The graph eliminates the flesh and blood, as represented by the sinuosities and the flows, for what is left is the skeleton. As in any skeleton, there are links joined at specific places. Skeletal structures have definite arrangements, although the specific arrangements may differ somewhat among different species and over time. By reducing the complex transportation network to its fundamental elements of nodes and links, it is possible to evaluate alternative structures, The Geography of Movement.
Having considered general categories of structure, the thesis now turns to matters of specific structural detail. As we shall see, the precise nature of what is being described is crucial: how structure is analyzed will depend to some extent on how structure is conceptualized, and what exactly is interpreted to be the 'structure' under analysis in the first place.
Contemporary advocacy for some kind of hierarchy incorporating different types of route and specific advocacy for route types such as 'connector streets', which are conceptualized in terms of their structural role in the network.
So far, we have noted that the structural role of such route types in a network is not well defined, it is not clear how to work out a robust and transparent means for relating one route type to another, structurally, in a hierarchy, to support these contemporary aspirations. In conventional transport networks, sections of road are commonly represented by links, and junctions by nodes. However, dealing at the level of component links loses some of the strategic or structural properties of networks. For example, the definition of route types and properties such as arteriality seem to rest on the recognition of continuous routes, rather than elemental links.
The aim of this chapter is to establish an effective means of analyzing urban structure, based on the properties of routes. This will involve, firstly, a review and critique of existing analytic techniques for quantitatively describing different aspects of urban structure. The different ways that these tackle description will assist in understanding urban structure itself. Secondly, the chapter will develop an analytic method to suit the particular needs of urban structure as constituted by transport routes.
7.1 Quantitative descriptors of urban structure
As we saw , street patterns may be described qualitatively with terms such as 'grid' and 'grid-like'. However, as Groth implies, structures of a given 'type' may be differentiated at a finer level. This chapter therefore attempts to gain a finer-resolution appreciation of the morphological continuum.
In contrast to the qualitative descriptors of Chapter 6, which were all trying to describe the same thing - some particular pattern - but which came up with different results, many possible quantitative descriptors apply to parts of networks, describing different components or component properties. They do not say 'this form is X-like or Y-like'; rather that 'this form may be represented by x or y, or contains properties x or y'. Here, x and y are quantifiable - and hence directly comparable.
The next five subsections discuss a series of different types of structural indicator. This is followed by general discussion on their implications.
7.1.1 Transport network parameters
Vaughan describes a series of descriptors of network structure. These include two that are potentially of interest in capturing structural properties:
route factor = average distance via the routing system/average direct distance
crossing factor for roads = road-intersection density/(road density)
Since the route factor gives a measure of directness of route, it could distinguish between, say, a highly impermeable free-like network and a highly permeable grid-like network. However, this depends self-evidently on routes taken by traffic, and because it uses averages it implicitly attributes the same weight to all potential routes. In such a way it might imply that less permeable networks were less efficient. However, some tributary layouts may be quite efficient in getting traffic say out of a residential development and on to the arterioLnQ6pGOvU7RHhzAUfnphQ==al road system, where access between cul-de-sac may be relatively unimportant. The crossing factor is a means of relating the number of intersections to overall road density. This measure evaluates junction density, but does not differentiate what kinds of junction are present, and therefore would not essentially differentiate traditional grids composed of crossroads from modem tributary layouts bristling with cul-de-sac.
In contrast, specifying junction nodality directly would home in on those particular features - cul-de-sac and crossroads - most strongly associated with, and more directly differentiating, 'conventional suburban' and 'neo-traditional' layouts. The proportion of junctions of different nodality in a network is a simple informal indication of the configurational properties of a network. Each junction is categorized by its nodality (number of arms), and the proportion of each category occurring in a network may then be calculated.
In practice, most networks will be composed of junctions with a nodality of less than five, and so characteristic trade-offs between those with more or fewer crossroads (4-arm nodes), or culs-de sac (1-arm nodes) relative to T junctions (3-arm nodes) would be identifiable.
