The topology of urban road networks and its role to urban mobility

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Transportation Research Procedia 24C (2017) 482–490 www.elsevier.com/locate/procedia

3rd Conference on Sustainable Urban Mobility, 3rd CSUM 2016, 26 – 27 May 2016, Volos, Greece

The topology of urban road networks and its role to urban mobility Dimitrios Tsiotasaa* , Serafeim Polyzosaa a aDepartment

Department of of Planning Planning and and Regional Regional Development, Development, University University of of Thessaly, Thessaly, Pedion Areos, Areos, Volos, Volos, 38 38 334, 334, Greece Greece Pedion

Abstract Abstract This This article article studies studies how how the the topology topology of of Urban Urban Road Road Networks Networks (URNs) (URNs) is is linked linked with with socioeconomic socioeconomic aspects aspects of of their their urban urban systems, systems, aiming both the the aiming in in revealing revealing patterns patterns that that are are related related to to urban urban mobility. mobility. The The rationale rationale of of the the study study is is based based on on the the consideration consideration that that both structure structure of of urban urban networks networks and and the the conduct conduct of of urban urban mobility mobility are are controlled controlled by by complex complex mechanisms, mechanisms, where where aa primary primary driving driving factor factor affecting, affecting, either either directly directly or or indirectly, indirectly, their their planning, planning, evolution evolution and and development development is is the the existence existence of of spatial spatial constraints. constraints. The The analysis examines how some fundamental network measures of global URNs studied in literature are related to analysis examines how some fundamental network measures of global URNs studied in literature are related to socioeconomic socioeconomic indices indices and and focuses focuses on on the the case case study study of of four four URNs URNs of of the the region region of of Thessaly, Thessaly, in in Greece, Greece, where where their their socioeconomic socioeconomic framework framework is is familiar. familiar. Overall, Overall, the the analysis analysis provides provides interesting interesting insights insights about about the the effects effects of of spatial spatial constraints constraints on on the the network network topology, topology, the the magnitude of of the the examined examined URNs URNs comparatively comparatively to to global global cases, cases, the the growth growth patterns patterns between between connectivity connectivity and and distance distance and and about about magnitude how the network topology is related to urban mobility, population and market information. how the network topology is related to urban mobility, population and market information. © © 2016 2016 The The Authors. Authors. Published Published by by Elsevier Elsevier B.V. B.V. © 2017 The Authors. Published by Elsevier B.V. committee of the 3rd CSUM 2016. Peer-review under responsibility of the organizing Peer-review under responsibility of the organizing committee of of the the 3rd 3rd CSUM CSUM 2016. 2016. Peer-review under responsibility of the organizing committee Keywords: Keywords: spatial spatial networks; networks; transportation transportation networks; networks; lattice lattice networks; networks; city city organization organization index; index; urban urban planning planning and and development development ** Corresponding Corresponding author. author. Tel.: Tel.: +30 +30 24210 24210 74446; 74446; fax: fax: +302421074493. +302421074493. E-mail E-mail address: address: [email protected] [email protected]

1. Introduction The evolution of cities through time has caused an increase in their structural and functional complexity, setting the acts of manipulating and planning of such systems into a real challenge, both for the everyday policy making and for the academic research (Strano et al., 2012; Polyzos, 2015). Within the structured framework of the evolving cities, urban mobility becomes more and more a complex procedure. The purpose of the everyday movements, the choice of the transport mode, the time of executing the transportation and its cost are some aspects illustrating this complexity (Chowell et al., 2003; Van Ommeren and Fosgerau, 2009; Barthelemy, 2011; Polyzos et al., 2013, 2014). However, the common factor that affects, directly or indirectly, all the aspects of urban mobility and that it sets the rules for the development of urban systems and for the consequent conduct of urban communication is the cost of overcoming the spatial constraints governing each movement between geographical places (Barthelemy, 2011). Recent research on the structure and the topology of urban road networks using complex network analysis (Albert and Barabasi, 2002; Newman, 2010) has shown the existence of quantitative similarities (at least at a macroscopic level) between road networks of cities with different geographical, architectural and socioeconomic characteristics (Cardillo et al., 2006; Scellato et al., 2006; Buhl et al., 2006; Chan et al., 2011; Barthelemy, 2011). Such outcomes appearing in the newly established research field of complex network analysis compose a new perspective in the study of urban transportation

