GeoJournal DOI 10.1007/s10708-015-9671-1

A methodology to assess the spatial configuration of urban systems in Iran from an interaction perspective Hashem Dadashpoor . Atoosa Afaghpoor . Andrew Allan

Ó Springer Science+Business Media Dordrecht 2015

Abstract The aim of this paper is to develop a methodology for identifying various dimensions of the spatial configuration of urban systems in Iran from an interaction perspective. Through the provision of empirical evidence of different types of flows of people including air passenger flows, passenger flows by bus and car, this paper compares the resulting spatial constellations of these flows through the innovative use of indices to systematically describe and measure five dimensions of an urban system’s spatial configuration that include: (1) centrality and dominance of vertices, (2) network cohesion, (3) network strength, (4) network symmetry, and (5) communities and levels. The findings show that although the spatial configurations of different flows are not the same, all were characterized by having a significant distance within a polycentric urban system due to the primacy of the Tehran metropolis. In regard to passenger flows by car and bus, it was found that for various functional regions, there was a balanced distribution of centrality and urban hierarchy evident in Iran. By contrast, air passenger flows were not able to determine centrality within a national urban hierarchy because of the limited distribution of centers for air travel in Iran at higher levels of spatial organization.

H. Dadashpoor (&)  A. Afaghpoor Tarbiat Modares University, Tehran, Iran e-mail: [email protected] A. Allan University of South Australia, Adelaide, Australia

Keywords Spatial configuration  Urban systems  Flows of people  Interaction perspective  Methodology  Iran

Introduction Studying spatial configuration of urban systems and inter-urban relationships in particular have occupied special place in the context of urban and regional studies over the past several decades (Meijers 2007; Taylor et al. 2010; Neal 2010; Hou et al. 2015). Since the late 1960s and the emergence of this approach, an urban system has not been defined as only a set of physical instances of urban nodes, but included the spatial inter-urban linkages (Simmons 1978) and was defined through relations and flows amongst cities and their position in the outer areas of a complex network. Therefore, any change in an urban system’s defining components (nodes and linkages) can be associated with a change in its spatial constellation (Dadashpoor et al. 2014). One of the main consequences of this constellation is the shift from simple mono-centric to polycentric urban systems (Kloosterman and Musterd 2001; Dieleman and Faludi 1998). It could be argued that these changes are caused by the position and centrality of urban nodes that are increasingly determined by relations and flows within networks (Derudder and Witlox 2005; Neal 2010) rather than by what is fixed within them (Smith 2003).

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An urban system can be described as polycentric when two-way flows between cities exist and where a notably unbalanced distribution would yield monocentric urban systems (Burger 2011; Burger and Meijers 2012; Vasanen 2013). However, the spatial configuration of cities implies that transition from mono-centric to polycentric does not happen in all cases (Zabardast and Hajipoor 2010) and even when it does occur, is not necessarily similar (Burger et al. 2014a, b). Therefore, an urban system which may be polycentric at one mode may be considered as monocentric at another mode (Hall and Pain 2006; Taylor et al. 2010; Vasanen 2013; Burger et al. 2014a, b). Furthermore, Lambregts (2009) states that the degree of interdependencies between cities observable in a specified territory is highly dependent on the indicators used to measure it, where urban interactions can be studied through evaluating various kinds of flows (Burger et al. 2014a, b; Ma et al. 2015) such as flows of people, goods, information and money (Pred 1977; Neal 2010; Van Oort et al. 2010; Hanssens et al. 2014); however, the limited access to relevant and updated data makes most of the research dependent only on one type of linkage like air passenger flows (Smith and Timberlake 2001; Derudder and Witlox 2005) which differ from flows of people by other transport modes where they mostly capture the interaction over longer distances. Therefore, it is of great significance to extend air passenger flows to cover flows of people by other transport modes (Limtanakool et al. 2007b). It seems that in recent studies, there has been a lack of direct comparison of differences in urban configurations that has resulted from flows of people via various transport modes between cities. Furthermore, in the absence of relevant data, previous studies were based on the analysis of the exchanges through the use of various infrastructures that make relationships between cities possible (Short et al. 1996), but these studies have been inattentive to the data requirements associated with quantifying network capacity. In fact, flows described in these studies do not present a completely accurate understanding of the complete range of interactions occurring between cities (Neal 2010). This failure to identify the cities that provide the origins and destinations for inter-urban flows comes from infrastructure-based methods which often yield inappropriate results for investigating urban networks. However, slightly different types of networks utilizing origin–destination data can more

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appropriately and accurately reflect the inter-urban occurring interactions (Nordlund 2004). Apart from these shortcomings, few attempts have been made to propose a methodology for assessment of urban systems configuration based on an analysis of flows. Precursor efforts in this regard are studies by Limtanakool et al. (2007a, b, 2009) in which the constellation of urban systems is identified and classified with the introduction of three S-dimensions of spatial configuration, that are: strength, symmetry and structure which appears incomplete. Therefore, the aim of this paper is to develop a methodology for identifying various dimensions of spatial configuration of urban systems in Iran from an interaction perspective. It is worth mentioning that other factors such as geographical, socioeconomics and institutional implications have deterministic effects on the spatial configuration of urban systems, but the focus of the present research is on interactions between cities which reflect the outcome of considering all of these factors in the context of the urban system. For this reason, five dimensions of spatial configuration in urban systems are investigated: (1) centrality and the dominance of the vertices, (2) network cohesion, (3) network strength, (4) network symmetry, and (5) communities and levels, which are described systematically and made measurable due to the values of the indices. According to the calculated values of the five dimensions, the network will achieve a unique position within a five-dimensional space. In addition, unlike previous studies that have focused on the inter-metropolitan interactions occurring on global scale (Derudder and Witlox 2005; Derudder and Witlox 2008; Smith and Timberlake 2001), or on intra-metropolitan scale (e.g. Irwin and Hughes 1992; Van Der Laan 1998; Van Nuffel and Saey 2005) while the scale of study in this research is national and the spatial level of analysis was limited to thirty provincial capital cities of Iran in 2006 based on origin–destination data.1 This level can provide a relatively complete picture of the network constellation based on the flows of people at a territorial scale. The rest of this article is organized as follows: the second section describes the conceptual and 1

Alborz Province has Karaj as its capital and was formed in 2010/06/28 after separation from Tehran Province. Hence, this province was not taken into consideration in calculations of this research.