Permeability relates to the degree of difficulty of through movement in a given sub-network; approachability is a form of micro-level accessibility to local facilities, while tortuosity quantifies the extent of deviation from a direct path43. In general, this analysis requires more data than purely configurational indicators: approachability and tortuosity require measurement of absolute differences over a series of pairs of points in the network, while permeability requires information about relative travel times, which are hardest to quantify and may rely on real time data.
Other characterizations of networks tend to relate to theoretical, regularized networks.
These are useful for discerning certain principles, but are not so useful for real networks. For example, evaluated theoretically optimal shapes for the motorway system - but the motorway network is more liable to be determined by the actual scattering of cities and towns rather than a notional uniform distribution. Smeed's analysis treated the road network "as a continuum of roads at infinitely small spacing" surely an unrealistic scenario for present purposes, since we are concerned with irregularities that distinguish different networks, and hierarchical distinctions between different types of route.
The work of Wright et a!. themselves describes ways of optimizing networks to minimize traffic crossings: but this is only one very narrow grounds for optimization so narrow as to make any theoretically optimal network hardly likely to be optimal, functional or likely in practice. The same goes for Alexander's attempt at optimizing street pattern.
The desire to err on the side of the simplest configurational indicators which most realistically represent network structure leads us to consider further the basis of networks of nodes and links.
7.1.2 Graph-theoretic measures
Graph theory provides a range of measures which may be applied to the structure of networks based on 'graphs'. A graph is a set of discrete points joined by lines: the points and lines may be referred to as vertices and edges, or, more familiarly in terms of transport networks, nodes and links. Lowe and Moryadas describe graph theory as a branch of combinatorial topology which offers "a powerful, versatile language which allows us to disentangle the basic structure of transportation networks".
Broadbent draws attention to two potentially useful graph-theoretic indicators of connectivity, with reference to urban networks:
Koenig number: the maximum number of edges in the shortest path by which any particular vertex is connected to any other vertex in the system.
Although these are suggestive of the connectivity of networks, they say nothing of continuity of routes, which is a significant aspect of road networks. Moreover, they do not adequately capture properties that appear to be important in distinguishing the kinds of urban structure considered so far in the thesis. For example, Two hypothetical networks having the same Beta index, but which have quite different properties of 'connectivity' as planners would use the term. perhaps resembles a kind of traditional connective network, looks more like a looping suburban layout.
There is a fuller set of graph-theoretic measures available, developed by Kanski and others, including the alpha index, gamma index and accessibility index. Many of these are concerned with nodal connectivity, which distinguishes the relative hierarchical importance of nodes. Or, they give a general indicator of the aggregate connectivity of a network . However, they do not seem to capture the ways in which overall connectivity is affected by the disposition of major and minor routes.
In general, it seems that graph-theoretical indicators such as the 3 index are useful for dealing with large-scale networks such as the railway, airline or river transport system of a nation. These differ from the consideration of local street patterns in a number of ways. Their typical shapes are different: an airline service network will have a series of multi-spoke hubs and non-intersecting paths, while a river system will be quintessentially 'tributary'. These networks also tend to represent point-to-point connections, as opposed to routes that are continuous through nodes.
Additionally, national or regional transportation networks will be significantly influenced by considerations relating to regional or global flows of people or goods.
However, at the urban scale of concern in this research, these factors are less important when it comes down to the shape of urban street blocks, which are more likely to be governed by the locally specific pattern of land ownership, the type of land use and the type of built form (e.g. courtyard housing, suggesting rectilinear street patterns, or point blocks which allow an irregular, curvilinear road geometry).
