTNM) and Road LevelWeightTrafficNetworkModel (RLWTNM)) Firstly based onthe complex network theory RTN is constructed by using road mapping method according to the topological features SecondlyRandom Attack (RA) and Deliberate Attack (DA) strategies are used to analyze network vulnerability in three rural traffic networkmodels By analyzing the attack tolerance of RTN under the condition of different attack patterns we find that the road level weighttraffic network has a good performance to represent the vulnerability of RTN

1 Introduction

Complex networks play an important role in real life Withthe development of Chinarsquos economy the nationwide trans-portation network has been continuously improved andmore emphasis has been placed on the construction andmanagement of township town and county transportationnetworks and the overall goal of the construction of the ldquoFourGoodRural Roadsrdquo has been comprehensively promotedTheimprovement of Rural Traffic Network (RTN) can improvethe connectivity of urban traffic network and promote theoverall economic development At present the nationalexpressway and the dry line network are basically fixedand the depth of the urban road network is expanded bycontinuously improving the RTN

For the study of the network characteristics of complexnetworks V Latora and M Marchiori describe cost asa measure of the cost (time money manpower materialresources etc) needed to build a network thereby analyz-ing the results of economic development in weighted andunweighted networks in the topology [1] Ake J Holmgrenmodels the network of the Northern European and WesternEuropean power transmission networks calculates the eigen-values of the network topology and compares its errors andattack tolerance (structural vulnerability) [2] P Luathep A

Sumalee and H W Ho propose a sensitivity analysis-basedapproach to improve computational efficiency and allowfor large-scale applications of road network vulnerabilityanalysis [3] J Wu Z Gao and othersrsquo discovery of scale-free characteristics are reported on the network constructedfrom the real urban transit system data in Beijing It is shownthat the connectivity distribution of the transit networkdecays as a power-law and the exponent 120582 is about equalto 224 from the simulation graph [4] A Q H Tran andA Namatame have shown that some topological propertiesof complex networks have a great impact on their stabilityThis observation study aims to understand the organizationprinciple of these networks and the interaction betweentopology and network dynamics [5] R M May S A Levinet al mainly evaluated the reliability and vulnerability of thenetwork The results showed that the failure of the networkcaused by errors interference of environmental conditionsor attacks may lead to global economic losses and social orderdestruction [6 7] O Woolley-Meza T Verma et al havestudied the high socioeconomic costs of large-scale disastersthat interfere with global social and technological infrastruc-tures (such asmobile and transport networks) and havemadeconsiderable efforts to understand how networks respond todamage [8 9] X Yang A Chen B Ning et alrsquos definition ofroutes and route diversity and a solution algorithm based on

HindawiJournal of SensorsVolume 2019 Article ID 6530469 9 pageshttpsdoiorg10115520196530469

2 Journal of Sensors

characteristics of metro networks are described to calculatethe route diversity index and also develop the route diversityindex for measuring passenger route choice and networkvulnerability [10] Q H Tran and Akira Namatame describethe application of complex network analysis in theWorldwideAviationNetwork (WAN) to clarify the hidden characteristicsof the network and provide insights on building stablenetworks and improving network recovery capabilities [11]M Liu et al developed a hierarchical model of road circuitcluster formed at various granularity levels of road networkand proposed a vulnerability index to measure a series ofevents in failure scenarios and the damage consequencescaused by these events [12] Based on the complex networktheory Li Chengbing et al analyzed the complex trafficnetwork structure of urban agglomeration constructed theroad-track complex traffic network model and analyzed thetopological characteristics and vulnerability of the complextraffic network [13] In summary the existing methods alwaysanalyze the urban traffic network by using multiple modelswithout considering the property of roads especially thecharacteristics of rural traffic networks

Generally speaking the contributions of this paper aretwofold Firstly according to the characteristic of the presentrural traffic network in China we build a proper rural ratingsystem including National Road (G) Provincial Road (S)County Road (X) Rural Road (Y) and Special Road (Z)Secondly three static networks (No-power Traffic NetworkModel (NTNM) Distance Weight Traffic Network Model(DWTNM) and Road Level Weight Traffic Network Model(RLWTNM)) are modeled in order to explore the vulner-ability of the RTN in Zhangwu in China By employingdifferent attack patterns we analyze the ability of threeconstructed networks in maintaining their connectivity afterbeing attacked

