Classification of Urban Street Networks Based on Tree-Like

sustainability

Article Classiﬁcation of Urban Street Networks Based on Tree-Like Network Features

Baorui Han 1 , Dazhi Sun 2,*, Xiaomei Yu 1, Wanlu Song 1 and Lisha Ding 1

1 Department of Traﬃc Engineering, College of Automobile and Traﬃc Engineering, Nanjing Forestry University, Nanjing 210037, China; [email protected] (B.H.); [email protected] (X.Y.); [email protected] (W.S.); [email protected] (L.D.) 2 Department of Civil and Architectural Engineering, Texas A&M University-Kingsville, Kingsville, TX 78363, USA * Correspondence: [email protected]

Received: 16 December 2019; Accepted: 10 January 2020; Published: 15 January 2020

Abstract: Urban street networks derive their complexity not only from their hierarchical structure, but also from their tendency to simultaneously exhibit properties of both grid-like and tree-like networks. Using topological indicators based on planning parameters, we develop a method of network division that makes classification of such intermediate networks possible. To quantitatively describe the differences between street network patterns, we first carefully define a tree-like network structure according to topological principles. Based on the requirements of road planning, we broaden this definition and also consider three other types of street networks with different microstructures. We systematically compare the structure variables (connectivity, hierarchy, and accessibility) of selected street networks around the world and find several explanatory parameters (including the relative incidence of through streets, cul-de-sacs, and T-type intersections), which relate network function and features to network type. We find that by measuring a network’s degree of similarity to a tree-like network, we can refine the classification system to more than four classes, as well as easily distinguish between the extreme cases of pure grid-like and tree-like networks. Each indicator has different distinguishing capabilities and is adapted to a different range, thereby permitting networks to be grouped into corresponding types when the indicators are evaluated in a certain order. This research can further improve the theory of interaction between transportation and land use.

Keywords: planning parameters; street network; network division; tree-like network

1. Introduction The geometric structure of the street network is determined by the functions the network servers for as well as the physical geographical context. In most cases, the road network has a fixed form because of the nature of the area that it serves; the density and pattern of a network of street blocks are usually determined by location and history. Boeing analyzed 27,000 U.S. street networks, including metropolitan, municipal, and residential areas, and discussed the types of connection (T-intersection ratio, X- intersection ratio, and cul-de-sac ratio) for different types of street networks. This is a remarkable feature of the network form between the city center and the suburbs; that is, the network located in a center usually has a grid-type structure, while those located in suburbs commonly have a branching shape, like that of a tree or a river [1].Other street networks are sometimes classed as belonging to one or the other of these two patterns, but they often have aspects of both; at small scales, there seems to no clear border between grid-like and tree-like patterns distinguishable by conventional traffic planning indicators, such as density and road interval.

Sustainability 2020, 12, 628; doi:10.3390/su12020628 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 628 2 of 13 Sustainability 2020, 12, x FOR PEER REVIEW 2 of 13

Figure 11 showsshows howhow streetstreet networksnetworks typicallytypically changechange withwith location,location, apparentlyapparently evolvingevolving fromfrom grid-like to tree-like. The intermediate stages raise several questions.questions. How much does the actual street network at a given stage vary from an ideal grid? Do these irregular-looking networks in fact conform to several basic types?types? If If so so,, what indicators can be adoptedadopted forfor furtherfurther division?division? From Figure 11,, the existence of representative street network types in different diﬀerent regions of cities may be inferred, thereby suggesting potential lawslaws governing urban network patterns.patterns.

FigureFigure 1. 1. FourFour representative representative street street network network types types in in different diﬀerent regions of a city.