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theoretical issues related to spatial configuration of urban system as well as the five spatial interaction dimensions. The third section reviews the data sources, spatial interaction indices and methods. In the fourth section, the spatial constellation of Iran’s urban system is analyzed based on the flow of people via air, bus and car modes, and discussed. Finally, the section ends with conclusion and suggestions for further research.

Conceptual and theoretical issues Cities are not isolated systems, but linked together to form networks (Boix and Trulle´n 2007; Marull et al. 2013). A network of cities is a structure where the nodes are the cities connected by different kinds of links through various flows (Boix and Trulle´n 2007). Notably, the work of Christaller (1933) and Lo¨sch (1941) developed what came to be known as central place theory and their seminal work launched this field of research. In the 1960s, it became an important part of urban systems research (Meijers 2007). During this period, Berry (1964) first introduced the functional concept of an urban system; he defined an urban network as a group of interdependent cities. Pred (1977) further developed Berry’s work by focusing on the study of inter-urban relationships at national and regional scales, which implies that the relationship between cities is not only vertical but also horizontal in nature (Meijers 2007). Based on these concepts, Simmons (1978) defined the urban system as consisting of two elements: urban settlements as the nodes and the inter-urban relationships which are reflected in different kinds of flows such as people, goods, money, and information (Hall and Hay 1980; Parr 2004). The appearance of the urban network concept coincides with a number of recent studies on changing urban systems. Ins this literature, it is argued that demographic changes and the rise of the networked economy have had a significant impact on the spatial structure of cities and regions (Burger et al. 2014a, see also Hoyler et al. 2008; De Goei et al. 2010; Batten 1995 and many other). Therefore, the traditional central place theory of urban systems, characterized by a strict urban hierarchy, is outdated and can be replaced by a network view of urban systems with no urban hierarchy and a significant degree of spatial integration between different cities (Kloosterman and

Musterd 2001, Meijers 2007; Burger et al. 2014a). Accordingly, the identification and classification of urban networks constellations is related to characteristics of the vertices and the lines connecting these vertices. In each network, size is the attribute of the vertices where weight, direction, and distribution are the characteristics of these lines. These attributes are derived from the fact that in network analysis, in addition to the relationships, their spatial arrangement and distribution have their own properties (Fararo 1989). Hence, the properties of the whole are different from its components and as a macro community organization, it is made up of some groups called community structure that are akin to vertices and lines, thereby possessing an ontological value. Each community has its own special organizational properties called levels (Wellman 1988). In this research, the study of these five characteristics that shape the network constellation are made possible through the five dimensions of spatial interactions as described in Table 1. The first dimension is the Centrality and Dominance of vertices which relates to the magnitude of the flows attributed to each vertex, and measures their dominance and centrality in the network. This dimension is obtained by comparing the size of the vertices in relation to each other and represents the level of urban hierarchy and intensity of primacy (Irwin and Hughes 1992). From this dimension, urban systems can range from completely mono-centric to completely polycentric (Batten 1995). A mono-centric system refers to a situation that arises as a result of the concentration of specialized functions, in which only one or a few nodes dominates the system; by contrast, a completely polycentric system refers to a situation where cities have similar centrality without any superiority over each other (Kloosterman and Musterd 2001). In each network, the vertices are connected via lines; therefore, the level of network cohesion is a function of the sum of allies distributed there in (Simmons 1986) which can be measured through its Network Cohesion. This second dimension, which works at the network level, examines how the relationships are distributed amongst vertices and measures the level of network integration. In other words, this dimension can define the study network over a scale ranging from completely discrete in which none of the nodes are connected to a completely coherent network and networked arrangement in

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GeoJournal Table 1 Relation between network elements, its attributes and spatial configuration dimensions Network element Attribute

(1) Vertices

Dimension Min

_

Size Centrality and Dominance Monocentric

(2) Interaction

(3) Groups

Distribution

Weight

Direct

Cohesion

Strength

Symmetry

Community and Level

Discrete

Concentrate

Asymmetrical

Mono-cluster

Coherent

Deconcentrate

Symmetrical

Poly-cluster

Pattern Spatial Configuration

Max

Polycentric

Pattern +

which all the vertices have the maximum interconnections. However, network cohesion only focuses on the topological aspects and cannot take into consideration the weights of the connections in a weighted network. Therefore, the third dimension Network Strength focuses on how the magnitude of the flows is distributed in the network and assesses its constellation over a continuous scale ranging from completely dispersed in which the strength of flows is equally distributed among the vertices to that which is completely concentrated with the strength of the flows totally focusing on one vertex. Depending on the nature of the interaction, the connections amongst the vertices can be directed or undirected. Focusing on the direction of interactions, the Network Symmetry dimension was also applied in studies conducted by Sinclair (1983) and Smith and Timberlake (1995). In those networks, where the direction of the flows is significant, the interactions

Fig. 1 Five dimensions of spatial configuration of an urban system

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can be defined as a scale ranging from completely asymmetric which involves a mono-directional relationship to completely symmetric which involves a bidirectional relationship with an equal size in both directions. The aim of the fifth dimension Community and Level is to permit detection of modules and, possibly, their organizational hierarchies by only using the information encoded in the topology of graphs (Girvan and Newman 2002). This dimension defines the network constellation over a continuous scale ranging from a mono-cluster to completely polyclustered network. Due to the connection of all vertices to a central vertex in the mono-cluster situation, only one cluster is detectable, while in the poly-cluster state, due to the complete connection amongst all of the vertices, each vertex forms a separate cluster. The five forenamed dimensions, each concerned with one attribute of a network element, are depicted in Fig. 1 in five steps. The resulting spatial

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constellation of the flows is in accordance with the obtained values from the five dimensions and reveals a unique position in space which makes them comparable.

provinces as a delimitation of the study area to allow for easier comparability (Fig. 2). For this reason, the study included 30 provincial capital cities in 2006. As a result, the spatial level has been restricted to interurban relations through flows of people.