2352-1465 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the organizing committee of the 3rd CSUM 2016. 10.1016/j.trpro.2017.05.087



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systems and provide evidence for considering the network topology as a determinative factor for the urban mobility and development. Within this framework, this article studies the topology of the urban road networks among the capital cities of the prefectures in the region of Thessaly, in Greece, aiming to reveal links among the structural, the functional (mobility) and the socioeconomic aspects of their urban systems. The remainder of this article is organized as follows: Section 2 presents the methodology followed in the study, the network modeling, along with the measures and empirical tools used in the analysis. Section 3 presents and evaluates the results of the analysis and, finally, in section 4 conclusions are given. 2. Methodology and Data Each urban road network (URN) of the Thessaly’s capital cities, Karditsa (KURN), Larissa (LURN), Trikala (TURN) and Volos (VURN) is constructed in the L-space representation (Barthelemy, 2011; Tsiotas and Polyzos, 2014, 2015a), into an undirected and connective graph G(V,E) with spatial weights, where nodes (V) represent road intersections and edges (Ε) represent road segments intermediating between successive nodes (without a change in their route). Such representation complies with the common practice for modeling urban road networks (Buhl et al., 2006; Cardillo et al., 2006). The network models for the of Thessaly were self–edited using data from openstreetmap.org©, while data for the 62 worldwide urban networks considered in this paper were drafted from relevant studies available in the literature (Buhl et al., 2006; Cardillo et al., 2006; Scellato et al., 2006; Chan et al., 2011). The available socioeconomic information for the analysis of the URNs of Thessaly was drafted from the Greek National Census, (ELSTAT), the Greek General Secretariat of Information Systems (GSIS), the official web sites of the Urban Buses Enterprises for each capital city and Polyzos (2015). Apart from the classic network measures, the city organization index proposed by Courtat et al. (2010) is computed, measuring city organization accordingly to the proportion of incomplete crossovers and dead ends. When rn≈0, the urban system has a well-organized pattern, while when rn≈1 the urban system is deficient of organization and planning (Barthelemy, 2011). Afterwards empirical analysis is applied, consisting of various statistical and empirical techniques, such as descriptive statistics and correlation analysis (Norusis, 2004) between vector variables. Finally, patterns of magnitude consisting of scores of the URNs of Thessaly per measure are compared in pairs, between cases of network and socioeconomic measures. This approach aims in detecting potential relations between network and socioeconomic measures and in highlighting addresses of further research. 3. Results and Discussion 3.1 Network Analysis At first, the network measures along with some socioeconomic indicators are calculated and their results are shown in table 1, where all URNs show a leading performance in some aspects of their topology, while for the socioeconomic indicators the LURN excels in the majority of cases. In particular, KURN seems to describe an accessible network (highest C C value), but with the longest edge distances (highest s and d ij ), which has also the smoothest decay in its degree distribution as it is shown in figure 1, describing a pattern of homogenous connectivity, which is also reflected on its city’s organization index (rn). Also, VURN has the best city’s organization network pattern (rn), while KURN possess the second optimum place followed by the LURN and TURN. This status seems to reflect the city plans of these networks, where in the two leading cases there are obvious hippodamian characteristics (Polyzos, 2015), while the last cases describe more pericentral city plans (figure 2).

Table 1. Network and socioeconomic measures of the capital cities of Thessaly.

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CAPITAL CITY Measure NETWORK MEASURES No. Vertices / n No. Edges / m Average degree / k

Unit

KURN

LURN

TURN

VURN

#(a) #

1392 2094

4018 6041

1887 2710

4285(b) 6788

#

3

3.007

2.872

3.168

City’s organization index (rn)(c) Graph Density / ρ Average clustering coefficient / C

net(d) net

0.7329 0.001

0.7917 0.002

0.6369 0.001

net

0.6739 0.002 0.023

0.03

0.044

0.024

Network Diameter / dG -//Average strength / s

# km

56 9.369

86 8.562

77 10.864

km

0.261

0.205

77 11.335 0.244

km

183.12

416.53

235.3

405.02

m

86.745

68.174

85.018

58.335 30.778

Total edge length /

 d ij

Average Edge Length /

d ij

Average Path Length (bin) / l

0.185

#

20.68

35.469

28.437

km

1.9291

1.3121

2.0638

2.3589

net

0.907

0.948

0.935

0.938

net

20.680

35.469

28.437

30.778

net

13687.43

69231.86

25873.06

63783.79

SOCIOECONOMIC INDICATORS Urban Bus Routes (UBR) City's population (POP) Workers within the residence area (Lab) Commuters (Com) Aver. fair market values/ ( FMV )