2 The Vulnerability Analysis of RTN

In this section we analyze the vulnerability of RTN inZhangwuThe construction processes of three static networksare introduced in Section 21 Section 22 gives the topologicalfeature analysis of the three networks Section 23 implementsthe vulnerability analysis by three networks under the condi-tion of two kinds of attacks

21 Rural Traffic Network Construction The constructionmethods of traffic network mainly include Road MappingMethod (RMM) and Site Mapping Method (SMM) [14ndash16]The RMM is road intersection to the node of the trafficnetwork according to the actual geographical location andthe section connecting the intersection to the edge of thetraffic network the SMM is road intersection to the edgeof the traffic network according to the actual geographicallocation and the section connecting the intersection to thenode of the traffic network For the RTN the SMM cannotbe used to connect the whole network well because sometownship roads or village roads have no stations so that SMMcannot express the connectivity of the traffic network RMMcan reflect the characteristics of the RTN more intuitively

All the intersections of the traffic network are the nodes(N) and the lines connecting the nodes are the edges (M)constructing a topology model of the RTN

Three traffic network models are established based on theactual situation of the existing rural traffic network Thereare few important infrastructure and economically developedareas in rural transportation network which is generallythe scope of Peoplersquos Daily travel activities and the overalltransportation network has few special properties Thereforethe NTNM is established to analyze the characteristics ofthe overall rural transportation network The most obviousmeasurement index of rural traffic network is distance factorso a DWTNM is established to further analyze the character-istics of the overall rural traffic network Considering the factthat the current rural traffic network includes National RoadProvincial Road County Road and Rural Road a RLWTNMis established to analyze the current situation of the ruraltraffic network in a more specific way which is more in linewith the actual application of the rural traffic network andthe analysis results aremore accurate (the weight of road levelis set according to Chinarsquos highway engineering technicalstandards (JTG B01-2014))

(1) No-Power Traffic Network Model (NTNM) All roadnetworks exist in the study area there is noweight on the roadside roads are restricted without direction constructing theNTNM

(2) Distance Weight Traffic Network Model (DWTNM) Basedon NTNM considering the influence of the spatial distanceon the traffic the longer walking time of the road affects thetraffic efficiency The traffic network is weighted by the actualspatial distance the road traffic has no direction restrictionconstructing the DWTNM

(3) Road LevelWeight TrafficNetworkModel (RLWTNM)Thetraffic road network is classified to five categories according tothe road administrative level which are divided into NationalRoad (G) Provincial Road (S) County Road (X) Rural Road(Y) and Special Road (Z) Considering the RTN integritythe Special Roads are exclusively used for factories minesforests farms oil fields tourist areas military sites etcSpecial Roads are built maintained and managed by specialunits that may cover National Road Provincial Road CountyRoad and Rural Road Therefore instead of using SpecialRoads in this study Village Roads (C) are used to improvethe overall traffic network According to the traffic volumetask and nature of Chinarsquos highway engineering technicalstandards (JTG B01-2014) different levels of traffic networkhave different annual average daily traffic volume (ADT)National Road is a highway connecting important politicaleconomic and cultural centers It can generally adapt toADT = 15000-55000 vehicles Provincial Road is the trunkhighway connecting the political and economic center orlarge industrial and mining areas It can generally adapt toADT = 3000-7500 vehicles County Road is a branch roadlinking county or above cities which can adapt to ADT =1000-4000 vehicles Rural Road and Village Road are branchroads connecting counties or towns and townships which

Journal of Sensors 3

Table 1 Road level weight value

Road level National Road(G)

ProvincialRoad (S)

County Road(X)

Rural Road(Y)

Village Road(C)

Weight 04 03 02 005 005

can adapt to ADT less than 1500 vehicles So the weights ofdifferent levels of traffic network are set as shown in Table 1(which meets the criterion of weights sum of 1)

Assume that RTN construction is defined as 119866 = (119881 119864)where 119881 = V1 V2 V3 sdot sdot sdot V119899is a set of all road nodes 119864 =

(V119894 V119895)|V119894 V119895 isin 119881 and 119894 = 119895 represent the traffic networkedge The weighting matrix119882 is defined with the number ofroad nodes as the size of 119873 times 119873 119881119894 and 119881119895 are any nodes inthe road network respectively the adjacency matrix of graph119866 = (119881 119864) is 119860 = (119886119894119895)119899times119899 and it is defined as follows