Characterizing Iran’s Urban System Data Description Iran, in west Asia, extends over an area exceeding 1,648,198 km2; the Zaghros Mountains determine Iran’s western and southwestern borders whilst the Alborz Mountains and Caspian Sea mark Iran’s northern and northeastern borders. The challenging mountainous topography and high elevations that characterizes a large portion of Iran, together with extreme heat and dryness in these regions, has restricted access to natural endowments, particularly water, resulting in a concentration of population in the northern and western areas of Iran. Imbalanced population distribution in different urban nodes as well as imbalance in the dispersion of these nodes over territorial zones has led to the formation of a hierarchical urban system that is dominated by Tehran. On the other hand, the transformation in life patterns and the structure of Iran’s economy has dramatically increased Iran’s urban population. This proportion rose from 31 in 1956 to 71 % in 2011. Along with a rapidly increasing urbanization ratio, the number of cities increased from 199 in 1956 to 1139 in 2011 (Seifolddini et al. 2014). Whilst the population of Iran experienced a threefold increase during these years, the population of many Iranian cities underwent a sixfold increase in growth. This trend was accelerated by high natural population growth and a high rate of rural urban migration and was accompanied by rapid socio-economic and political changes, large increases in the establishment of new industries, and facilitated by Tehran’s strong tradition of centralization of government activities (Bihamta et al. 2014; Tayyebi et al. 2011). However, the study of the changes in Iran’s urban system during this period reveals that although the changes since 1976 onward were toward decentralization, the country’s urban system has yet to achieve a balanced urban system. With this mind, the spatial scale of this study is national; however, with respect to the limitations in providing geographical information on the origin and destination of longdistance travels within three different networks, it would be preferable to use the political division of

In this study, data on long-distance personal travel were used. Generally two kinds of data exist for long distance travel: origin–destination and traffic counts; however, with regard to the purpose of this research, only origin–destination data were applied. This is because traffic count data can causes errors associated with an inability to identify the city of origin and destination (Short et al. 1996). For example, with traffic count data, the volume of the flows along transportation routes are easily counted, but what initiates these flows and the ultimate destinations of these trips is relatively unclear. This deficiency with traffic flow data creates difficulties in accurately determining the role of cities that are affected by such traffic flows. In this study, three modal flows of people were analyzed: air passenger flows, passenger flows by bus, and passenger flows by car.2 The span of the road network makes it possible to capture most of the trips or passenger movements by buses or personal cars. On the other hand, the broad geographical extent of the national aerial transportation network has led to a significant increase in the number of air passengers in the last decade and this has dramatically facilitated access to areas located at the geographical periphery of central cities, especially Tehran. The importance of each of these modes necessitated analysis of flows of people in three networks simultaneously in order to achieve a comprehensive understanding of how the flows of people influenced the different types of interurban relationships within the Iranian urban system.

2

It should be noted that at present, due to various factors such as height or desert areas and high administrative costs, the interurban rail transport network is still incomplete and some of Iran’s major cities are not connected to the rail network. Furthermore, since some of the provincial capitals still do not have access to the rail transportation network, these flows for assessing Iran’s urban system were excluded from the analysis in this study.

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Fig. 2 Study scope in thirty capital cities, 2006 (Ministry of Road and Transportation 2006, prepared by authors)

Since inter-urban long-distance flows of people are more important at the macro level (Frandberg and Vilhelmson 2003), daily commuting flows that focus on shorter physical distances have been excluded from the data. Therefore, in this study ‘‘long-distance travel’’ is defined as travel that includes a destination that exceeds 100 km. Because all of the provincial capital cities3 are more than 100 km away from each other, the choice of this threshold permits a focus on those interactions in which the origin city’s location (as determined by its province) is distinct from that of the destination city. In most of the studies done, the origin–destination data on passenger flows were extracted from travel surveys; however, in the current study, to ensure that the collected data included the movement of people via cars, origin–destination travel surveys by the Comprehensive Transportation Studies 3

The smallest distance among the studied cities was IsfahanShahrekord with 84 km and other cities were located more than 100 km away from each other.

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of Iran were used (Ministry of Road and Transportation 2006). This survey was carried out across Iran’s 56 regions on the 26th of April 2006 and covered a period of 96 consecutive hours for all of the transportation routes and modes but the limitation of this data is that it only includes passenger flows for the travel mode by car. As mentioned earlier, in order to exclude short-distance commuting flows from the calculations for the data of the origin–destination travel survey of Iran’s inter-urban road network, data was merged across 30 provinces’ boundaries, resulting in more accurate estimates of travel flows between regions and better similarity of geographical areas for comparing passenger flows. The Statistical yearbook of road Transport of Iran (as reported by RMTO) provided the required data on the flows of people by bus based on the status statements issued by travel agencies. This data is available for the origins and destinations of provinces (Country Road Maintenance and Transportation Organization (RMTO) 2006). Further, the Statistical

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Fig. 3 Spatial configuration dimensions and indices

yearbook of air Transport of Iran reported by the IAO provides the required data on air flows based on the origins and destinations by domestic airport. According to this report, there were 59 domestic airports in Iran in 2006 and the nearest city to each airport utilized as the relevant node in the calculations (Iran Airlines Organization (IAO) 2006). Although the Annals do not provide any information about passengers’ actual city of origin and destination and only provides the number of passengers travelling on airline routes, because flights into and out of domestic airports are direct non-stop routes, nevertheless, they can serve as a proximate estimate for origin–destination data. For example, due to the lack of Tehran-Jam direct flights, a person intending to travel from Tehran to Jam, would transfer at Shiraz airport for their onward journey on another flight to Jam. Non-direct flights involving airport transfers to another domestic flight are very small in comparison with the total volume of travel, nevertheless, to address these shortcomings and better coordinate the results of this research, inward flights to/outward flights from cities located in each of the provinces were integrated into 30 provinces’ boundaries.

Symmetry; and (5) Communities and Levels. Since the primary aim of this study is to develop a methodology for defining these dimensions so that the spatial configuration of urban systems in Iran can be characterized from an Interaction Perspective, each dimension is systematically described and measured through spatial interaction indices (see Fig. 3). The combination of results from these indices provided the position of a dimension within a continuous range that were then used to determine the configuration of urban systems in the case study. Table 2 details the mathematical relationships applied in determining the values of the indices. Centrality and dominance of vertices This dimension which applies to the nodal level, has been calculated from the sum of four indices: (1) weighted centrality degree or strength of vertices; (2) betweenness centrality of vertices; (3) closeness centrality of vertices; and (4) eigenvector centrality of vertices. The obtained values for each index range from 0 to 100, so the values for this dimension is in the range of 0–400.4 The weighted centrality degree or 4

Spatial configuration indices and methods As mentioned earlier, five dimensions were devised to recognize the spatial constellation of the urban systems. These dimensions define the essential characteristics of a network: (1) Centrality of Vertices; (2) Network Cohesion; (3) Network Strength; (4) Network

Extracting valid mathematical relations for each dimension is needed in rectifying the multicolinearity effects because the indices have direct relations to each other. In this article the combination of results for each dimension has been made possible by algebra summation and it has been done this way to allow comparison of a dimension’s values for each network. Hence, this does not mean that for example the centrality of vertices is the simple sum of its indices (i.e. strength ? betweenness ? closeness ? eigenvector).