Brindle proposedproposed that that there there are are only only two two major major types types of street of networkstreet network structures: structures: the grid the network grid networkand the treeand network, the tree distinguishednetwork, distinguished by the degree by th ofe connectivity degree of connectivity of the roads of [2 ].the This roads viewpoint [2]. This is viewpointalso the starting is also pointthe starting of the presentpoint of paper.the present However, paper. this However, theory doesthis theory not address does not the address question the of questionhow exactly of how the restexactly of intermediate the rest of intermediate networks are networks different. are Due different to its strict. Due hierarchical to its strict and hierarchical isolating andcharacteristics, isolating characteristics, a tree-like network a tree-like is thought networ to guaranteek is thought pedestrian to guarantee safety pedestrian and reduce safety unwanted and reducethrough unwanted traffic. Although through it hastraffic. been Although applied init urbanhas been planning applied practice in urban by planning planning pioneers practice since by planningthe 1930s pioneers [3,4], there since is still the no193 clear0s [3,4], theoretical there is answer.still no clear theoretical answer. In the aspect of of urban urban geometry, geometry, Strano et al. [5] [5] divided the European urban road network into differentdifferent groups by principal component analysis. However, However, because because the the research research is is based on the statistical analysis of the macro urban structure, the results cannot have an impact on small regional land planning. Von Von and and Jaber Jaber systematically anal analyzedyzed the relationship between the structure and texture ofof urban urban road road network network and and cultural cultural characteristics characteristics in the in Middle the Middle East, and East, discussed and discussed measures measuresto improve to the improve traditional the traditional Arab road Arab network road combined network combined with Western with ideas Western [6]. ideas [6]. Developing a method toto describedescribe thethe structuralstructural di differencesfferences of of networks networks by by planning planning indicators indicators is isalso also a dia difficultfficult issue. issue. Traditionally, Traditionally, the the indicators indicators adopted adoptedin in street-networkstreet-network planningplanning have usually been relatedrelated toto thethe geometry geometry of of the the network: network: distance, distance, density, density, area, area, etc. etc. However, However, the values the values of these of theseindicators indicators for the for two the kinds two of kinds networks of networks may sometimes may sometimes be very close, be very even close, when even huge when differences huge differencesexist in patterns exist andin pa functions.tterns and functions. In recent years, research research on on street network structure structure has has mainly mainly focused focused on on three three aspects: aspects: hierarchical structure,structure, connection connection structure, structure, and and layout layout structure structure [7]. Hierarchical [7]. Hierarchical structure structure is usually is usuallyrelated torelated the internal to the compositioninternal composition of the network, of the whichnetwork, has which an important has an impactimportant on the impact distribution on the distributionof traffic flow. of traffic Jiang [flow.8] and Jiang Buhl [8] et and al. [ 9Buhl] have et providedal. [9] have new provided evidence new as ev toidence how a as city to networkhow a city is networkself-organized is self-organized for available mobilityfor available by using mobility geographic by using information. geographic Marshall information. described Marshall network describedforms which network fundamental forms which impacted fundamental travel behavior, impacted distribution travel behavior, of homes distribution and workplaces, of homesland and use, workplaces,and urban form land [10use,]. Xieand andurban Levinson form [10]. proposed Xie and three Levinson new measures, proposed including three new heterogeneity measures, including(entropy), heterogeneity connection pattern, (entropy), and connection continuity, patt specificallyern, and examining continuity, the specifically structure examining of urban road the structurenetworks of [11 urban]. Barthelemy road networks and Flammini [11].Barthelemy have shown and Flammini in their study have shown of street in networks their study that of instreet the networksabsence of that a global in the design absence strategy, of a the global development design strategy, of many dithefferent development transportation of many networks different does transportationfollow a simple, networks general mechanismdoes follow [a12 simple,]. general mechanism [12]. The search for a relationship between street network structure and urban land use has become a major research trend [13]. Researching hierarchical and functional structure, Southworth and Ben-Joseph applied spatial syntax theory to analyze the connection and accessibility of street Sustainability 2020, 12, 628 3 of 13

The search for a relationship between street network structure and urban land use has become a major research trend [13]. Researching hierarchical and functional structure, Southworth and Ben-Joseph applied spatial syntax theory to analyze the connection and accessibility of street networks [4]. This research was partly successful in interpreting how common people understand the spacious structure of a street network by their experiences. Marshall et al. [14], Southworth et al. [15], and Lovegrove et al. [16] used network density, connectivity, and presence of cul-de-sacs, respectively, as essential indicators for analyzing the connection effect and topological relationships of the network. These results show that street network characteristics do play a role in road safety outcomes. Derrible observed the network complexity and robustness of 33 metro systems around the world [17], and testified that the structure of street networks, therefore, is a result of the interplay between travel cost minimization and efficient land use. Marshall, Gil et al. used a large amount of data and a variety of analysis methods to study the street network, proposed a network modeling method, and outlined the main street network model features and the complex relationship between different network models [18]. Boeing0s research on the structure of street networks, which calculates the structural indicators of street networks around the world and classifies them into clusters, helped to reveal the scope and nuances of street networks [19]. Shi and Wang believed that the street network structure is not simply a hierarchical, connection, or layout structure, but an organic combination of the three [20]. Porta et al. analyzed the structure and function of urban road network with spatial syntax, which showed that spatial syntax can analyze the in-depth connotation and internal organization of urban road network [21]. In addition, the spatial structure analysis of complex networks has also made important breakthroughs. For example, Mocnik’s research into polynomial volume law verified that the spatial dimension of urban road networks is very stable, but the concentration is quite different [22,23]. These studies have an important reference for later network type identification and network attribute function analysis. These research results not only show that the road network structure has many variations, but also indicate that the topological parameters of the road network can explain these changes.

2. Methodology In this paper, we attempted to redeﬁne the tree-like street network and analyze its basic topological features. Based upon several reasonable properties which a street network should possess, we then constructed several basic network patterns, and showed real-world examples of these patterns from various real cities in China and elsewhere. By calculating the topological parameters of each network, a comparative analysis was carried out.

2.1. The Topological Features of the Tree-Like Street Network In topology, a pure tree-like pattern is called a standard tree graph. By deﬁnition, a tree graph is a connected graph that is acyclic (i.e., no sub-graph of the network includes a circle graph). Additional topological characteristics of a tree graph are as follows: (1) Its degree (number of vertices) V is exactly one greater than the number of its edges E; (2) there exists only one path connecting any two separate nodes; and (3) all connected sub-graphs are also tree graphs [24]. In the real world, however, there are almost no tree-shaped networks in the pure topological sense. In a physical street network, traﬃc characteristics as well as topology should be taken into account. There are three distinct features that can be used to distinguish between a tree network and a grid-like network:

(1) As is usually obvious by inspection, tree-like street networks have a clearer and more deﬁned hierarchical structure than grids. This condition is necessary for a network to be tree-like; in traﬃc engineering terms, the artery road runs through the entire area, while the branch road clearly serves a smaller one. A road is only allowed to connect with roads of the same grade or Sustainability 2020, 12, 628 4 of 13

next grade roads. For example, expressway could connect with another expressway or an artery street, but not a local branch. (2) There exist only a few route switches of different length between any two interior points of a tree-like network. This is an essential difference from the grid street network; it is a necessary Sustainabilityand su 2020fficient, 12, x conditionFOR PEER REVIEW for a network to be a tree network. In most cases, fewer loop routes4 of are 13 found in tree-like street networks. The scarcity of cycles alone, however, is not enough to judge networkwhether is tree-like. a network It is is also tree-like. necessary It is also to confirm necessary if tothese confirm cycles if thesecan provide cycles can multipath provide like multipath a grid network.like a grid network. (3) (3)There There are are more more T-type T-type intersections intersections and and broken broken roads roads inin thethe tree-liketree-like streetstreet system. Undoubtedly,Undoubtedly, these these T-type T-type intersectionsintersections and broken and broken roads roads reduce reduce alternative alternative paths paths for traffic for tra flow,ffic but theyflow, provide but they a more provide secure a more environment secure environment and the typical and the appearance typical appearance characteristics characteristics of a tree-like of road anetwork. tree-like road network.

2.2.2.2. Abstracted Expression of Tree-Like StructureStructure inin thethe StreetStreet NetworkNetwork This paper is is based based on on the the classification classiﬁcation of street of street networks networks proposed proposed by Chan by Chan et al. et[25]. al. Their [25]. Theirresearch research resultsresults divided divided a specific a speciﬁc road network road network model model into four into basic four styles basic of styles street of network street network which whichare laid are out laid in outFigure in Figure 2 [26].2[ These26]. These patterns, patterns, which which conform conform to the to thereal-world real-world design design requirements requirements of ofa street a street network, network, can can often often be beobserved observed in incities. cities.

Figure 2. Abstract structures of four kinds of urban street networks.networks.

(1) (1)Pure Pure tree-like tree-like network network pattern pattern (Figure (Figure2a). There 2a). There are obvious are obvious backbone backbone roads through roads through the region, the region,while while T-type T-type cross cross and end-roadsand end-roads are also are often also adopted,often adopted, forming forming a low-connected a low-connected level network level networkstructure. structure. This This type type of street of street network network helps tohelps protect to protect the privacy the privacy of the residents of the residents and the stabilityand the stabilityof the of the traffi trafficc but but may may be less be less robust robust than than the others.the others. (2) (2)The The cul-de-sacs cul-de-sacs network network pattern pattern (Figure (Figure2b).There 2b). There are several are several trunks trunks passing passing through through a region a regionwith with many many end-roads. end-roads. This This type type of of network networkhas has goodgood accessibility,accessibility, butbut mightmight bebe weakerweaker onon interiorinterior connectivity connectivity than thanthe others. the others. (3) (3)T-type T-type network network pattern pattern (Figure (Figure2c). This 2c). street This networkstreet network is similar is tosimilar a pure to grid-shaped a pure grid-shaped network, network,but thebut T-type the T-type intersections, intersections, while possiblywhile possibly reducing reducing the connectivity, the connectivity, may improve may theimprove efficiency the efficiencyof trunk of trunk transportation. transportation. (4) (4)Pure Pure grid-like grid-like network network pattern pattern (Figure (Figure2d). The 2d). connectivity The connectivity within within this network this network is higher is than higher in than thein the others; others; however, however, due todue the to excessive the excessive number number of intersections of intersections and the and short the distance short betweendistance betweenthem, them, transportation transportation efficiency efficiency is usually is usually lower. lower. The street network system is generally broken into three to five functional classes. The Theconnection street network between system different isgenerally classes ensures broken the into order threely to running five functional of traffic; classes. thus, for The example, connection an betweenarterial road different can only classes can ensures join directly the orderly to a sub-arterial running of street traffic; or thus, an expressway, for example, not an to arterial local lanes. road can only canFigure join 3 directlyshows a to street a sub-arterial network constructed street or an expressway,according to not orderly to local connecting lanes. rules, resulting in a tree-likeFigure appearance.3 shows a street This networkkind of network constructed can often according reduce to unnecessary orderly connecting through-traffic, rules, resulting guarantee in athe tree-like securityappearance. of entries and This exits kind of of local network branch canes, often and reduceeven improve unnecessary the environmental through-traffic, quality guarantee and thesafety security situation of entries of the region. and exits of local branches, and even improve the environmental quality and safety situation of the region. Sustainability 2020, 12, 628 5 of 13 SustainabilitySustainability 2020 2020, ,12 12, ,x x FOR FOR PEER PEER REVIEW REVIEW 55 ofof 1313

FigureFigure 3.3. TypicalTypical tree-liketree-like streetstreet networknetwork structure.structure.structure.