# # # #

4 56747 13073 1048

15 162591 44372 3851

13 81335 18457 1856

15 144449 25663 3678

net

663.04

1106.25

857.14

1124.07

Aver. marketability coefficient/

net

1.565

2.617

1.704

1.453

Average Path Length (wei) / l

bin wei

Modularity / Q Average closeness centrality / C C Average betweenness centrality /

CB

MC

a. Number of cases b. Higher performance per measure (row) is shown in bold

c. Proposed by Courtat et al. (2010) d. Non-dimensional number

Next, TURN seems to have a deficient peripheral structure, evident by the highest scores in ρ, dG and C . In particular, greater values in ρ describe the existence of more links comparatively to the number of nodes, while in dG describe that the network is more distant. Concerning the C , greater values interpret that nodes are linked with comparatively more interconnected neighbors. According to the spatial distribution of betweenness centrality shown in figure 2, the clustering coefficient’s pattern describes that the peripheral structure of this network operates more as a direct access to central places than as a ring route for the detonation of the central traffic.

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Dimitrios Tsiotas et al. / Transportation Research Procedia 24C (2017) 482–490 a. KURN

b. LURN

c. TURN

d. VURN

485

Figure 1. Degree distributions of the URNs of Thessaly.

The measure of C operates as an index of mobility, under the condition that the traffic in the network is considered constant (Barthelemy, 2011). According to figure 2, the spatial distribution of CB for the URNs of Thessaly presents three distinct patterns. The first pattern describes the TURN, where the mobility load in the network is undertaken by central nodes and the contribution of peripheral or ring roads to urban mobility is negligible. The second pattern describes the case of VURN, where the mobility load in the network is undertaken by peripheral nodes addressed mainly across the ring road of the city, while in other nodes the traffic seems to be evenly distributed. The third pattern is a composition of the previous two and it describes the cases of KURN and LURN. Overall, the spatial distribution of betweenness centrality illustrates the utility of the ring roads in urban planning, which undertake a major proportion of the city’s traffic.

a. LURN

a. KURN

B

4

c. TURN

c. VURN

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Figure 2. Spatial distributions of betweenness centrality for the URNs of Thessaly.

Next, the URN of Larissa (LURN) shows a leading performance in the majority of network measures (dG,

d

ij

,

a. KURN

b. LURN

c. TURN

d. VURN

l , A, Q, CB), along with the majority of cases of the socioeconomic indicators. The overall picture of this network addresses directions for linking network topology and its socioeconomic background in the study of urban systems. Further, the correlations (k, CB) (figure 3) and (k, s) (figure 4) are examined. The correlations (k,CB) illustrate (bTURN>1) that for the KURN, VURN and LURN hubs undertake the biggest proportion of urban mobility, while for the TURN (bURN<1) illustrate that the traffic load is not concentrated exclusively to hubs. The correlations (k,s) are shown in figure 4, where the KURN and LURN have the power-law exponent of the relation s=f(k) approximately to monad, showing trends of regularity in the spatial distribution of their nodes. On the other hand, the TURN and VURN have their power-law exponents smaller than monad illustrating a “rich-club”-alike pattern (Colizza et al., 2006), where hubs have shorter connections than the expected average.

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c. TURN

d. VURN

b. LURN

a. KURN

Figure 3. Correlations between degree (k) and betweenness centrality (CB) for the URNs of Thessaly.

Figure 4. Correlations between degree (k) and strength (s) for the capital cities of Thessaly.