119886119894119895 = 119882119894119895 119881119894 is directly connected to V119895 (Use weight to indicate liquidity)0 Not directly connected

(1)

22 Topological Characteristics Analysis Currently it is dif-ficult to evaluate the vulnerability with a universal metricA proper way to quantify the vulnerability of a networkshould be designed based on the demand of a real-worldsystemTherefore considering the commuting efficiency andthe underlying network structure we use three evaluationmetrics to estimate the vulnerability of RTN The threemetrics include average distribution clustering coefficientand average path length The definitions of the three metricsare given as follows

(1) Average Distribution At present many complex networkshave a heterogeneous topology phenomenon that is somenetwork nodes have a very large number of edges connectedbut most network nodes only connect several edges Thedegree 119896119894 represents the number of connection edges of thenetwork node 119894 and the network node degree is characterizedby a distribution function 119875(119896) which gives a probability thatthe randomly selected network node has 119896 edges Thus fora large value 119896 the degree distribution is as follows 119875(119896) sim119896minus120574(119894119891 119896 997888rarr infin119875(119896)119896minus120574 997888rarr 1) Therefore the averagedistribution of RTN graphics is

⟨119896⟩ = 2119872119873 (2)

where119873 is the number of road nodes and119872 is the numberof road links between road nodes

(2) Clustering Coefficient Many complex networks now showa tendency to cluster In social networks this represents acircle of friends that each member knows about each otherThe meaning of the clustering coefficient is to express thelocal attribute of the triangle ldquodensityrdquo in the captured graphThe two vertices connected to the third vertex are alsodirectly connected to each other The degree 119896119894 of node 119894in the network simultaneously expresses 119896119894 neighbor nodesThe maximum number of edges between neighbor nodes is( 1198961198942) = 119896119894(119896119894 minus 1)2 The clustering coefficient 119862119894 of the

network node 119894 the ratio of the number of edges119872119894 actuallyexisting between the 119896119894 neighbor nodes to the maximum

number of edges is 119862119894 = 2119872119894119896119894(119896119894 minus 1) The clusteringcoefficient of the entire network is

119862 = ( 1119873sum119894

119862119894) (3)

119862 = 0 indicates that all nodes are isolated nodes 119862 = 1indicates that the network is globally coupled that is any twonodes are connected

(3) Average Path Length The average path length representedas ℓ refers to the average distance between a pair of nodes inthe giant component It is defined as follows

ℓ = ⟨ℓ119894119895⟩ = [[1119873 (119873 minus 1) sum119894 =119895isin119881ℓ119894119895]]

(4)

where ℓ119894119895 is the distance between nodes 119894 and 119895 in a networkIn particular ℓ119894119895 is equal to finite value only if the 119894 and 119895 bothexist in the giant component A short average path lengthmeans a high effective connectivity of RTN

23 e Vulnerability Analysis of RTN At present domesticand foreign research scholars have no clear concept ofvulnerability and some scholars will combine the words ofvulnerability stability and risk Combined with the currentresearch conclusions the road network suffers from the unex-pected external events resulting in the loss of the use of someroad nodes and road sections resulting in the redistributionof load within the road network The nature of the ability toresume normal traffic is vulnerability Therefore each roadnode and road section in the transportation network havedifferent traffic levels and the vulnerability analysis of thetraffic network needs to consider the overall network (globalanalysis) The traffic level at the time of no accidents is takenas the initial value and the traffic volume is redistributed atthe fastest speed after the accident The traffic level after thetraffic returns to normal operation is used as a vulnerabilityanalysis value compared with the initial value to analyze theseverity of the vulnerability


(a) (b)

Figure 1 Traffic network structure diagram of the experimental area ((a) traffic network containing nodes (b) traffic network road level)

Table 2 Detailed parameters of the traffic network model

TrafficNetworkModel

Nodesnumber (N)

Linksnumber (M)

Averagedegree (K)

Clusteringcoefficient

(C)

Average pathlength (L)

Networkefficiency (E)