A final point is that measures of the connectivity or accessibility of national transportation networks tend to imply that there is equal significance in getting from any point to any other within the network. Since each city in a nation is singular and largely self contained, it is meaningful to consider travel patterns from each city to any other, albeit that some city pairs will generate greater flows than others. By contrast, within an urban area, there tends to be a zoning of functions (however informal) and an overlapping of spheres of influence. This means that the importance of accessibility between each and every pair of nodes is not of the same significance as in a national transportation network.
Put another way, while the traffic between two distinct cities may be inversely related to the distance between them, the same cannot necessarily be expected within a settlement, where, for example, travel between two neighboring housing estates may be less significant than between either and the central business district.
At least, this would apply to motorized trips. For walk trips between neighbors, one might expect the distance factor to apply more strongly. However, at this micro scale, the network behaves as a smaller, self-contained 'universe', where the network of pedestrian trajectories becomes like a point-to-point system again: the criss-cross pattern of paths resembles an air network more than a road network.
The foregoing suggests that there is a need to consider alternative forms of analysis more appropriate to the urban scale.
7.1.3 Space syntax
Space syntax is a method of configurational analysis developed by Bill Hillier and associates, which has been applied to the structure of space in buildings and the structure of urban space. Space syntax is a quantitative analysis based on the configuration of 'axial lines of sight'. An interesting feature is that although it is 'configurational ', in that it analyses the topology of graphs, the axial lines of sight themselves directly reflect 'compositional' features, in that they are derived from the absolute disposition of bounded space.
A key property of space syntax is that the axial lines can continue through intersections, and so each line has a value of connectivity that relates to the number of intersections along its length (rather than being dependent only on the status of the nodes at either end). Space syntax also makes use of the concept of depth, which is a measure of network 'distance' between network components. The depth of any axial line relative to any other can be calculated, and hence an average depth calculated for the whole network.
Space syntax makes considerable use of the property of 'integration', which is based on the distribution of depth in a network, and which provides an indication of where the most central, connective routes in a network lie. Using the property of 'integration', space syntax has been employed to predict the intensity of pedestrian activity and even vehicular flows.
However, the significance of axial lines of sight to movement patterns is somewhat open to question, particularly as regards vehicular flows, which do not seem intuitively to be particularly sensitive to local irregularities in alignment. Indeed, Hillier stresses that "connectivities... and their topological arrangement into a network by the geometry of the system, are by far the most important formal attributes of the system from the point of view of movement" , and "Deviation ... from strict rectilinearity will make no difference provided the connective topology of an orthogonal grid is realized".
This seems to suggest that it is the abstract connectivity of a system that is important, which may be independent of the definition of the unit by which connectivity is measured. In other words, the axial line is not necessarily sacrosanct as the fundamental unit on which to base measures of connectivity. This opens up the horizon to experiment with alternative route-based units.
That said, space syntax does provide some important insights. It is useful insofar as it can provide an explicit representation of structure which is subject to configurational analysis.
We have contrasted the structural properties of traditional settlements, such as French hill towns, with modern housing estates. They demonstrate how a certain housing estate, though superficially resembling a traditional town, is structurally quite dissimilar, and in fact dysfunctional in a way that is attributable to its structure. This has important lessons for neo-traditional urbanism, since it implies the importance of a clear grasp of the structural implications of design.
Secondly, it is also interesting in the way that it uses the concept of 'depth', related to the number of steps of adjacency between different lines. The way in which depth is distributed about major streets, which tend to be constituted by the most 'integrated' lines, gives an impression of hierarchy, a distinction between major and minor routes. Since main routes tend to be relatively straight and continuous, they will tend to be constituted by a relatively small number of relatively well-integrated lines, hence giving the impression of continuity of 'hierarchy'.
Whatever the extent of the correlation between road hierarchy and 'integration', the notion of depth from some 'datum' line does set space syntax apart from the general graph-theoretical indicators discussed. It builds in the notion that some parts of the network are more important than others, and some are more alike in their importance than others. This hints that while space syntax may not be the complete or only answer to the structure of networks, it allows interpretation that meaningfully captures some key properties - of urban street networks that other network indicators fail to capture.