3.2 Data and empirical analysis At first, the available in the literature (Buhl et al., 2006; Cardillo et al., 2006; Scellato et al., 2006; Chan et al., 2011) worldwide URN data are edited into vector variables and further a statistical descriptive and correlation analysis is applied. The available data concern the measures n, m, k , l, d ij , POP, city’s area (A) and population density (ρPOP), for 62 worldwide urban networks referring to cities of Germany, France, India, Belgium, Spain, Peru, Algeria, Syria, Italy, Brazil, Egypt, USA, UK, S.Korea and Austria. Based on these worldwide URN data, percentiles of lag 10% are constructed for each variable, without considering the URNs of Thessaly. The respective scores of KURN, LURN, TURN and VURN are placed to the proper category, according to their magnitude, as it is shown in table 2, where the overall picture from this classification illustrates that the considerable level of connectivity of the URNs of Thessaly is more an effect of dense housing rather than of population, while global road networks seem to provide greater space for urban communication. Table 2. Order of magnitude for network measures of the Thessaly’s URNs, classified according to the percentiles constructed from data of the available global URNs. Percentiles (%) 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100

n

m K,T L V

K,L,T,V

k

d

l

L,V K,T K,L,T,V

POP K L,T,V

A K,L,T,V

ρPOP

K,T,V L K,L,T,V K=KURN, L=LURN, T=TURN, V=VURN

Next correlation analysis is applied in two steps, the first without the cases of the Greek URNs and the second including them. This double consideration allows estimating the contribution of the Greek URNs in the observed correlations. The analysis applied excluding missing values in pairs (pair-wisely) (Norusis, 2004) and the results are shown in table 3. The most interesting observation in table 3 is that, whether considering the Greek URNs in the

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correlation analysis, the coefficient r k

, d

changes its sign and its magnitude approximately 180%. In terms of urban

planning, the relation k  d interprets the existence of a growth motif favoring the attachment in the network of new links preserving the existing nodes, so as average distance to be increased. Reversely, the relation k   d interprets a growth motif favoring the attachment in the network of new links along with new nodes, so as average distance to be decreased. Table 3. Results of the correlation analysis for the URN vector variables(a,b,c) .

ρPOP

A

POP





m

n

Without Greek URNs rxy p N rxy p N rxy p N rxy p N rxy p N rxy p N rxy p N

m

k

.998* .000 39 1

.677* .000 44 .490# .024 21 1

39

d

.480* .002 39 .477* .002 39 -.651* .001 21 1

44

Including Greek URNs A

POP

39

-.001 .992 62 -.155 .345 39 .302# .046 44 -.530* .001 39 1 62

ρPOP

-.030 .814 62 -.034 .838 39 -.186 .226 44 .001 .997 39 .209 .104 62 1 62

l

-.099 .435 62 -.313 .053 39 .142 .359 44 -.530* .001 39 .733* .000 62 -.100 .437 62 1

.018 .913 41 -.794* .000 18 -.554* .006 23 1.00* .000 18 .264 .095 41 .219 .170 41 .412* .007 41

62

k

m

d

A

POP

.658* .000 48 .522* .007 25 1

.480* .002 39 .492* .001 43 .517* .008 25 1

.004 .976 66 -.121 .440 43 .278# .056 48 -.436* .003 43 1

ρPOP

-.026 .838 66 -.020 .901 43 -.188 .199 48 .020 .897 43 .215 .083 66 1

l

-.038 .804 45 -.714* .000 39 22 -.503* .007 44 27 .866* .000 39 22 .273 .075 62 45 .225 .137 62 45 .418* .004 62 45 a. High correlations (≥0.65) are shown in bold b. The upper triangular matrix is shown due to symmetry c. Correlations significant at the 0.1 level (2-tailed) are shown in italics *. Correlation is significant at the 0.01 level (2-tailed). # . Correlation is significant at the 0.05 level (2-tailed) .997* .000 43 1

-.092 .462 66 -.263 .088 43 .117 .430 48 -.415* .006 43 .738* .000 66 -.088 .483 66 1

Finally, patterns of magnitude of rows in table 3 are compared, between cases of network and socioeconomic measures. This approach examines whether the ranking in magnitude of scores for a certain row (network measure) and for the given sorting of cases (KURN, LURN, TURN, VURN) is the same with any of the rows of the socioeconomic indicators. In case this is true it returns the value 1 otherwise the outcome is 0. The analysis aims in detecting potential relations between network and socioeconomic indices and its results are shown in table 4. Table 4. Correlations among ranking patterns of magnitude the network and socioeconomic measures of each capital city(a,b,c,d,e) . UBR n m