FigureFigure 4 4representsrepresents4represents another anotheranother special specialspecial form formform of ofof street streetstreet network, network,network, consisting consistingconsisting of ofof di differentdifferentfferent rectangles.rectangles. AlthoughAlthoughAlthough thisthis networknetwork lookslooks grid-like,grid-like, it it isis inin generalgegeneralneral didifficultdifficultfficult toto findfindfind multiplemultiplemultiple roadsroadsroads withwithwith similarsimilarsimilar lengthslengthslengths betweenbetweenbetween anyany twotwotwo pointspointspoints withinwithinwithin thethethe network.network.network. As As wewe havehavehave alreadyalreadyalready mentioned,mentioned,mentioned, thisthis kindkindkind ofofof mono-pathmono-path isisis aaa necessarynecessarynecessary andandand susufficientsufficientfficient conditionconditioncondition forfoforr a aa network networknetwork to toto be bebe tree-like. tree-like.tree-like. TheThe networknetwork conformsconforms tototo thethethe principleprincipleprinciple ofofof sequential sequentialsequential connectionconnectionconnection (i.e.,(i.e.,(i.e., eveneveneven thoughthoughthough aaa circular circularcircular sub-network sub-networksub-network existsexistsexists withinwithinwithin thethethe roadroadroad network),network), soso thatthat while whilewhile topolo topologicallytopologicallygically itit isis notnot not aa a treetree tree graph,graph, graph, itit it isis is neverthelessnevertheless nevertheless aa atreetree tree network.network. network.

Figure 4. Rectangle structure forming a tree-like street network. FigureFigure 4.4. RectangleRectangle structurestructure formingforming aa tree-liketree-like streetstreet network.network. 2.3. Differences between the Basic Patterns of the Road Network 2.3.2.3. DifferencesDifferences betweenbetween thethe BasicBasic PatternsPatterns ofof thethe RoadRoad NetworkNetwork The traditional indicators for describing the rationality of a road network, such as density, The traditional indicators for describing the rationality of a road network, such as density, grade,The and traditional length, are indicators largely concernedfor describing with the size rationality and appearance. of a road However, network, theysuch do as notdensity, well grade, and length, are largely concerned with size and appearance. However, they do not well reflectgrade, theand di length,fference are between largely the concerned internal relationshipswith size and and appearance. the composition However, of the they street do networks. not well reflect the difference between the internal relationships and the composition of the street networks. Accordingreflect the difference to the research between of Marshall, the internal the relation T-type ratioships can and e fftheectively composition distinguish of the the street pure networks. tree-like According to the research of Marshall, the T-type ratio can effectively distinguish the pure tree-like streetAccording network to the from research other kinds of Marshall, [10], but the the T-type problem ratio of dividingcan effectively mixed distinguish networks into the di purefferent tree-like types street network from other kinds [10], but the problem of dividing mixed networks into different onstreet a spectrum network from from pure other tree-like kinds to[10], pure but grid-like the prob remainslem of didividingfficult. mixed networks into different types on a spectrum from pure tree-like to pure grid-like remains difficult. typesIn on Figure a spectrum2, the mainfrom dipurefference tree-like between to pure (a) grid-like and (b) remains is whether difficult. there are multiple major roads In Figure 2, the main difference between (a) and (b) is whether there are multiple major roads runningIn Figure through 2, thethe region.main difference The most between significant (a) di anfferenced (b) is between whether (b) there and are (c) multiple is whether major there roads exist running through the region. The most significant difference between (b) and (c) is whether there end-roads.running through The di thefference region. between The most (c) and significant (d) is whether difference there between exist T-type (b) and intersections. (c) is whether Based there on exist end-roads. The difference between (c) and (d) is whether there exist T-type intersections. Based thisexist analysis, end-roads. it should The difference be feasible between to determine (c) and the (d) typeis whether of street there network exist T-ty by consideringpe intersections. the relative Based on this analysis, it should be feasible to determine the type of street network by considering the prevalenceon this analysis, of through it should roads, be cul-de-sacs, feasible to anddetermi T-typene intersections.the type of street Combined network with by previous considering research the relative prevalence of through roads, cul-de-sacs, and T-type intersections. Combined with previous resultsrelative [ 2prevalence,4], the penetrating of through street roads, ratio, cul-de-sacs, cell ratio, and and T-type T-type ratio intersections. are introduced Combined for network with previous division. researchresearch resultsresults [2,4],[2,4], thethe penetratingpenetrating streetstreet ratio,ratio, cellcell ratio,ratio, andand T-typeT-type ratioratio areare introducedintroduced forfor networknetwork division.division.

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3. Parameters Describing the Network Pattern

3.1. T-Type and X-Type Intersection Ratios The T-type and X-type ratios are the ratios of the number of T-type and four-leg intersections, respectively, to all intersections in a given area. If T-type and X-type intersections are the only ones that appear in a region, the T-type and X-type ratios of the street network add up to 1. These ratios can very easily be found by simple counting.

3.2. Penetrating Street Ratio A penetrating street (run-through road) is one that completely crosses an area of interest. The penetrating street ratio is the ratio of the number of run-through roads to the total number of roads in a speciﬁc area. This index directly reﬂects the number and proportion of trunk roads in the network, and the opening level of the region. As the value of this indicator becomes lower, the street network comes closer to having a tree-like structure.

3.3. Cul-De-Sac and Cell Ratios There are two types of road segments in a street network: cul-de-sacs (end streets) and ordinary road segments (cells, i.e., stretches of road between intersections). The cul-de-sac and cell ratios of a street network are the ratios of the number of end roads and cells, respectively, to the sum of all road sections in a region. In general, the sum of the cell ratio and the cul-de-sac ratio in a single network is 1. In a pure grid-like street network, there are no end roads, so the cul-de-sac ratio is 0 and the cell ratio is 1. In a real street network layout, the cul-de-sac and cell ratios of the street network both lie between 0 and 1.