7.1.4 Urban morphological description
Urban morphology is concerned with 'formative, generative and adaptive processes operating in space and through time'. Urban morphology may be used as an analytic tool to explain as well as describe urban structure in its component parts (hence its inclusion here, rather than merely as a descriptive tool for the 'naming of parts' of patterns). Anne Vernez Moudon provides an overview of urban morphology as an emerging interdisciplinary field, identifying major schools of thought therein, and a more detailed analysis of classification of forms.
Larkham and Jones distingd3946bb3eeed153b7f4ca1f60a32132e999eff8f64dcc8f881273112f11b77fduish morphographic description, which describes features, from morphological description, which also considers their origins and development.
Indeed, urban morphology provides a rich vocabulary of urban forms and processes, and indeed forms defined by processes. Conzen's terminology includes terms such as 'arterial ribbon', which imply a combination of route and built form. Other terms, such as 'breakthrough street' and 'consequent street' connote the manner of formation, with the term 'Street' itself connoting the built form. Discussion of the structural formation of pattern in general will be dealt.
However, morphological approaches appear to give greatest attention to cellular plots and 'plan-units', rather than routes, or overall network patterns as constituted by routes. For example, a grid pattern is typically seen as a frame defining a set of rectangular subdivisions, rather than as series of intersecting paths of movement . As Erickson and Lloyd-Jones point out, "Authors on urban morphology recognize that one of the most enduring artefacts of the city is the pattern of the street network. Despite this, most concentrate on the form of buildings and collections of buildings that make up urban blocks".
Morphological approaches tend to be more interpretative rather than design-oriented, ie, dissecting existing settlements rather than providing a rationale for how settlements or networks could or should be configured.
What we take from urban morphology is more in its approach, addressing and explaining formative processes as a basis for description ,than in the actual objects of description.
7.1.5 Morphogenetic classification
Morphogenesis may be defined as the creation of form as a developmental or evolutionary process. A morphogenetic classification would therefore be one which categorizes forms based on the way in which they developed or evolved.
A key to classification in this respect is to consider processes or rule-sets that might generate observed patterns. Once a rule-set has been determined, then a complete enumeration of possible forms that would be generated by it can be explicitly expressed. Each pattern may then be uniquely identified with respect to how it was (or might have been) generated, on the basis of that rule-set, and its position relative to the other patterns.
Some form of morphogenetic classification could be useful in being able to uniquely identify each pattern within the morphological continuum, in a way that can relate each pattern to each other in a systematic way.
It is also potentially very useful in that it can help explain the way patterns come to be the way they are. This includes taking cognisance of the order of growth of structure, as well as the geometric probability that particular patterns will arise in the first place. March discusses the issue of 'possible worlds', and how the likelihood of certain patterns being observed may be related probabilistically to the total number of theoretically possible patterns, or paths of generation . Indeed, this probabilistic effect can be regarded as a further influence on the form of urban structure, albeit largely a hidden one.
Mitchell enumerates all possible forms of layout generated from a given rule set. Since every possible form can be worked out, each actual form may be catalogued definitely with respect to the whole set: this can form the basis of a 'morphogenetic classification'. Given the original rule set, there is nothing 'arbitrary about the multiplication of forms here: each member of the set no more and no less is systematically related to each other.
With a morphogenetic approach, patterns can be classified not simply by what they resemble as a whole, nor what they are made up of (the naming of parts); they can be classified with cognition of how they came to be, and in relation to other theoretical positions in the morphological continuum, whether occupied by real patterns or not.46 This is conceptually a taxonomy based on actual growth and development of form, which has parallels with biological taxonomy.
The examples of morphogenetic classification referred to here have all been applied to buildings or abstract shapes. Ultimately, what would be needed is a way of applying these concepts to street patterns.