POP Lab Com NETWORK MEASURES 0 0 0 0 0 0 1 1 1

FMV

MC

UBR

1 1 0

0 0 0

UBR POP Lab

1 0 0 0

1

1

1

0

0

1

0

0

0

1

0

d(G)bin

1 1 0

d

ij

0

1

1

1

0

0

Com

bin

0

1

1

1

0

0

FMV

0

1

1

1

0

0

CC

0

1

1

1

0

0

B

0

1

1

1

0

0

l

Q

C

POP Lab Com FMV SOCIOECONOMIC INDICATORS 0 0 0 1 0 1 1 1 0 1 1 1

MC 0 0 0

1 = scores of KURN, LURN, TURN, VURN have the same ranking pattern for row i and column j 0 = different ranking patterns

According to table 4, the variables UBR and FMV have the same ranking pattern with n and m across the scores of the URNs of Thessaly. Considering UBR as an aspect of urban mobility, since the establishment of a bus route (line) complies with the law of supply-demand for the need of urban mobility, and the FMV as an economic aspect of the

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city, this observation reveals links between URN size, urban mobility and urban market. All the other network measures have the same ranking pattern with the population-based socioeconomic indicators, illustrating a potential gravity pattern controlling the mobility (CB), the accessibility (CC), the geometry (dG,  dij , l bin ) and community structure of these URNs. 3.3 Implications to urban planning and addresses of further research The foregoing analysis addressed some issues of practical importance to urban policy and planning. A major contribution of this article to the study of urban systems is the introduction of a new variable in the urban planner’s agenda, which is the network’s topology. The newly established discipline of Network Science (Brandes et al., 2013) instructs considering the map of an urban network more as a set of measurable attributes composing the concept of the network topology, rather than as simple illustrations of spatial arrangements of roads and intersections. The study of network topology suggests currently an intuitive process for urban modeling, immanent in the set of the practical rules governing the architectural design and urban planning. The methodological orientation of this article aims in widening the current modeling perspectives and comprehending the existing interdependencies among the structure of an urban system and its functionality expressed as urban mobility, by using the network paradigm. Complex network analysis is proven an effective tool of evaluation and feedback for the process of urban modeling. Network measures quantifying the structure, intermediacy and the grade of organization can be used to evaluate the efficiency of urban designs, providing feedback for correcting, improving or upgrading the urban models, before they proceed to the stage of construction. For example, evaluating an urban network model using the city’s organization index (rn) (Courtat et al., 2010) may provide feedback about the effectiveness of the overall city plan and the necessity to implement more hippodamian or pericentral characteristics. Moreover, the consideration of the spatial distribution of betweenness centrality in an urban network is capable to reveal deficiency zones for the allocation of traffic loads or to instruct optimal places for attaching new routes, such as ring roads. Developing procedures for standardizing such considerations in the process of urban planning suggest topics of further research. Finally, comparisons made with worldwide cases interpret that the examined Greek URNs are densely connective, disproportionally to their population size, illustrating the existence of an unconventional pattern ruling urban road network development in Greece. Such observations address issues for the urban policy, highlighting the necessity Greece to overcome problems immanent in urban structure due to intense urbanization occurred in past decades. Further research into this direction should be implemented by considering more data. 4. Conclusions This article studied how the topology of Urban Road Networks (URNs) is linked with socioeconomic aspects of their urban systems, aiming in revealing patterns that are related to urban mobility. The network analysis for the Greek URNs showed the imprint of spatial constraints on their degree distributions and showed consistency with their city plans described by either hippodamian or pericentral characteristics. The network study provided also information about the proportion of the network traffic that hubs undertake and whether they serve distant communication. Focusing on CB, as an aspect of urban mobility, the examination of the spatial distributions of the URNs of Thessaly revealed three distinct patterns, where the mobility in the network is undertaken either by central nodes, or ring roads, or a mixture of the previous two. Overall, the spatial distribution of CB illustrated the utility of the ring roads in urban planning, which undertake a major proportion of the city’s traffic. Correlations applied on worldwide data, first without and then including the cases of Greek URNs, demonstrated that the considerable level of connectivity describing the URNs of Thessaly is more an effect of dense housing rather than of population size, while global road networks spend greater space for urban road communication. Also, the relation between average degree and kilometric edge distance revealed different motifs of URN growth when considering or not the Greek cases, illustrating an unconventional pattern in urban road network development in Greece. Finally, patterns of magnitude consisting of scores of the URNs of Thessaly per measure were compared in pairs, which revealed potential relations between network size and urban mobility and a potential gravity pattern controlling the mobility, the accessibility, the geometry and the community structure of these URNs. Overall, the analysis provided interesting insights about how the network topology is related to urban mobility, population and market information.