4. Sample Analysis To analyze whether street network types in different regions have any identifiable differences, this study selected 15 urban street networks from around the world, having different shapes and characteristics, as samples. The number of 15 samples seems to be small, but considering the following reasons, this study considers that these samples show the reliability of the research objectives and results. Although the appearance of the city varies greatly, according to the analysis of Section 2.2., the main pattern differences of the urban road network lie in the form of intersections and the density of the road network. As a classification study, it is only necessary to find out the characteristics of the reference point or the reference network, and it is not necessary to identify all the networks one by one. In fact, relying too much on large-scale statistical data may not be able to accurately identify road network features, because some features may be submerged in the massive statistical values. In addition, about 30 road network samples were preliminarily selected in this study. In order to express the road network boundary and data distribution clearly, the city samples with similar or repeated patterns and parameters were removed. By extracting the values of basic attributes from map, such as road-section length, grade, type, and rank of intersections, several indexes of topological structure were evaluated, and then analyzed by ArcGIS software to compare with each other.

4.1. Principles of Sample Selection (1) Most of the street network samples come from historic Chinese cities, such as Nanjing and Suzhou. Others were taken from a classic scholarly work on streets and patterns [2]. (2) The samples represent diﬀerent parts of urban areas: new development zones, cores of downtown districts, ring areas around the city, and outer suburban residential areas. Sustainability 2020, 12, 628 7 of 13

(3) For convenience of comparison, each sample’s area was limited to four square kilometers Sustainability 2020, 12, x FOR PEER REVIEW 7 of 13 (2 km 2 km). Considering the inﬂuence of ground facilities or terrain features, such as railways × rivers,and an rivers,irregular an irregularboundary boundary was also wasacceptable also acceptable when the when sample the had sample an obvious had an obviousshape feature. shape Figurefeature. 5Sustainability shows Figure two 2020 5different, 12 shows, x FOR PEER twoexamples REVIEW di ﬀerent of urban examples areas of from urban the areas sample from set. the sample set. 7 of 13

rivers, an irregular boundary was also acceptable when the sample had an obvious shape feature. Figure 5 shows two different examples of urban areas from the sample set.

(a) (b)

Figure 5. Typical street network(a) samples. (a) Typical gird network (Nanjing);(b) (b) Typical tree0like

Figurenetwork 5. (LondonTypical Thames).street network samples. (a) Typical gird network (Nanjing); (b) Typical tree0like networkFigure (London 5. Typical Thames). street network samples. (a) Typical gird network (Nanjing); (b) Typical tree0like 4.2. Data Collectionnetwork (London and Analysis Thames). 4.2. Data Collection and Analysis The4.2. data Data sourceCollection collection and Analysis in this paper mainly used OpenStreetMap and ArcGIS to screen, extract,The construct, data source correct collection, analyze, in andthis abstractpaper main streetly network used OpenStreetMap maps in urban and core areas,ArcGIS urban to screen, areas, The data source collection in this paper mainly used OpenStreetMap and ArcGIS to screen, extract,and communities construct, .correct, OpenStreetMap analyze, and is a globalabstract collaborative street network mapping maps projectin urban that core can areas, provide urban its spatialareas, extract, construct, correct, analyze, and abstract street network maps in urban core areas, urban areas, data through various APIs (Application Programming Interface: are some predefined functions to and communities.and communities. OpenStreetMap OpenStreetMap is ais global a global colla collaborativeborative mapping mapping project thatthat can can provide provide its its spatialprovide spatialdata applications throughdata through and various developers various APIs withAPIs (Applicatio the(Applicatio abilityn tonProgramming accessProgramming a set of routinesInterface:Interface: based areare some onsome certain predefined predefined software functionsor hardware,functions to provide but to No provide applications need applications to access and the anddevelopers source developers code with orwith understandthe the ability ability to to the aaccessccess details aa setset of of theof routines routines internal based based working on on certainmechanism). certainsoftware software This or hardware, database or hardware, resource but Nobut needNo is veryneed to reliable.Theaccessto access the the source source method code code was oror understand simply to collectthe the details details and of screen ofthe the internalstreet networkinternal working examples,working mechanis mechanis extractm). Thism). street This database network database resource samples resource fromis isvery very OpenStreetMap, reliable.Thereliable.The methodmethod export was OpenStreetMapwas simply simply to to collectfiles, use andcollect Geo screen and Converter screen street street network software network examples, to convertexamples, extr them extractact tostreet ESRIstreet network Shapefiles,network samplessamples modify fromfrom the OpenStreetMap, OpenStreetMap, wrong paths in exportArcGIS OpenStreetMapexport software, OpenStreetMap and obtainfiles, files,use the Geouse relevant GeoConverter Converter attributes softwa softwa ofrere eachto to convert convert road segment themthem to ESRIESRI in the Shapefiles, Shapefiles, sample modify network. modify the wrong paths in ArcGIS software, and obtain the relevant attributes of each road segment in the Whenthe wrong processing paths inthe ArcGIS road network, software, the and edge obtain path the of each relevant geometry attributes was buofff eachered road by 0.1 segment km in order in the to sample network. When processing the road network, the edge path of each geometry was buffered by samplecollect thenetwork. “node When types” processing and “paths” the in road the network, road network. the edge path of each geometry was buffered by 0.1 km in order to collect the “node types” and “paths” in the road network. 0.1 kmThe in 15orderThe street to15 collectnetworkstreet network the samples “node samples ty maypes” bemay and seen be “paths” seen in Figure in in Figure the6. The road 6. samplesThe network. samples can can be dividedbe divided into into the the four basicThe patternfour 15 basicstreet types pattern network mentioned types samples mentioned previously may previously be (2.2): seen standard in(2.2): Figure standard rectangular 6. The rectangular samples grid, T-type,grid,can beT-type, cul-de-sacdivided cul-de-sac into based, the fourand purebasicbased, tree-like pattern and pure (seetypes tree-like Table mentioned1). (see Table previously 1). (2.2): standard rectangular grid, T-type, cul-de-sac based, and pure tree-like (see Table 1).