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GeoJournal Table 2 Spatial configuration dimensions, indices and equations Dimension

Indices

Centrality and power of vertices

Strength of vertices

Equation si ¼

N P

aij sij

j¼1

Betweenness centrality of vertices

Pg gjik cBi ¼ Pjg

Closeness centrality of vertices

cNi

Eigenvector centrality of vertices

cIs i ¼ a

j

Network cohesion

Network density Network centrality Network betweenness centrality Network closeness centrality Network eigenvector centrality Network clustering coefficient

¼

gjk

n1 P d j ij

P j

aij csj

P aij D ¼ ðn1j Þn P ðki maxki Þ C ¼ Max Pj ðk maxk Þ i j i P B B c maxc ð Þ i i C B ¼ Max Pj cB maxcB ði i Þ j P N N c maxc ð Þ i i C N ¼ Max Pj cN maxcN ði i Þ j P I I c maxc ð Þ i i C I ¼ Max Pj cI maxcI ði iÞ j X 1 C C2 ¼ cC n i i number of triangles connected to vertex i number of triples centered on vertex i 6  number of triangles in the network CT ¼ number of pathes of length j two 3  number of triangles in the network CT ¼ number of connected triples of vertices P ðsi maxsi Þ C S ¼ Max Pj ðs maxs Þ i j i P Is Is ðci maxci Þ j C IS ¼ Max P ðcIi maxcIi Þ j P ðsij þsih Þ C CW ¼ si ðk1i 1Þ aij aih ajh 2 C C1 ¼

Network transitivity

Network strength

Network strength Network weighted eigenvector centrality Network weighted clustering coefficient

Network symmetry (Limtanakool et al. 2007a)

Interaction symmetry Node symmetry

Community and levels

Divisive algorithm Additive algorithm

j;h

P P sij  sji NSIi ¼ P s þP s ij ji 2  

 

LSIij ¼ 4

Lnð2Þ

dij ¼

Ln

sij sij þsji

þ

sji sij þsji

  Ln

sji sij þsji

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 P k6¼i;j Aik  Ajk

dint ðC Þ ¼ dext ðC Þ ¼

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sij sij þsji

#internal edges of C nc ðnc 1Þ 2

#intercluster edges of C nc ð n  nc Þ

3 5

GeoJournal Table 2 continued Key l

Link in the network (l ¼ 1; 2; 3; . . .; L)

i, j

i ¼ 1; 2; 3; . . .; I : j ¼ 1; 2; 3; . . .; J;

n aij

The number of vertices in the network The directed line from vertex i to j

for i 6¼ j

sij

The number of flows from vertex i to j

ki

The number of lines from vertex i/degree of vertex i

si

The number of flows from vertex i/strength of vertex i

gjk

The shortest path between vertex j and k/geodesic between vertex j and k

gjik

The shortest path between vertex j and k which passes through vertex i

dij

The length of the geodesic from vertex i to j/distance from vertex i to j

cj

The sum of degree(s) of the vertex/vertices which is/are connected to vertex i

csj

The sum of strength of the vertex/vertices which is/are connected to vertex i

ki ; si ; cBi ; cNi ; cIi ; cIs i max

Maximum value degree, strength, betweenness, closeness, eigenvector and weighted eigenvector in given network

Max ki ; si ; cBi ; cNi ; cIi ; cIS i

Maximum value possible degree, strength, betweenness, closeness, eigenvector and weighted eigenvector in a graph with the same number of vertices

cci

The clustering coefficient of vertex i

A

Adjacency matrix for given network, if vertex i is connected to vertex k: Aik = 1 otherwise Aik = 0

dint ðC Þ

The Intra- cluster density of the sub graph C

# internal edges of C nc

The number of internal lines (edges) of sub graph C The number of vertices in the sub graph C

dext ðC Þ

The Inter- cluster density

# intercluster edges of C

The number of lines (edges) running from the vertices of sub graph C to the rest of graph

strength of vertices calculates the total number of flows associated with a specific node and determines the dominance of a node in network. For nonsymmetric data, the inflow-degree of a vertex u is the number of ties received by u and the out-degree is the number of ties initiated by u. Furthermore, if the data is valued then the degrees (in and out) will consist of the sums of the values of the ties (Freeman 1979). Betweenness centrality of vertices index calculates the number of times that a vertex occurs on a geodesic, which is the shortest path that connects other vertices. The betweenness centrality of vertex is the proportion of all geodesics linking vertex j and vertex k which passes through the vertex into all of the geodesics connecting vertices j and k where i, j and k are distinct (Freeman 1979). The closeness centrality of vertices index describes the position of each vertex relative to its topological distance from other vertices. The closeness centrality of a vertex is the number of other vertices divided by the sum of all distances between the vertex and all others (Freeman 1979). Based on

eigenvector centrality of vertices, the centrality of each vertex is therefore determined by the centrality of the vertices it is connected to. The centrality of vertex I is given by multiplying the total centrality of its adjacent vertices byits Eigen value (Bonacich 1972).

Network cohesion Network cohesion operates at the network level and is topologically obtained from the sum of these indices: (1) network density; (2) network topological centrality degree; (3) network betweenness centrality; (4) network closeness centrality; (5) network topological eigenvector centrality; (6) network topological clustering coefficient; and (7) network transitivity. As each of these indices provide a distinctive definition of the network cohesion concept, quite different results occurred when compared to the others. The obtained values for each index ranged from 0 to 100, so that the values for this dimension were in the range of 0–700.