NTNM 1840 2054 2177 0031 25836 0039DWTNM 1840 2054 2177 0031 41181 0024RLWTNM 1840 2054 2177 0031 15203 0066

Based on the research in this paper 119873 is the num-ber of road nodes in the overall road network The roadlength between road nodes 119894 and 119895 is 119889119894119895 and ℓ119894119895 is theshortest path length from node 119894 to 119895 That is ℓ119894119895 =min119881(119894119895)119889119894119895(119889119894997888rarr119895 = 119889119895997888rarr119894 ℓ119894997888rarr119895 = ℓ119895997888rarr119894 = ℓ119894119895) therefore theroad network efficiency between road nodes 119894 and 119895 is definedas

120576119894119895 = 1ℓ119894119895 (5)

Under the overall analysis of the traffic network consider theefficiency of all networks

119864 = 1119873 (119873 minus 1)sum119894 =119895120576119894119895 =1119873 (119873 minus 1)sum119894 =119895

1ℓ119894119895 (6)

Considering the occurrence of an unexpected event 1198640is the initial efficiency of the initial network traffic state119864119894 is the efficiency of the traffic state after the accidentand 119863 is the difference between the efficiencies of thetraffic network before and after that is the traffic networkvulnerability

119863 = 119864119894 minus 11986401198640 times 100 (7)

The result is a dynamic response to the failure of theentire network system and how the location of the faultpropagates as well as the consequences for the entire trafficnetwork

3 Experimental Data Analysis

31 Experimental Data and Statistical CharacteristicsZhangwu County which is affiliated to Fuxin City LiaoningProvince is located in the northwestern part of LiaoningProvince with a total area of 3641 square kilometers Amongthem three National Roads pass through the county theactual mileage is 250 kilometers there are two ProvincialRoads the actual mileage is 169 kilometers and the totalmileage of the countyrsquos transportation network is 2875kilometers as shown in Figure 1

32 Statistical Analysis of Traffic Network We use the afore-mentioned method in Zhangwu rural road network to buildup a topological model By Matlab and Pajek software thebasic topological characteristics of three models are obtainedas shown in Table 2

In Table 2 the number of network edges is 2054 and thenumber of nodes is 1840 The average value of the vertexdegree is 21766 which shows that the intersections aremostlyconnected with 3 or 4 The average path length of RLWTNMis 15203 It shows that the rural roads account for a largeproportion of Rural Roads mostly broken roads and theroad network connection relationship is relatively simplethe distribution of traffic network degree and the probabilitydistribution of the node degree are shown in Figures 2 and3 respectively As shown in Table 2 the clustering coefficientof the RTN is C=00313 Generally speaking there are fewerconnecting lines between road nodes in the RTN thus theoverall accessibility is poor and the degree of grouping is not


0 200 400 600 800 1000 1200 1400 1600 1800 2000N

0

05

1

15

2

25

3

35

4

45

5

K

Degree Distribution

Figure 2 Distribution of traffic network degree

0 1 2 3 4 5K

0

005

01

015

02

025

03

035

04

045

05

P(K)

Degree Distribution

Figure 3 Probability distribution of traffic network degree

high by comparing the average shortest path lengths of thethree traffic network models the average shortest path lengthof the DWTNM has the best performance indicating thatthe RTN connectivity is relatively poor The average shortestpath length of the RLWTNM is the smallest indicating thatthe RTN connectivity is relatively good the RLWTNM hasthe highest efficiency value of the whole network Comparingwith the other two traffic network models different roadlevels in the RTN have different traffic carrying capacity andusage efficiency

33 Analysis of Two Attack Strategies for RTN In this paperwe use two attack strategies Random Attacks (RA) andDeliberate Attacks (DA) Based on the RTN structure thereis no protection measure and the attack cost and capacitylimitation are not considered When an attack is completedthe attacked road node can be invalidated and the connectedroad link is disconnected the road node is deleted and the

connected road link is deleted RA randomly selects roadnodes for attack each time until all road nodes have finishedattacking DA selects attack strategies which are based onnode-first attack strategies with high efficiency until the roadnodes are attacked

(1) Random Attacks (RA) The road vulnerability computedby NTNM is shown in Figure 4(a) and the highest vulnera-bility value is generated when the 50th road node is randomlyattacked the vulnerability of the DWTNM is shown inFigure 4(b) The vulnerability value of the entire RTN varieswith the increase of the distance weight Compared withthe NTNM the vulnerability value of the overall RTN hasincreased the vulnerability of the RLWTNM is shown inFigure 4(c) The traffic network with road level weightsconstraint improves the efficiency and carrying capacity ofhigh-level road networks Compared with the NTNM thetrend of vulnerability changes is basically the same but