7.1.6 Discussion
The conclusion of this brief review of quantitative indicators is to note that road networks have particular attributes which need to be captured, which go beyond mere connectivity or shape. They need to take account of structure. This includes the consideration of different types of route and the connectivity and continuity of routes of different type. These are important since they relate to the way that networks are formed, and because these in turn relate to particular transport system characteristics such as mode of travel, travel speed, interchange penalty, shared surfaces and presence of building frontages, which have significance for the use that is made of urban routes and spaces.
There is an implicit assumption here that there is something significant about the structure of the network which will have a bearing on transport and urban design objectives. Of course, independent of any implied determinism, identification of different structural types can at least differentiate between whatever layouts are being advocated.
We have now seen a variety of quantitative indicators which may be used to characterize network form. So far, none seems ideal. Patterns seem to be complex in that they seem not to be able to be 'reduced' much without losing a proportionate amount of 'character'. Put another way, their description often seems to require as much information as the pattern itself.
Following on from the discussion in the preceding sub-sections, it seems that not only is there a wide variety of descriptors in use, but a variety of things being described: traffic routes, axial lines, cellular plots, floor-plan dissections. This echoes Batty's comment that there is no clear agreement on the fundamental units of morphological analysis.
However, even if we limit consideration to the transport context, it seems that there is clearly a distinction between the kind of structure that a road network represents, in contrast to the networks for other modes such are air networks or pedestrian paths across space. Indeed, it is possible to propose a distinction between these two types of network. Following Mata's use of the terms, we could style these as 'vertebrate' and 'invertebrate' structures.
Here, it is proposed that a vertebrate structure is one which comprises a series of discrete elements (routes) some of which are continuous through intersections with other routes (cf. main street as a 'backbone' of a settlement). Here, each link or route has a physical counterpart along which the actual paths of movement are channeled. Each link is linear: movement goes along the link between the nodes at either end.
In contrast, an invertebrate structure would be one:
(1) where discrete elements or links cannot be identified, such as in the case of an amorphous agglomeration of spaces.
(2) where discrete links are identifiable, but these do not correspond with physical channels.
(3) where an identifiable system of physical links does exist, but where the logic of the movement network so formed does not lend itself to being treated as a formation of routes continuous through nodes (e.g. a skeletal plan of a national rail network, where nodes represent whole settlements).
On this basis it is possible to propose a subdivision of structural types.
The modem road network is a 'vertebrate' network in that it comprises discrete roads
or routes, which are continuous through junctions. These routes may then be hierarchically differentiated.
Both an airline network and a series of pedestrian trajectories across an open public space, would be considered 'invertebrate' by the above definitions . In these invertebrate cases, each link simply links one point to another point, and in a sense each link may be considered to be hierarchicallyjKExToJ5a+WMabyOITPmtw== equal (any structural differentiation of links would really be based on the status of the nodes joined). An 'invertebrate' system is commensurate with a nodal hierarchy. In the airline case, this means the 'biggest hub' is at the top of the nodal hierarchy.
The conclusion from this section is that 'vertebrate' representations of structure are those worth pursuing as far as the analysis of road networks is concerned. This translates into a route-based approach, which is the subject of the remainder of this chapter.
7.2 Analysis of route structures
So far in this chapter we have seen a number of ways of analyzing structure. This has revealed not only distinctions between what kinds of property were of interest in a structure (e.g., its connectivity) but distinctions between different types of structure. In other words, the process of investigating different ways of analyzing structure ended up with another kind of characterization of structural types, to add to the structural characterizations explored or developed earlier in the thesis. Specifically, the investigation in the first half of this chapter culminated in the suggestion that there is a particular type of structure - the 'vertebrate & or route-based structure - that is of most interest when analyzing urban structure.