JianyeNewDistrict (Nanjing) New Town (Shanghai) Blythewood (US)

Figure 6. Cont. JianyeNewDistrict (Nanjing) New Town (Shanghai) Blythewood (US) Sustainability 2020, 12, 628 8 of 13 Sustainability 2020, 12, x FOR PEER REVIEW 8 of 13

Gaomiao road area (Nanjing) Sipailouarea (Nanjing) Acropolis (Athens)

Gulou District (Nanjing) Bayswater (London) Old Town (Suzhou)

Laguna West (UK) Xuzhuang Software (Nanjing) Thames Meade (London)

Daming road area (Nanjing) East Finchley (London) Jiangbei New District (Nanjing)

FigureFigure 6. 6.Street Street networknetwork diagram of of 15 15 samples. samples.

The four sample indicatorsTable (X-type 1. Parameter ratio, T-type values of ratio, sample cul-de-sac cities. ratio, and penetrating street ratio) were calculated, and are also marked in Table1. It can be seen that thePenetrating X-type and Types T-type ratios Serial X-Type T-Type Cul-de-Sac Network Location Street of were wellNumber correlated with pattern type. However,Ratio theRatio penetrating Ratio street ratio was loosely correlated with the X-type and T-type ratios. Therefore, the X-type and T-type ratio wereRatio selected Image as the ﬁrst JianyeNewDistrict factor to identify1 the tree-like attributes of the0.95 road network.0.05 0 0.92 A (Nanjing) The cul-de-sac ratio, on the other hand, did not correlate well with the pattern type. Figure7 2 New Town (Shanghai) 0.83 0.17 0.07 0.84 A shows the relationship of T-type ratio and cul-de-sac ratio for all the samples. 3 Blythewood (US) 0.71 0.29 0.06 0.67 A From4 Figure 7, Gaomiao the T-type area ratio (Nanjing) is seen to be 0.52 higher 0.48 than 0.65 in 0 most sample 0.50 cities. This B indicates that most urban5 streetSipailouarea networks (Nanjing) contained a0.33 large number0.67 of T-intersections.0.03 0.28 On the other B hand, the cul-de-sac6 ratio ofAcropolis most samples (Athens) was lower0.31 than 0.3.0.69 0.04 0.22 B 7 GulouDistrict (Nanjing) 0.30 0.70 0.2 0.26 B 8 Bayswater (London) 0.26 0.74 0.16 0.30 B 9 Old Town (Suzhou) 0.23 0.77 0.22 0.22 B 10 Laguna West (UK) 0.22 0.78 0.44 0.04 C 11 XuzhuangSoftware 0.19 0.81 0.33 0.17 C Sustainability 2020, 12, 628 9 of 13

Table 1. Parameter values of sample cities.

Penetrating Serial X-Type Cul-de-Sac Types of Network Location T-TypeRatio Street Number Ratio Ratio Image Ratio JianyeNewDistrict 1 0.95 0.05 0 0.92 A (Nanjing) 2 New Town (Shanghai) 0.83 0.17 0.07 0.84 A 3 Blythewood (US) 0.71 0.29 0.06 0.67 A Gaomiao area 4 0.52 0.48 0 0.50 B (Nanjing) Sipailouarea 5 0.33 0.67 0.03 0.28 B (Nanjing) 6Sustainability Acropolis 2020, 12, x FOR (Athens) PEER REVIEW 0.31 0.69 0.04 0.229 of 13 B GulouDistrict 7 0.30 0.70 0.2 0.26 B (Nanjing)(Nanjing) 812 BayswaterThames (London) Meade (London) 0.26 0.09 0.740.91 0.98 0.16 0.03 0.30 C/D B Daming road area 913 Old Town (Suzhou) 0.230.08 0.770.92 0.45 0.22 0.21 0.22 D B 10 Laguna West(Nanjing) (UK) 0.22 0.78 0.44 0.04 C 14 XuzhuangSoftwareEast Finchley (London) 0.08 0.92 0.67 0.09 D 11 Jiangbei New District 0.19 0.81 0.33 0.17 C 15 (Nanjing) 0.07 0.93 0.24 0.20 D Thames Meade(Nanjing) 12 0.09 0.91 0.98 0.03 C/D Notes: The(London) road network instances in the table are sorted by type. The types are (A) Pure grid-like networkDaming pattern, road (B) T-type area network pattern, (C) cul-de-sac network pattern and (D) pure tree-like 13 0.08 0.92 0.45 0.21 D network pattern.(Nanjing) East Finchley 14 The four sample indicators (X-type0.08 ratio, T-type 0.92 ratio, cul-de-sac 0.67 ratio, and penetrating 0.09 street D (London) ratio) wereJiangbei calculated, New and District are also marked in Table 1. It can be seen that the X-type and T-type ratios 15 0.07 0.93 0.24 0.20 D were well correlated(Nanjing) with pattern type. However, the penetrating street ratio was loosely correlated with the X-type and T-type ratios. Therefore, the X-type and T-type ratio were selected as the first Notes: The road network instances in the table are sorted by type. The types are (A) Pure grid-like network pattern, factor to identify the tree-like attributes of the road network. (B) T-type network pattern, (C) cul-de-sac network pattern and (D) pure tree-like network pattern. The cul-de-sac ratio, on the other hand, did not correlate well with the pattern type. Figure 7 shows the relationship of T-type ratio and cul-de-sac ratio for all the samples.