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Network density measures the number of existing arcs to the maximum number of possible arcs in the network. If the obtained value is closer to 1, then there will be more links with a fixed number of vertices. Consequently, the network spatial arrangement is similar to the network model. The definition of other four indices including network topological centrality/betweenness/closeness/eigenvector degree, is the total difference between the maximum centrality degree of vertices and centrality degree of each vertex within the existing network divided by the maximum possible value in a network with the same number of vertices (Freeman 1979); As the obtained values for these indices would be higher, the network will have greater similarity to an incoherent and discrete network which encompasses fewer relationships among vertices. Clustering another feature of networks means that if in a network, vertex «a» is connected to vertex «b» and vertex «b» is connected to vertex «c», then there is a greater possibility that vertex «a» is connected to vertex «c». Here the direction of the connection is not important. Network Topological Clustering Coefficient can be calculated through both average values (C1: division of the number of connected triples in the network which lack the third line to be converted to form a triangle) and the average of the values obtained for each vertex (C2: division of the number of the triangles connected to vertex i by the connected triples which have vertex i at the center) (Watts 1999).5 Unlike the previous four indices, the higher obtained values for this coefficient means that there is greater coherence in the network due to a larger distribution of relations amongst the vertices. Network Transitivity is very similar to network clustering coefficient as they are occasionally used interchangeably. However, unlike the network clustering coefficient, it considers the direction of the connection. That is to say in a directed graph, if vertex «u» is connected to vertex «v» and vertex «v» is connected to vertex «w», vertices «u», «v», and «w» are transitive if vertex «u» is also connected to vertex «w» (Newman 2003). The higher values obtained for network transitivity signify the higher number of connections among vertices as well as more cohesion in the network. 5

For the vertices with a degree of 0 or 1, the network topological clustering coefficient is 0 by convention and it decreases as the increase in the degree of the vertex.

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Network strength Network strength focuses on how the strength of flow is distributed in a network. It is calculated from the sum of the values obtained from: (1) Network weighted centrality degree; (2) Network weighted clustering coefficient; and (3) Network weighted eigenvector centrality. As was stated earlier, unlike network cohesion which does not consider the strength of flow in the calculations and the fact that some neighbors of a vertex are more important than others as well, network strength focuses on how the network strength is distributed. So the definition of indices for this index is similar to indices for network cohesion but the difference is on considering the weight of interactions in the calculations. To avoid repetition, the definitions are excluded. The obtained values for each index ranged from 0 to 100, hence the values for this dimension were in the range of 0–300. Network symmetry Network symmetry is considered in some networks such as urban networks in which the direction of flows is significant. The sum of values obtained from (1) interaction symmetry and (2) node symmetry results in network symmetry. The obtained values for each index ranged from 0 to 100; hence the values for this dimension were in the range of 0–200. Interaction symmetry measures the size of the involved flows in an interaction in one direction with their size in another direction (Smith and Timberlake 1995). The obtained values ranged from 0 to 1; 1 indicates that the intensity of flows between the two vertices of interaction from node i to j and from node j to i is equal and the relationship is symmetrical. Node symmetry measures the absolute value of the difference of the incoming and outgoing interactions for all the network nodes (Smith and Timberlake 1995). The obtained values for this index range from 0 to 1; 0 indicates that the intensity of the incoming flows to the vertices is equal to the volume of the outgoing flows. Communities and levels Although several algorithms have been proposed to identify the social structure of networks, depending on the purpose of the study, each algorithm can be applied only for some specialized requirements. Since the

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purpose of the fifth dimension is to find out how the vertices within the communities are organized and is focused on analyzing the multi-level structure of urban networks, this study only focuses on the use of additive algorithms of hierarchical clustering methods which calculates the distance between clusters through the average of the similarity among vertices (WTD-Average) (Johnson 1967). Theoretically the number of clusters can range from 1 to n (number of network vertices). The higher number of clusters indicates a more complex multi-level hierarchy with a more dispersed structure in the networks. By contrast, in concentrated, mono-polar and incoherent networks, a simpler two-level hierarchical organization is expected.

Results The values of first dimension are represented in Table 3 by the three modes of networks. Accordingly, the total number of passengers moved via the inner aerial public transportation fleet Iran in 2006 was 12,225,183 and in Tehran in the same year, the passenger flows were 5,047,480 and 5,061,894, respectively for inward and outward passengers, underlining Tehran’s importance as a dominant node in Iran’s urban systems. The minimum number of passenger flows were 1001 (inward) and 830 (outward) was attributed to Zanjan. According to the last column of Table 3, the value of centrality and power for Tehran is 271.17 and Mashhad with a centrality of 166.17, which is substantially less than Tehran, was ranked second. Bandar Abbas (111.75) and Ahvaz (111.18) were ranked third and fourth. The significant difference in the distribution of values and the considerable difference between minimum and maximum centrality (Table 4) for the vertices shows that the constellation of nodes in air flow is mono-centric, due to connectivity of the majority of nodes focused on Tehran. The total number of passengers moved via road public transportation fleet in 2006 was 93,174,000. Tehran had the maximum number of inward and outward passengers of 23,793,000 and 25,033,000 trips, respectively. The minimum number of inward and outward passengers was 730,000 and 786,000 respectively, for Birjand. According to Table 3, Tehran had a value of 234.92 and Isfahan with a centrality index of 150.12 was significantly less dominant than Tehran despite its ranking as Iran’s

second city in this analysis. The calculated centrality for Mashhad and Qom were 146.18 and 118.28 respectively, which positions these cities as the third and fourth most important nodes in the network. It can be concluded that because the distribution ranges of values (Table 4) for this dimension and the minor difference in values for cities placed at the bottom of the table in comparison with the values for the central vertices, that this network does not resemble a polycentric structure. The total size of the passenger flow by car for Iran was 393,457,227 with Tehran generating the maximum number of inward and outward passengers at 77,390,808 and 77,390,808 persons respectively. At the other end of the spectrum, the city of Ilam generated the minimum number of inward and outward passengers at 1,989,522 and 1,989,522 persons respectively. According to Table 3, the centrality value for Tehran was 203.57. Qom with a centrality of 157.33 was ranked second; Arak (151.57), Sari (147.29), and Qazvin (144.97) were ranked third to fifth with only small differences in relation to each other. It is remarkable that Tehran had achieved the minimum centrality and dominance values in regard to flows by car in comparison to two other networks with a more balanced distribution of values for other nodes. Therefore, it can be stated that the strength of centralization and the exclusion of the central vertex in this network is lower. According to Table 5, air passenger flows had the minimum network cohesion with an index of 242.3, which differs significantly to a networked constellation and it has greater similarity to discrete structures. The values of this dimension for flows by bus and flows by car were 480.84 and 670.05, indicating that they have more coherence as networked structures than is the case for air flows, at least topologically. According to the calculated values for the third dimension, air flows have the most centralized network (169.13), whilst flows by bus and car were ranked second and third (Table 6). The comparison of the results for network cohesion illustrates that although flow by car and bus have the characteristics of a networked structure in term of topology, they have considerable concentration with regard to the weight of interactions, whereas the mono-centric constellation is the best description for air flow in regard to both topology and weight of connections. According to the obtained values for the network symmetry dimension as presented in Table 6, it can be