Section 7.1 found that existing analytic methods do not seem ideally suited to the analysis of route-based structures, suggesting the need for developing dedicated analytic methods for application to route-based structure. Ideally, there would be an analytic method that would: (1) reflect the hierarchical differentiation of routes; (2) take account of junction connectivity; (3) be simply topological, like graph-theoretic measures; (4) build in the notion of depth, like space syntax; (5) take account of the method of formation, as in morphological approaches; (6) while also relating each structure to each other, with respect to all possible structures, as possible by morphogenetic classification.
A route-based method of analysis to handle the first four of these points will now be developed. This will require an amount of preparatory explanation and demonstration, constituting the remainder of this chapter, before a fuller application in Chapter 8. Route based structures will also be the focus for further analysis and interpretation, to the extent that structural analysis is considered, in the remainder of this thesis. This will include consideration of the final two points above.
7.2.1 Introduction to Route Structure Analysis (RSA)
Street networks may be considered as possessing 'vertebrate' structure, in which the basic elements are routes which may be continuous through intersections with other routes. With such a structure, the differentiation of routes becomes possible. For a start, routes can be distinguished by their relative continuity (which may be related to the number of junctions passed through). The connectivity of routes will also be discernible, in a way that relates to the number and nodality of junctions a route passes though.
Additionally, it will be possible to incorporate the concept of 'depth', with respect to routes. Together, these properties can distinguish between different kinds of main and minor road. Overall, it will be possible to analyze not only the general distribution and
differentiation of routes, but to recognize different types of network, based on their structure of routes. The structural roles of routes, and structural properties of networks, will have a bearing on their performance in the urban context. The remainder of this chapter is mainly concerned with explaining and interpreting the properties of routes, albeit within the context of network structure. The implications for different types of network and network performance.
7.2.2 Forming a route-based network
We may start our investigation of routes by first considering the conventional road network composed of links and nodes. In this context, a route may be considered as a serial aggregation of links.
The way in which links are aggregated into routes will affect the structural performance of the network. This thesis will use a series of conventions for choosing the pattern of aggregation, and will be set out in the course of this section.
Route convention: A route is a linear array comprising one or more conjoined links.
Junction convention: All junctions are nodes, but not all nodes are junctions. In common terms a junction would be regarded as a node at which two or more routes join. Here, a junction is taken to mean a node through which one and only one conjoined (through) route passes. This convention simplifies certain calculations and relationships used in route structure analysis (these points are demonstrated). In practice this means, for example, that a 4-way junction is deemed to have a single through route, and two side routes, i.e., no 'crossovers'.
The route and junction conventions described above form a basic system of compliance,
controlling how links are to be aggregated into routes (Box 7.1).
Patterns of aggregation
A given network configuration, represented as a graph of links and nodes, may be aggregated in a variety of permutations or patterns of aggregation. The number of possible patterns of aggregation will depend on the number of junctions of different nodality present, for the given convention for aggregation.
Equations for calculating the number of permutations of aggregation are derived and demonstrated in Appendix C3.
However, within the given convention of aggregation, the number of routes formed will be independent of the pattern of aggregation chosen. Therefore, for a given graph of nodes and links, it will be known in advance how many routes will be formed, irrespective of which links are aggregated to form which routes.
Convention for route formation (pattern of aggregation)
So far, it is established that for a given network topology, and the convention set of Box 7.1, we will have a given number of routes, which can be formed into a calculable number of permutations. For example, given the graph in (a), we know that there will be six routes formed. The layout suggested in (b) - repeated below as (a) - is just one possibility. (b) and (c) show two other possibilities.
In fact, it may be shown that there will be over a thousand permutations of aggregation possible. The question is: which one shall we choose?
Numbers are used to identify routes. Line thickness indicates 'depth from route .