Random Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Random Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Random Attack

level

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(c)

Random Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)

Figure 4 Random Attack traffic network ((a) NTNM (b) DWTNM (c) RLWTNM (d) three traffic network model comparison graphs)

the road node vulnerability of high-level road networks isenhanced As shown in Figure 4(d) the three traffic networkmodels show that the vulnerability value calculated by theDWTNMchanges greatly and the value of the RLWTNMhasa large contrast

(2) Deliberate Attacks (DA) Figures 5(a)ndash5(c) show thevulnerability calculated from the RTN The three trafficnetwork models have the same trend and the attacks areperformed in descending order of the link efficiency Thehigher the efficiency the greater the vulnerability of the roadlink Traffic links with high vulnerability and high risk needsto be maintained

In Figure 5(d) the slope of the vulnerability curve ofthe RLWTNM is higher than the other two traffic networkmodels In line with the actual traffic conditions whenthe important road sections fail it will quickly lead to theoverall RTN The vulnerability of different levels in actualtraffic networks is different The utilization rate and carryingcapacity of high-level road networks are relatively high andthey also have high vulnerability

34 Vulnerability Analysis of RTN With the topologicalstatistics the vulnerability of traffic networks can be learnedfrom the decline of their performance compared to theinitial state Different network characteristics can be used


Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)

Figure 5 Deliberate Attack traffic network ((a) NTNM (b) DWTNM (c) RLWTNM (d) three traffic network model comparison graphs)

for describing the performance of network In this sectionwe analyze the vulnerability of RTN via those three modelsas described in Figure 6 The results of the vulnerabilityanalysis of the traffic network in the experimental areashow the following In the traffic network constructed bythe NTNM the most vulnerable link of the experimentalarea is shown in Figure 6(a) The constructed traffic networkis based on the theoretical model of European space Thehighly vulnerable road link is generated by the high effi-ciency of the theoretical road link so the location of thevulnerable link is deviated from the actual traffic situationIn the traffic network constructed by the DWTNM themost vulnerable link of the experimental area is shown in

Figure 6(b) The weight assignment of the RTN is basedon the length of the actual distance so the road link withhigh vulnerability is caused by the actual distance lengthIn the traffic network constructed by the RLWTNM themost vulnerable link of the experimental area is shownin Figure 6(c) The constructed traffic network divides theweight value according to the road level and the high-levelroad link has a higher utilization rate and a higher relativeweight assignment Therefore the highly vulnerable roadlinks are distributed on the National Road G101 JingshenLine and the utilization rate is high and the bearing capacityis strong which is in line with the actual traffic condi-tions


noneTownship governmentAdministrative villageNatural villagenone networkNational RoadProvincial RoadCountry RoadTownship RoadVillage RoadCountryTownship

(a)

distanceTownship governmentAdministrative villageNatural villagedistance networkNational RoadProvincial RoadCountry RoadTownship RoadVillage RoadCountryTownship

(b)

levelTownship governmentAdministrative villageNatural villagelevel networkNational RoadProvincial RoadCountry RoadTownship RoadVillage RoadCountryTownship

(c)

Figure 6 The severe traffic link of the RTN in the experimental area ((a) NTNM (b) DWTNM (c) RLWTNM)

4 Conclusion

Based on the existing complex network theory this paperconstructs the No-power Traffic Network Model (NTNM)the Distance Weight Traffic Network Model (DWTNM) andthe Road Level Weight Traffic Network Model (RLWTNM)By analyzing the distribution results of the Rural TrafficNetwork (RTN) the traffic network of Zhangwu Countyshowed no scale phenomenon The three types of trafficnetwork models were attacked by two kinds of manners inorder to analyze the vulnerability The results show that the

average degree of the three traffic network models is 21766and the overall trend of single link connection is relativelysimple The clustering coefficient is 00313 indicating thepoor accessibility of the transportation network in ZhangwuThe average path length of the Road Level Weight TrafficNetwork Model is 152032 and the median value of thethree models is the minimum It is most suitable to analyzethe actual traffic network of Zhangwu county (the actualtraffic network of Zhangwu county is not as bad as theother two models) The road network efficiency of theRoad Level Weight Traffic Network Model is 00658 and