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References Albert, R., Barabasi, A.-L., 2002. Statistical mechanics of complex networks. Review of Modern Physics 74, 47–37. Barthelemy, M., 2011. Spatial networks, Physics Reports 499, 1–101. Brandes, U., Robins, G., McCranie, A., Wasserman, S., 2013. What is Network Science?. Network Science 1, 1 -15. Buhl, J., Gautrais, J., Reeves, N., Solé, R. V., Valverde, S., Kuntz, P., Theraulaz, G., 2006 Topological patterns in street networks of self-organized urban settlements. European Physical Journal B 49, 513–522. Cardillo, A., Scellato, S., Latora, V., Porta, S., 2006. Structural properties of planar graphs of urban street patterns. Physical Review E 73, 066107. Chan, S. H. Y., Donner, R. V., Lammer, S., 2011. Urban road networks – spatial networks with universal geometric features?. European Physical Journal B 84, 563–577. Chowell, G.., Hyman, J. M., Eubank, S., Castillo-Chavez, C., 2003. Scaling laws for the movement of people between locations in a large city. Physical Review E 68, 066102. Colizza, V., Flammini, A., Serrano, M. A., Vespignani, A., 2006. Detecting rich-club ordering in complex networks. Nature Physics 2, 110–15. Courtat, T., Gloaguen, C., Douady, S., 2010. Mathematics and morphogenesis of the city: a geometrical approach. Physical Review E 83(3), 036106. Koschutzki, D., Lehmann, K., Peeters, L., Richter, S., 2005. Centrality Indices. In: Brandes, U., Erlebach, T., (Eds.), Network Analysis, SpringerVerlag Publications, Berlin, Germany, pp.16-61. Newman, M. E. J., 2010. Networks: An Introduction, Oxford University Press, Oxford, UK, pp.784. Norusis, M., 2004. SPSS 13.0 Statistical Procedures Companion. Prentice Hall Publications, New Jersey, USA, pp.368. Polyzos, S., 2015. Urban Development. Kritiki Publications, Athens, Greece, pp.541 [in Greek]. Polyzos, S., Tsiotas, D., Minetos, D., 2013. Determining the Driving Factors of Commuting: An Empirical Analysis from Greece. Journal of Engineering Science and Technology Review 6(3), 46 -55. Polyzos, S., Tsiotas, D., Papagiannis, K., 2014. Determining the changes in commuting after the Ionian Motorway’s construction. MIBES Transactions 8, 113–131. Scellato, S., Cardillo, A., Latora, V., Porta, S., 2006. The backbone of a city. European Physical Journal B 50, 221–225. Strano, E., Nicosia, V., Latora, V., Porta, S., Barthelemy, M., 2012. Elementary processes governing the evolution of road networks. Scientific Reports 2(296), doi:10.1038/srep00296. Tsiotas, D., Polyzos, S., 2013. Introducing a new centralities measure from the interregional road transportation network analysis in Greece. Annals of Operations Research 227(1), 93-127 Tsiotas, D., Polyzos, S., 2014. Analyzing the Maritime Transportation System in Greece: a Complex Network approach. Networks and Spatial Economics 15(4), 981-1010. Tsiotas, D., Polyzos, S., 2015. Decomposing multilayer transportation networks using complex network analysis: A case study for the Greek aviation network. Journal of Complex Networks 3(4), 642-670. Van Ommeren, J., Rietveld, P., Nijkamp, P., 2000. Job mobility, residential mobility and commuting: A theoretical analysis using search theory. The Annals of Regional Science 34(2), 213-232.

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