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123

In

Tabriz

Urumia Ardebil

Isfahan

Ilam

Bushehr

Tehran

Shahrekord

Birjand

Mashhad

Bojnurd

Ahvaz

Zanjan

Semnan

Zahedan

Shiraz

Qazvin

Qom Sanandaj

Kerman

Kermanshah

Yasuj

Gorgan

Rasht

Khorramabad

Sari

Arak

BandarAbbas

1

2 3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18 19

20

21

22

23

24

25

26

27

28

11

1

3

1

2

2

2

3

6

1

8

5

2

9

1

19

2

1

24

8

1

10

3 1

6

In

Degree

City

No

11

1

4

1

3

2

2

3

7

1

7

5

1

9

1

19

2

1

25

8

1

9

3 1

5

Out

Strength

DT

Graph type

945,692

5465

45,558

23,502

64,680

30,701

8915

227,611

254,955

29,143

842,640

218,158

830

970,254

6858

1,496,108

43,332

8578

5,061,894

495,863

18,137

664,251

138,113 89,974

397,899

DW

Air passenger flow (A)

Network

968,320

5784

44,215

20,350

64,049

32,717

9964

229,874

258,408

26,698

835,752

237,780

1001

967,651

6679

1,466,815

42,843

7372

5,047,480

505,429

18,322

663,966

142,468 91,328

392,798

Out

111.75

45.04

55.80

50.89

56.16

53.89

51.04

65.63

71.39

51.22

98.00

67.75

48.45

111.18

49.93

166.17

54.36

50.02

271.17

83.79

50.59

89.70

61.31 54.83

78.43

Centrality and power*

13

18

21

14

23

19

7

24

21

26 21

15

24

11

7

14

23

6

27

7

15

29

16

19

28

18 12

21

In

13

17

21

15

21

21

6

23

20

25 13

18

23

10

10

14

21

11

29

10

15

29

17

22

27

18 10

20

Out

Degree

DT

1,002,000

2,422,000

3,406,000

2,196,000

2,376,000

2,116,000

791,000

2,902,000

1,588,000

2,923,000 2,999,000

1,639,000

3,313,000

1,466,000

1,592,000

959,000

2,739,000

876,000

6,116,000

786,000

2,008,000

25,033,000

1,309,000

1,102,000

6,566,000

3,793,000 1,371,000

3,635,000

In

Strength

DT

915,000

2,593,000

2,345,000

1,725,000

2,463,000

1,672,000

800,000

3,138,000

1,426,000

2,490,000 3,260,000

2,418,000

3,496,000

1,799,000

1,756,000

1,145,000

2,430,000

1,113,000

6,370,000

730,000

2,045,000

23,793,000

1,178,000

1,103,000

7,057,000

3560000 1,279,000

4,012,000

Out

Passenger flow by bus (B)

Table 3 Centrality and power of vertices at defined indices in air flow, flow by bus, flow by car

69.47

102.08

114.31

88.65

110.83

100.21

60.05

109.25

87.48

118.28 100.76

99.61

107.44

70.15

79.94

80.80

97.20

68.48

146.18

63.95

83.40

234.92

77.39

87.38

150.12

102.43 77.19

109.91

Centrality and power*

29

29

29

28

28

28

23

28

29

29 27

28

29

27

28

27

29

24

29

24

28

29

28

27

29

28 28

29

In

29

29

29

28

28

28

23

28

29

29 27

28

29

27

28

27

29

24

29

24

28

29

28

27

29

28 28

29

Out

Degree

DT

2,079,364

11,878,878

12,847,696

3,613,505

8,442,088

4,664,190

1,814,788

4,376,260

3,244,925

13,061,156 4,461,536

10,322,887

5,096,237

1,019,701

5,506,742

3,651,450

2,040,588

2,280,771

4,883,192

1,155,861

9,799,707

38,657,952

1,825,702

995,047

15,403,364

5,854,743 3,142,574

7,343,877

In

Strength

DT

2,066,039

11,874,364

12,830,736

3,631,426

8,439,049

4,638,992

1,812,563

4,363,614

3,198,666

13,097,873 4,463,488

10,329,371

5,089,090

1,018,735

5,505,328

3,651,886

2,032,644

2,281,221

4,924,791

1,156,612

9,721,490

38,732,860

1,831,106

994,475

15,438,596

5,841,564 3,143,230

7,362,380

Out

Passenger flow by car (C)

101.75

151.57

147.29

105.53

125.74

111.19

84.51

102.08

103.91

157.33 98.48

144.97

105.21

94.55

126.25

107.61

103.14

87.53

108.12

86.38

120.24

203.57

98.26

94.68

136.87

103.69 102.69

111.04

Centrality and power*

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Yazd

2

4

2

4

‘‘D’’ is a contraction of ‘‘direct’’; ‘‘T’’ is a contraction of ‘‘topological’’; ‘‘S’’ is a contraction of ‘‘symmetry’’ and ‘‘w’’ is a contraction of ‘‘weighted’     þ Betweenness þ ðInþOutÞ2Closeness þ Eigen vector * Centrality and power ¼ ðinþoutÞStrength 2

102.93

112.32 5,373,672

1,882,757 1,887,910

5,375,930 29

29 29

29 113.08

81.49 1,050,000

4,013,000 3,004,000

1,146,000 18

19 19 2367

134,753

2724 Hamedan

30

Out In

In 29

Out

133,348

52.15

18

Out In Out In

Strength Degree Degree City No

Strength

DT Graph type

DW

Air passenger flow (A) Network

Table 3 continued

61.65

Out In Out In

Strength Degree

DT DT DT DT

Centrality and power*

Passenger flow by bus (B)

Centrality and power*

Passenger flow by car (C)