the median value of the three models is the largest whichbetter reflects the actual application efficiency of the trafficnetwork in Zhangwu county The Road Level Weight TrafficNetwork Model of Zhangwu county reflects the actual trafficsituation more and the road links with high vulnerabilitywere analyzed on the high-level traffic network (NationalRoad G101 Jingshen Line) It is necessary to take protectivemeasures for high-vulnerability road links which preventednatural disasters or unexpected events from affecting trafficIn the future we would consider more factors that affect theRural Traffic Network and optimize the expansion directionof the Rural Traffic Network

Data Availability

The Zhangwu County Traffic Network data used to supportthe findings of this study have not been made availablebecause the original road network data is the traffic situationof the real county location in China and it is real and effectivereality data It can reflect the real data of Chinarsquos geographicallocation Therefore it cannot be made public However theresults of the later results can be referenced and applied

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This paper is supported by the Liaoning Province Doc-toral Liaoning Provincial Natural Science Fund ProjectKey Project (20170520141) and Liaoning Provincial PublicWelfare Research Fund Project (20170003)

References

[1] V Latora and M Marchiori ldquoEconomic small-world behaviorin weighted networksrdquoe European Physical Journal B vol 32no 2 pp 249ndash263 2003

[2] A J Holmgren ldquoUsing graph models to analyze the vulnerabil-ity of electric power networksrdquo Risk Analysis vol 26 no 4 pp955ndash969 2006

[3] P Luathep A Sumalee HW Ho and F Kurauchi ldquoLarge-scaleroad network vulnerability analysis A sensitivity analysis basedapproachrdquo Transportation vol 38 no 5 pp 799ndash817 2011

[4] JWu Z Gao H Sun andH Huang ldquoUrban transit system as ascale-free networkrdquoModern Physics Letters B vol 18 no 19-20pp 1043ndash1049 2004

[5] A Q H Tran and A Namatame ldquoDesign robust networksagainst overload-based cascading failuresrdquo International Jour-nal of Computer Science amp Artificial Intelligence vol 4 no 2 pp35ndash44 2014

[6] R M May S A Levin and G Sugihara ldquoComplex systemsecology for bankersrdquo Nature vol 451 no 7181 pp 893ndash8952008

[7] S V Buldyrev R Parshani G Paul H E Stanley and S HavlinldquoCatastrophic cascade of failures in interdependent networksrdquoNature vol 464 no 7291 pp 1025ndash1028 2010

[8] O Woolley-Meza D Grady C Thiemann J P Bagrow andD Brockmann ldquoEyjafjallajokull and 911 the impact of large-scale disasters on worldwide mobilityrdquo PLoS ONE vol 8 no 8Article ID e69829 2013

[9] T Verma N A M Araujo and H J Herrmann ldquoRevealing thestructure of the world airline networkrdquo Scientific Reports vol 4p 5638 2014

[10] X Yang A Chen B Ning et al ldquoMeasuring route diversityfor urban rail transit networks a case study of the beijingmetro networkrdquo IEEETransactions on Intelligent TransportationSystems vol 18 no 2 pp 259ndash268 2017

[11] Q H Tran and A Namatame ldquoWorldwide aviation networkvulnerability analysis a complex network approachrdquo Evolution-ary and Institutional Economics Review vol 12 no 2 pp 349ndash373 2015

[12] M Liu J Agarwal and D Blockley ldquoVulnerability of roadnetworksrdquoCivil Engineering and Environmental Systems vol 33no 2 pp 147ndash175 2016

[13] B C Li L Wei X F Li and Y Z Lu ldquoStudy on vulnerability ofurban group composite transportation network based on attackstrategyrdquo Journal ofHighway andTransportation no 03 pp 101ndash109 2017 (Chinese)

[14] MGWangAStudy on Property and Evolution of RoadNetworkof Urban Agglomeration Central South University 2012

[15] H M Zeng X M Li and D Liu ldquoThe properties of trafficnetworks in urban clustersrdquo Systems Engineering vol 27 no 3pp 10ndash15 2009 (Chinese)