FigureFigure 7. Distribution 7. Distribution of of topological topological indexesindexes of of different diﬀerent road road network network samples. samples.

From Figure 7, the T-type ratio is seen to be higher than 0.65 in most sample cities. This indicates that most urban street networks contained a large number of T-intersections. On the other hand, the cul-de-sac ratio of most samples was lower than 0.3.

4.3. Data Analysis and Interpretation The above results shown that the variations of the indicators (the penetrating street, T-type, X-type, and cul-de-sac ratios) could be used to judge a given street network’s structural subtype. Sustainability 2020, 12, 628 10 of 13

4.3. Data Analysis and Interpretation The above results shown that the variations of the indicators (the penetrating street, SustainabilityT-type, X-type, 2020, 12 and, x FOR cul-de-sac PEER REVIEW ratios ) could be used to judge a given street network’s structural subtype. 10 of 13

• From Figure8a, it is obvious that, when the samples are listed in order of monotonically increasing • From Figure 8a, it is obvious that, when the samples are listed in order of monotonically T-type ratio, three distinct regimes emerge, namely T-type ratio [0,0.3), [0.3,0.9), [0.9,1.0]. increasing T-type ratio, three distinct regimes emerge, namely T-type∈ ratio ∈ [0,0.3), [0.3,0.9), [0.9,1.0].These three Theseparts three respectively parts resp correspondectively correspond to a pure grid-like to a pure network, grid-like a transitional network, a state transitional network, stateand anetwork, pure tree-like and a network. pure tree-like This method network. can This clearly method define can the clearly boundary define between the boundary pure tree- betweenand pure pure grid-like tree- roadand networks.pure grid-like However, road netw becauseorks. the However, indicator because values in the the indicator transitional values region in theare transitional very close together, region are it is very hard close to distinguish together, anyit is finerhard divisions to distinguish in that any regime. finer divisions in It can be seen from Figure8b that the penetrating street ratio and the X-type ratio are highly • that regime. • Itcoincident can be seen and from have Figure almost 8b the that same the general penetrat tendenciesing street in ratio the figure. and the When X-type the ratio value are of eitherhighly is coincidentmore than and 0.3, ithave can almost be used the to distinguishsame general a pure tenden gridcies road in the network figure. from When a rectangular-type the value of either street is morenetwork. than However,0.3, it can when be used the valueto distinguish is less than a pure 0.3, agrid pure road tree-like network road from network a rectangular-type and a T-shaped streetroad networknetwork. cannot However, be accurately when the identifiedvalue is less from than these 0.3, indicators a pure tree-like alone. road network and a T-shapedFrom Figure road8 b,network the trend cannot of the be cul-de-sacaccurately ratioidentified seems from to be these nearly indicators opposite alone. that of the X-type • • Fromratio, Figure but it might8b, the be trend more of active the cul-de-sac (i.e., have ratio more seems discriminating to be nearly power) opposite when that it of is closethe X-type to the ratio,area ofbut the it tree-likemight benetwork more active pattern. (i.e., Whenhave mo there cul-de-sac discriminating ratio power)[0,0.3), when the network it is close could to the be ∈ areapredicted of the totree-like be either network grid-shaped pattern. or T-type.When the When cul-de-sac the cul-de-sac ratio ∈ ratio [0,0.3),[0.3,0.5), the network the network could ∈ becould predicted be of the to cul-de-sacsbe either grid-shaped type. Finally, or when T-type. the cul-de-sacsWhen the ratiocul-de-sac[0.5,1.0], ratio the ∈ network [0.3,0.5), might the ∈ networkbe purely could tree-like. be of the cul-de-sacs type. Finally, when the cul-de-sacs ratio ∈ [0.5,1.0], the networkThe penetrating might be street purely ratio tree-like. is an important and effective indicator for objectively measuring the • • Thesimilarity penetrating of a general street ratio network is an to important a tree-like an network.d effective It hasindicator not received for objectively enough attentionmeasuring in theprevious similarity analyses. of a general network to a tree-like network. It has not received enough attention in previous analyses.

(a)

Figure 8. Cont. Sustainability 2020, 12, 628 11 of 13 Sustainability 2020, 12, x FOR PEER REVIEW 11 of 13

(b)

FigureFigure 8.8. RelationsRelations between between urban urban street street network network types types and indicators. and indicators. (a) Cities (a arranged) Cities arranged by increasing by increasingT-type ratio. T-type (b) The ratio. variation (b) The of variation X-type ratio,of X-type cul-de-sac ratio, cul-de-sac ratio, and penetratingratio, and penetrating street ratio street with streetratio withnetwork street types. network types.