Conventions for route formation are intended to represent the typical relationships between major and minor roads, particularly as found within urban sub-networks: . main routes tend to more continuous than minor roads, while not being unnecessarily circuitous. (c) looks 'unlikely' since the main route is not a continuous through route; (b) looks 'unlikely' because it looks too circuitous. deeper routes often tend to be less connective or continuous, and vice versa (but clearly this is not a rigid rule). In all three cases, the deepest routes are indeed the shortest. the arrangement of continuity of routes tends not to generate unnecessary depth, i.e., there is a relatively 'flat' hierarchy between the shallowest to the deepest route, relative to the deepest possible layered system.
Some suggestions for determining appropriate patterns of aggregation that would give rise to typical, recognizable route structures are given in Box 7.2.
It would be possible to introduce further, more systematic rules, based on explicit structural considerations. These might be used to assist with consistent interpretation of appropriate patterns of aggregation.
However, the designation of routes properly relies on some degree of contextual interpretation. In other words, the network aggregation will not necessarily be completely determined by its intrinsic topology. Although this in a sense introduces some indeterminacy into the proceedings, it is necessary to allow significant characteristics of the actual site context to be taken into account, which are not reflected in the abstract topology.
Such indeterminacy is really no more subjective than is the choice of network boundary in the first place. That is, choosing any network boundary involves some degree of contextual interpretation and judgment, and this judgment will affect the properties of the resultant network. Similarly, the choice of pattern of aggregation of routes will influence the pattern of depth for the route network, and the properties of the routes so formed. Indeed, the appropriate role of contextual interpretation can be seen as a kind of compensation for any capriciousness in choosing network boundaries in the first place. A national route passing through any local area will be the most 'globally connective', and this can and should be reflected in the choice of 'datum route'. (For example, (c) might give a correct interpretation of the network if this represented, say, a port town, in which the main route (1) terminated at a loop, and where routes 2, 4 and 6 are short side roads.)
Having arrived at a system for deriving a route-based interpretation of a network, it is now possible to consider the structural properties of different routes. Some definitions, or conventions for specifying these properties, are therefore required.
7.2.3 Continuity, connectivity and depth
Route structure analysis makes use of three key route properties which are described below.
Continuity is taken as the number of links that a route is made up of. Continuity reflects how many junctions a route is continuous through.
Connectivity is taken to mean the number of routes with which a given route connects. Connectivity reflects the number and nodality of junctions along a route. The convention here is that all routes intersecting at terminal junctions are included in the count (therefore a route terminating at a crossroads is deemed to be connective with both of the other routes joining at that junction), and where two routes meet at more than one point along their lengths, connectivity is counted on each occasion.
Depth is a property which measures how distant a route is from a particular 'datum', measured in number of steps of route. This datum could be (1) the national route network (eg, the A road network); (2) the exterior to a sub-network; or (3) any selected route (the 'datum route'), such as a national route passing through the network, or some other externally connecting through route. In this thesis the third convention will be used, throughout.
The more steps distant a route is from the datum, the deeper it is; the fewer steps distant, the shallower. The convention used here will be that the datum route will have a depth of 1, and routes connecting to the datum will have a depth of 2, and so on. Routes may be numerically labeled according to their branching. Thus, route 2 in (a) becomes route 1.1, and route 4 becomes 1.1.1. In this way, length of the label reflects the depth of the route.
The properties of continuity, connectivity and depth will be used from now on to quantify rod8e72209f4e08d9cecd2300a786d568fafebc234ed1bcb3a1dedb9fbcbf3f884ute-based networks.
7.2.4 Demonstration of use of Route Structure Analysis
A brief demonstration of route structure analysis, based on two networks previously encountered, will now be undertaken prior to application to a real site. Tables (a) and (b) demonstrate the properties of continuity, connectivity and depth calculated for the networks shown in (a) and (b) respectively.
This analysis says something both about the networks and something about the individual routes. Clearly, graph-theoretic measures like the index cannot express route properties, since they possess no routes, only links. What the route-structural properties say about the networks is, it is argued here, more significant also. For example, the median values shown differentiate between the less deep, more connective character of the 'focal' network (a) and the deeper, less connective character of the 'layered' one (b).