[16] MZhaoResearch of Characteristics of UrbanTransport NetworkBased on Complex Networkeory Chongqing Normal Univer-sity 2012

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characteristics of metro networks are described to calculatethe route diversity index and also develop the route diversityindex for measuring passenger route choice and networkvulnerability [10] Q H Tran and Akira Namatame describethe application of complex network analysis in theWorldwideAviationNetwork (WAN) to clarify the hidden characteristicsof the network and provide insights on building stablenetworks and improving network recovery capabilities [11]M Liu et al developed a hierarchical model of road circuitcluster formed at various granularity levels of road networkand proposed a vulnerability index to measure a series ofevents in failure scenarios and the damage consequencescaused by these events [12] Based on the complex networktheory Li Chengbing et al analyzed the complex trafficnetwork structure of urban agglomeration constructed theroad-track complex traffic network model and analyzed thetopological characteristics and vulnerability of the complextraffic network [13] In summary the existing methods alwaysanalyze the urban traffic network by using multiple modelswithout considering the property of roads especially thecharacteristics of rural traffic networks

Generally speaking the contributions of this paper aretwofold Firstly according to the characteristic of the presentrural traffic network in China we build a proper rural ratingsystem including National Road (G) Provincial Road (S)County Road (X) Rural Road (Y) and Special Road (Z)Secondly three static networks (No-power Traffic NetworkModel (NTNM) Distance Weight Traffic Network Model(DWTNM) and Road Level Weight Traffic Network Model(RLWTNM)) are modeled in order to explore the vulner-ability of the RTN in Zhangwu in China By employingdifferent attack patterns we analyze the ability of threeconstructed networks in maintaining their connectivity afterbeing attacked

2 The Vulnerability Analysis of RTN

In this section we analyze the vulnerability of RTN inZhangwuThe construction processes of three static networksare introduced in Section 21 Section 22 gives the topologicalfeature analysis of the three networks Section 23 implementsthe vulnerability analysis by three networks under the condi-tion of two kinds of attacks

21 Rural Traffic Network Construction The constructionmethods of traffic network mainly include Road MappingMethod (RMM) and Site Mapping Method (SMM) [14ndash16]The RMM is road intersection to the node of the trafficnetwork according to the actual geographical location andthe section connecting the intersection to the edge of thetraffic network the SMM is road intersection to the edgeof the traffic network according to the actual geographicallocation and the section connecting the intersection to thenode of the traffic network For the RTN the SMM cannotbe used to connect the whole network well because sometownship roads or village roads have no stations so that SMMcannot express the connectivity of the traffic network RMMcan reflect the characteristics of the RTN more intuitively

All the intersections of the traffic network are the nodes(N) and the lines connecting the nodes are the edges (M)constructing a topology model of the RTN

Three traffic network models are established based on theactual situation of the existing rural traffic network Thereare few important infrastructure and economically developedareas in rural transportation network which is generallythe scope of Peoplersquos Daily travel activities and the overalltransportation network has few special properties Thereforethe NTNM is established to analyze the characteristics ofthe overall rural transportation network The most obviousmeasurement index of rural traffic network is distance factorso a DWTNM is established to further analyze the character-istics of the overall rural traffic network Considering the factthat the current rural traffic network includes National RoadProvincial Road County Road and Rural Road a RLWTNMis established to analyze the current situation of the ruraltraffic network in a more specific way which is more in linewith the actual application of the rural traffic network andthe analysis results aremore accurate (the weight of road levelis set according to Chinarsquos highway engineering technicalstandards (JTG B01-2014))

(1) No-Power Traffic Network Model (NTNM) All roadnetworks exist in the study area there is noweight on the roadside roads are restricted without direction constructing theNTNM

(2) Distance Weight Traffic Network Model (DWTNM) Basedon NTNM considering the influence of the spatial distanceon the traffic the longer walking time of the road affects thetraffic efficiency The traffic network is weighted by the actualspatial distance the road traffic has no direction restrictionconstructing the DWTNM