Centrality and power*

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concluded that all three types of flows are symmetrical. It is worth mentioning that generally, in comparison with flows such as money, information and goods, the flows of people are substantially symmetrical throughout the year because permanent residential locations facilitates balanced interactions between people’s homes and their destinations. It seems that differences between calculated values for each index and the highest possible values (200) are due to changing of the transportation mode when returning and infinitesimal errors in the data records and calculations. The communities and levels of networks are represented in Figs. 4 and 6 (‘‘Appendix’’). It indicates that for air flows, which resembles a mono-centric network, that is a rather incoherent and completely concentrated constellation, only two communities of vertices are detectable and that there is an absence of the clusters in the other networks. With air flows, the first community is comprised of Tehran and regional cities whilst the other nodes form a community of peripheral and dependent cities without making a specific cluster since they are in functional relations with only Tehran. Terrestrial flows of people by car or bus tend to be restricted by distance and the median cities are the first interconnected nodes before reaching Tehran on longer trips, hence the number of achieved clusters for the flows by bus and car is more. In the second network, six functional regions were detected in which dominant cities play the role of regional centers as demonstrated by their interactions with other peripheral cities. For example, in the south west region of Iran, Bushehr, Shiraz, Ahvaz and Yasuj have formed a functional region in which Shiraz and Ahvaz are the dominant cities. In the third network, nine clusters have been detected, which shows that the locational interdependencies in the flows of people by car is higher than for the flows by bus and that they have occurred at smaller distances.

Discussion The findings indicate that Tehran as the prime city of Iran’s urban system completely dominates all other nodes. None of Iran’s networks can be characterized by a polycentric constellation in which some regional cities with similar centrality and dominance exist but without any superiority over another. For air flows, the significant difference between the centrality values for

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GeoJournal Table 4 Descriptive statistics of centrality and power of vertices Network

Number of vertices

A

27

B

30

C

30

Mean

SD

Variance

Amplitude

Maximum

Minimum

76.38

46.53

2164.86

226.12

45.04

271.17

99.75

32.92

1083.65

174.87

60.05

234.92

114.65

25.1

630.09

119.06

84.51

203.57

Table 5 Network cohesion at defined indices Network/indices

A

Density

B

C

19.66

61.61

96.09

75.44 79.44

39.72 39.72

4.04 4.04

59.19

3.5

0.04

In

78.51

54.58

7.42

Out

85.61

55.04

7.42

C1

82.9

77.4

C2

61.4

77.37

96.5

17.68

51.9

90.1

48.5

12.03

Centrality In Out Betweenness centrality Closeness centrality

Clustering coefficient

Transitivity Eigen vector centrality Network cohesion*

242.3 

 * Network Cohesion ¼ Density þ 100  ðinþoutÞ 2Centrality C1 þC2 2

96.6

1.19

480.84 670.05   Centrality þ ð100  Betweenness CentralityÞ þ 100  ðInþOutÞ Closeness þ 2

þ Transitivity þ ð100  Eigen Vector CentralityÞ

Table 6 Network strength and network symmetry at defined indices Network/indices

A

B

C

Strength In Out Weighted clustering coefficient

19.27

35.8

12.5

19.22 54.13

33.77 60.04

12.53 89.03

Weighted eigen vector centralitya

104.01

91.65

93.07

Network strength*

169.13

166.40

116.56

Interaction symmetry

0.986

0.946

Node symmetry

0.986

0.946

Network symmetry** * Network Strength ¼

193.43 

ðinþoutÞ Strength 2



188.37

0.994 0.994 199.26

þ ð100  Weighted Clustering CoefficientÞ þ Weighted Eigen Vector Centrality

** Network Symmetry ¼ Interaction Symmetry þ ð100  Node SymmetryÞ a

The differences in the obtained results depict a substantial differentiation in the indices which define the network strength locally and globally

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Fig. 4 Spatial configuration in air flow (a), road passenger flow by bus (b) and road passenger flows by car (c)

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Fig. 5 Graphical representation of spatial configuration of the Iran urban system

Tehran and Mashhad and the considerable number of cities with similar minimal values typifies a constellation with a mono-centric spatial pattern (Fig. 5). For flows by bus and flows by car, the smaller difference between the centrality values of cities located at the top of the table compared to the more equal range of values amongst other nodes demonstrates the distinguishing features of these networks from that evident for air flows. The centrality of inflows by car for Tehran was the minimum when compared to the other two networks. In addition, the comparison of centrality values for vertices at the top of the table in each of the three networks depicts a more balanced distribution of centrality among vertices for the flows by bus in comparison with the air flows. This situation demonstrates that, although calculated values reject the possibility of a polycentric structure for flows by bus and flows by car networks, they reduce their similarity with air flows. In this networks in many cities are interconnected only with Tehran, air flows are highly mono-centric; however, for flows by bus and flows by car as a result of connections between multiple nodes, the

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dominating role of Tehran over regional cities is reduced. The results of the analysis for the network cohesion dimension clearly show that Mashhad, Bandar Abbas, Ahvaz and Shiraz had substantially more interactions with Tehran than for air flows despite being located at long geographical distances from the central node of the network. It should be said that air flows had increased the movement and fluidity of people around Iran, inducing long-distance travel between cities and reducing the effect of distance as an exclusion factor. However, air networks in comparison with terrestrial modes, due to sensitivity to distance and demand factors, does not play a significant role in shorter geographical distances where terrestrial flows are dominant in the formation of interurban interactions. Further, inter-urban relations for flows by car involve more limited geographical distances which occur frequently but are not necessarily daily. As a result, Qom, Arak, Sari, and Qazvin, which are closer to Tehran geographically, achieve superior positions in this network. This can be explained as a reflection of flows by car being the most effective travel mode in

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facilitating local relations that are limited to their geographical hinterland, despite there being many relations at the level of regions close to Tehran. In addition, unlike other transportation modes such as aviation, rail and bus that require minimum demand to justify services with direct connection between cities, travel by car maximizes access between origin and destination cities which enhances the ease of movement of people and their utility of travel. The strong representation of regional cities (such as Isfahan, Mashhad, Tabriz, and Shiraz) in the terrestrial flows of people causes direct connections between cities located in functional regions and regional cities rather than with Tehran. This situation affects the spatial organization of nodes by reducing the Tehran’s dominance of regional cities and provides the basis for the formation of functional regions over the longer term, notwithstanding the fact that the air flows in such regions are not detectable. One of the reasons that explain formation of clusters despite an absence of air flows is the lack of cities at the median level that can attract significant air flows of passengers. The limitation of terrestrial extent and the capacity of an aerial network to facilitate long-distance travel do not allow median cities to have significant role in air flows, because the distances between these cities and peripheral nodes are relatively short and are substantially covered by other more cost effective and efficient terrestrial modes of transportation. However, terrestrial flows with significant interactions between peripheral and regional/median cities, have resulted in various communities of vertices that define functional regions and market areas which make them similar to poly-cluster constellation. Regional centers that have a strong connection with Tehran result in a multi-level configuration with the centrality of Tehran at the primary level and the centrality of regional cities at a secondary level. This difference in the social structure of each flow highlights substantial differences in representing the spatial organization of urban systems.