To draw more generalisable conclusions about the meaning and significance of the properties, it will be necessary to study more networks. This can allow the route-structural parameters to be 'calibrated' with respect to recognizable types of network, hence providing a basis for their characterization or classification. This will be done systematically in Chapter 8.
7.2.5 Application to a site: Bayswater case study
Here, a real site is analyzed for demonstrative purposes. Only limited interpretation will be given now, however, since a wider range of cases will be needed to draw out the significance of the different results .
The example chosen is Bayswater, a nineteenth century suburb of inner London (W2), equating with a 'traditional' urban layout, a kind of irregular grid. The site location plan, while the network under consideration is shown as a graph. (This is a simplification of the actual, in omitting some minor lanes and mews). For simplicity, only the centerlines of the boundary routes are used as shown, so that other routes leading off to the exterior are not calculated and do not contribute to connectivity values of internal routes or the boundary routes themselves.
In total there are 73 links (L) and 49 nodes (N), so the 3 index is 73/49 = 1.49. Of the 49 nodes, 46 are junctions proper (J), while the remaining 3 represent external connections. The number of routes formed by any permutation of aggregation will be R = 73 - 46 = 27. The number of possible permutations of aggregation will run into millions of millions ..
The chosen pattern of aggregation is based on actual junction priority; Figure The resolution of routes (for three of the crossroads, route continuity is shown by a solid line). The bottom route is taken as the 'datum', labeled route 1; d= I. Depth is measured from this 'datum'. The values of continuity, connectivity and depth. Note that the sum of continuities equals the number of links .
It can be seen that there is a general distribution of a small number of long, connective routes and a larger number of shorter routes. Though many routes are as short as one link long, they can still be relatively connective, continuity of only 1 while its connectivity is 4, since it joins two crossroads. Note that the deepest routes are short, all routes at depth 4 are one link long. Route 1.2.1, although a relatively 'deep' minor road, that is with no strategic traffic function, scores highly on continuity and connectivity, at least at this local scale.
Possible interpretations of the significance of different routes types will be considered in the following chapter, in the context of a wider range of cases.
7.3 Chapter Discussion
This chapter has reviewed a range of means of analyzing structure. None turned out to be ideal for describing and analyzing the kind of structure, characterized by differentiation of routes, found in urban road networks. Accordingly, a method for analyzing this kind of structure, identified as 'vertebrate' or route-based structure, has been developed and demonstrated.
Route structure analysis (RSA) has been used to differentiate two hypothetical networks, one representing 'traditional' and the other representing 'conventional suburban' layouts in a way meaningful to their representation of more connective and less connective layouts which were indistinguishable by the graph-theoretical indicator, index.
Route structure analysis is relatively straightforward to apply. Route-structural parameters can be derived from the nodes-and-links system of conventional transport network analysis. Route structure analysis is closer to the level of simplicity of graph-theoretic analysis than the level of computation required in space syntax, and its parameters are more transparent. Moreover, it handles those elements by which networks are normally designed.
That is, designers tend to consciously construct a network by adding discrete route sections, rather than by subtracting from the field of potential axial lines in a spatial continuum.
Route structure analysis is particularly appropriate for situations where discrete routes are identifiable (ie, road networks in general), while space syntax is particularly suitable for analyzing bounded spaces, such as within buildings or traditional settlement cores.
Finally, route structure analysis allows the recognition of discrete route types defined by their permutations of connectivity, continuity and depth. The use of the route as an elemental unit creates two brakes on combinatorial explosion of types. In real networks, junctions of nodality greater than five are rare, and depths greater than five are also rare.
Overall, route structure analysis is a potentially useful configurational tool, which opens up the possibility of characterizing both networks and network elements (such as routes) in terms of their continuity, connectivity and depth. This suggests that it may be feasible to unambiguously specify previously suggested desired features such as 'connective networks' and 'connector streets'.