(3) Road LevelWeight TrafficNetworkModel (RLWTNM)Thetraffic road network is classified to five categories according tothe road administrative level which are divided into NationalRoad (G) Provincial Road (S) County Road (X) Rural Road(Y) and Special Road (Z) Considering the RTN integritythe Special Roads are exclusively used for factories minesforests farms oil fields tourist areas military sites etcSpecial Roads are built maintained and managed by specialunits that may cover National Road Provincial Road CountyRoad and Rural Road Therefore instead of using SpecialRoads in this study Village Roads (C) are used to improvethe overall traffic network According to the traffic volumetask and nature of Chinarsquos highway engineering technicalstandards (JTG B01-2014) different levels of traffic networkhave different annual average daily traffic volume (ADT)National Road is a highway connecting important politicaleconomic and cultural centers It can generally adapt toADT = 15000-55000 vehicles Provincial Road is the trunkhighway connecting the political and economic center orlarge industrial and mining areas It can generally adapt toADT = 3000-7500 vehicles County Road is a branch roadlinking county or above cities which can adapt to ADT =1000-4000 vehicles Rural Road and Village Road are branchroads connecting counties or towns and townships which




ProvincialRoad (S)

County Road(X)

Rural Road(Y)

Village Road(C)

Weight 04 03 02 005 005





(1)



⟨119896⟩ = 2119872119873 (2)





119862 = ( 1119873sum119894

119862119894) (3)




(4)




(a) (b)



TrafficNetworkModel

Nodesnumber (N)

Linksnumber (M)

Averagedegree (K)


(C)





120576119894119895 = 1ℓ119894119895 (5)



1ℓ119894119895 (6)


119863 = 119864119894 minus 11986401198640 times 100 (7)







0 200 400 600 800 1000 1200 1400 1600 1800 2000N

0

05

1

15

2

25

3

35

4

45

5

K

Degree Distribution


0 1 2 3 4 5K

0

005

01

015

02

025

03

035

04

045

05

P(K)

Degree Distribution







Random Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Random Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Random Attack

level

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(c)

Random Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)







Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)






(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





ProvincialRoad (S)

County Road(X)

Rural Road(Y)

Village Road(C)

Weight 04 03 02 005 005





(1)



⟨119896⟩ = 2119872119873 (2)





119862 = ( 1119873sum119894

119862119894) (3)




(4)




(a) (b)



TrafficNetworkModel

Nodesnumber (N)

Linksnumber (M)

Averagedegree (K)


(C)





120576119894119895 = 1ℓ119894119895 (5)



1ℓ119894119895 (6)


119863 = 119864119894 minus 11986401198640 times 100 (7)







0 200 400 600 800 1000 1200 1400 1600 1800 2000N

0

05

1

15

2

25

3

35

4

45

5

K

Degree Distribution


0 1 2 3 4 5K

0

005

01

015

02

025

03

035

04

045

05

P(K)

Degree Distribution







Random Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Random Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Random Attack

level

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(c)

Random Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)







Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)






(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



(a) (b)



TrafficNetworkModel

Nodesnumber (N)

Linksnumber (M)

Averagedegree (K)


(C)





120576119894119895 = 1ℓ119894119895 (5)



1ℓ119894119895 (6)


119863 = 119864119894 minus 11986401198640 times 100 (7)







0 200 400 600 800 1000 1200 1400 1600 1800 2000N

0

05

1

15

2

25

3

35

4

45

5

K

Degree Distribution


0 1 2 3 4 5K

0

005

01

015

02

025

03

035

04

045

05

P(K)

Degree Distribution







Random Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Random Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Random Attack

level

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(c)

Random Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)







Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)






(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0 200 400 600 800 1000 1200 1400 1600 1800 2000N

0

05

1

15

2

25

3

35

4

45

5

K

Degree Distribution


0 1 2 3 4 5K

0

005

01

015

02

025

03

035

04

045

05

P(K)

Degree Distribution







Random Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Random Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Random Attack

level

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(c)

Random Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)







Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)






(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Random Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Random Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Random Attack

level

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(c)

Random Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)







Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)






(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Deliberate Attack

none

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

12

14

D

(a)

Deliberate Attack

distance

200 400 600 800 1000 1200 1400 1600 1800 20000N

minus2

0

2

4

6

8

10

D

(b)

Deliberate Attack

level

minus2

0

2

4

6

8

10

12

14

D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(c)

Deliberate Attack

nonedistancelevel

minus2

0

2

4

6

8

10

12

14D

200 400 600 800 1000 1200 1400 1600 1800 20000N

(d)






(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




(a)


(b)


(c)


4 Conclusion





Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References



















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Topological Characteristics and Vulnerability Analysis of ...

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