Conclusion This study attempted to present a more complete methodology on the study of a spatial constellation of urban systems of Iran from an interaction approach. The provision of empirical evidence from different types of flows of people including air passenger flows,

passenger flows by bus and car, has produced various spatial constellations modeling the flows of people. In this study, a network was described as having a set of vertices and lines between them that consequently has a community structure (i.e. the first dimension),a centrality and dominance of vertices, which determines the magnitude of vertices and network cohesion, network strength and network symmetry (i.e. the second to fourth dimensions) which in turn are respectively responsible for distribution, strength and direction of lines in the network. In addition, the fifth dimension, Community and Level, was proposed to determine the hierarchical structure of the network. The resulting spatial constellation in respect of the values obtained for the five dimensions reflected particular attributes of a unique spatial network. From the scientific literature, the results obtained for each of the dimensions were a combination of calculated values that yield systematically defined indices. These indices were able to assess different aspects of spatial constellations. With regard to the flows of people by air or terrestrial transport, the methodology conveys substantial and fascinating differences that are indicative of distinct space-place interactions in progressing the understanding of urban systems. The empirical findings demonstrated that by utilizing the centrality and power of vertices for all passenger flows of people, Tehran was confirmed to be the dominant city of Iran’s urban systems; hence the spatial constellation of the three networks is considerably different from a polycentric spatial pattern in which a number of cities with similar centrality act have similar levels of dominance. With the air flows, only a mono-centric spatial model was determined to be valid in explaining the urban spatial configuration, because of the significant differences between the centrality obtained for Tehran, Mashhad and other cities of lower spatial levels. In comparing flows by car with air flows and flows by bus, the minimum centrality belonged to Tehran; whilst, the centrality and dominance dimension for other vertices had a more balanced distribution. This feature means that the organization of cities in territories and the existence of more cities at the median levels of the hierarchy have reduced the importance of Tehran in favor of Iran’s regional cities. Therefore, it can be stated that in comparison with the other two flows, centralization and exclusiveness of the central city in this network is lower.

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In regard to the second dimension, network cohesion, air flows represent the lowest level of cohesion when compared to the other two terrestrial flows which had the highest cohesion respectively. This occurred because Mashhad, Bandar Abbas, Ahvaz and Shiraz are all located at further geographical distances to the network central city (Tehran), yet were able to achieve efficient interactions with Tehran. Air flow increased the movement and fluidity of people’s long-distance interactions and improved people’s access to distant places thereby reducing the effect of distance as an exclusion factor, despite terrestrial flows not playing a significant role for these cities due to sensitivity to distance and demand factors in comparison with travel by air. Inter-urban relations as reflected by flows by car involve more limited geographical distances that can be travelled by passengers terrestrially and frequently. That is why Qom, Arak, Sari, and Qazvin that are closer to Tehran geographically, are regarded as superior cities in this network. The expansion of the terrestrial transportation fleet and its lower costs in comparison with aviation in establishing direct travel routes between many of the cities has helped to increase passenger flows by bus. According to the results of network symmetry and dimensioning analysis, the annual flows of people are nationally symmetrical since people create symmetrical flows due to their connection and dependency to their residential location. The third dimension, network strength, shows that air flows had the most concentrated network whilst flows by car and flows by bus respectively are more de-concentrated networks. It is worth mentioning that flows by car and flows by bus, despite having topologically networked structures in respect of network strength, are more concentrated. The existence of regional cities (such as Isfahan, Mashhad, Tabriz, and Shiraz) located in the center of functional regions, developed increased interaction with regional cities instead of Tehran, which results in the shaping of a multi-level spatial organization and hierarchy, thereby reducing the role of Tehran in favor of other cities despite air flow not being detectable in many regional cities. Therefore, according to the community and hierarchical levels dimension, only two communities of vertices were detectable and recognition of the clusters differed from the other two flows. That is to say, one cluster was comprised of regional cities and other cities without forming a specific cluster—since they are in functional relations just with Tehran—thereby creating a community of

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peripheral and dependent cities. For terrestrial flows of people, especially by car mode, where movements are limited to the geographical hinterland of cities that can be travelled terrestrially, various interactions between peripheral cities and regional cities resulted in the formation of various communities of vertices from the communities that define functional regions by arranging them in a vertical hierarchy like a clustering model. Regional centers and their strong connection with Tehran resulted in a multi-level model with the centrality of Tehran at a primary level and the centrality of regional cities at a secondary level. Whereas it seems that the theoretical and methodological fundamentals in this paper can represent and describe an urban networks configuration, the absence of relevant flow data classified by the purpose of travel, has prevented research insights into how the economic attractiveness of destination cities influences travel demand. In addition, the lack of flow data over regular periods prevents the study of urban network evolution over time; to the extent that different configurations of urban systems evolve over time, the application of a proposed framework can be used to monitor the developments of urban systems and it would yield insights into the dynamics of urban systems. The proposed framework can be applied to other types of flow data: flows of daily commuters, goods, money, information and so forth; nevertheless, depending on the type of flow, some modifications of the interaction indices may be necessary, especially the directionality of flows needs to be taken into account. Finally, we believe that other factors such as geographical and socioeconomic factors are of great importance to urban systems and the analyzing of their reciprocal effects on an urban configuration is a question that can be pursued in further studies. Acknowledgments The authors would like to thank Dr. Amirreza Mamdoohi, Mrs Tayyebeh Shorkrnia and two anonymous reviewers for their valuable and insightful comments and suggestions which helped us to improve the manuscript. Compliance with ethical standards Conflicts of interest None.

Appendix See Fig. 6.

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Fig. 6 Functional regions and hierarchy of city system at air flow (a), flow by bus (b) and flow by car (c)

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