5.5. Conclusions Conclusions and and Further Further Research Research ThisThis paper paper tries tries to to answer answer the the most most basic basic question question about about the the geometric geometric structure structure of of urban urban road road networks:networks: how how to to distinguish distinguish between between road road networks networks with with different diﬀerent geometric forms. FromFrom a a topological topological perspective, perspective, both both in in terms terms of of hierarchical hierarchical connections connections and and pattern pattern features, features, thethe tree-like tree-like characteristics concealedconcealed in in a a road road network network can can now now be recognized,be recognized, opening opening another another way wayto understand to understand the roadthe road system system besides besides the traditional the traditional grid grid paradigm. paradigm.

(1)(1) TheThe main main point point ofof thisthis paper paper is tois recognizeto recognize that allthat urban all urban road networks, road networks, instead ofinstead being classifiedof being classifiedas grids oras trees,grids mayor trees, be arranged may be on arrang a spectrumed on between a spectrum these extremes.between theseSubdividing extremes. the Subdividinggeometric structurethe geometric of the structure road network of the further road network can be e fffurtherective forcan researchbe effective and for engineering research andtechnology, engineering improvements technology, in landimprovements use, road safety, in land and transportationuse, road safety, effi ciencyand transportation in the future. (2) efficiencyThrough in statistical the future. analysis of road samples in different cities or regions, it has been found that (2) Throughthe differences statistical in geometric analysis of and road topological samples in characteristics different cities between or regions, the networksit has been mainly found come that thefrom differences the number in geometric and the type and of topological intersections, characteristics the density andbetween hierarchical the networks structure mainly of the come road fromnetworks, the number the proportion and the oftype broken of intersections, roads, and thethe numberdensity and proportionhierarchical of structure through-roads. of the roadTherefore, networks, a road the network proportion can be of classified broken accordingroads, and to howthe closelynumber it resemblesand proportion a tree-like of through-roads.network in terms Therefore, of these variousa road parameters. network can be classified according to how closely it (3) resemblesThis study a tree-like initially network divides in terms road of networks these various into parameters. four types (pure tree-like networks, (3) Thiscul-de-sac study networksinitially divides, T-shaped road networks, networks and into grid-shaped four types networks) (pure tree-like based networks, on properties cul-de-sac such as networks,non-circular T-shaped traffic, number networks, of end and roads, grid-shaped and number networks) of alternative based paths. on properties such as (4) non-circularThe research traffic, proves number that it is of possible end road tos, use and di numberfferent indicators of alternative in a certainpaths. order (X-type/T-type

(4) Theratio, research cul-de-sac proves ratio, that and it penetrating is possible street to use ratio) different to classify indicators road networks. in a certain Four order specific, ( X-type/T-typequantitative, well-definedratio, cul-de-sac indicators ratio, forand classifying penetrating the street small-scale ratio) structureto classify of road street networks. networks Fourare proposed. specific, quantitative, well-defined indicators for classifying the small-scale structure of street networks are proposed. Although the study has found some evidence of pattern differences between networks, Although the study has found some evidence of pattern differences between networks, some some defects existed in the research procedure. The largest problem is that it is difficult to collect defects existed in the research procedure. The largest problem is that it is difficult to collect attributed data, such as the class of road or the features of the nodes, from the e-map; this may reduce accuracy when analyzing the connectivity of local roads, especially for topological analysis. Sustainability 2020, 12, 628 12 of 13 attributed data, such as the class of road or the features of the nodes, from the e-map; this may reduce accuracy when analyzing the connectivity of local roads, especially for topological analysis. Secondly, this study also partly neglected road link attributes, street function, accessibility, and other factors that may further reflect the structure of the street network in some way. On the other hand, adding more indicators would very likely increase the difficulty of the research and the uncertainty of the results. Additionally, it is found that when different observation scales are used, the indicator value may change, owing to data filtering or boundary effects. This is of great significance for the fractal characteristics of the network, which are another important method of judging the hierarchy and self-similarity of the street system. On the whole, a tree-like network reflects the basic characteristics of a transportation network better than a grid-like network. Indeed, a grid-like road network can be transformed into a tree-like one by restricting the direction of traffic flow. Subsequent research on the road network form should not be limited to geometric parameters; the spatial layout of the traffic flow lines should also be considered. Having distinguished the different types of networks, the next step is to analyze the differences in traffic and land use benefits between different micropatterns. This research will promote technological compatibility and coordination between street network and other land use.

Author Contributions: Conceptualization, B.H.; methodology, B.H. and D.S.; software, L.D.; validation, X.Y. and D.S.; formal analysis, X.Y. and D.S.; investigation, W.S. and L.D.; resources, L.D.; data curation, W.S.; writing—original draft preparation, X.Y. and W.S.; writing—review and editing, B.H. and D.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Science and Technology Project of the Ministry of Housing and Construction (MHC) of China, grant number (2017-k2-008, to Han BR) and The APC was funded by China Scholarship Council (CSC) funding, grant number (201808320054, to Han BR). Acknowledgments: We thank Zhou Yu for the technical assistance with software analysis. He LL collected the examples of documentaries. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

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