Extensions to the method

There are a number of ways in which the techniques introduced here could be refined in future work, with respect to the details of the technique itself and its potential uses. On one hand, there is clear scope for the investigation of network features

other than the motifs and chains considered here. The key theoretical innovation - the production of randomised event sets - provides a baseline against which any network property can be compared; there are likely to be several of these which correspond directly to spatio-temporal phenomena.

In addition to this, it may also be productive to explore the use of weighted event networks. The networks considered here are derived from the binary ‘close pair’ re- lationship and are therefore unweighted; while this is parsimonious and conceptually simple, it does imply a substantial loss of information. This could be remedied by the use of weighted links, which would represent proximity in a more granular form, and for which analytical methods do exist. The interpretation of network features in terms of real-world patterns would, however, be significantly more challenging. An alternative approach would simply be to introduce a number of spatial bands, as is done in more advanced forms of the Knox test. In this case, several event networks would be produced, corresponding to different levels of separation.

Finally, there is also an opportunity to adapt the approach from what is purely a means of statistical measurement to a predictive method. Pair-wise clustering analysis has inspired several methods of crime prediction based on the identification of a radial region around an initial event, in which a close pair might be expected to occur. 3-vertex motifs, however, correspond to a situation where a close pair of events have occurred and a third can be predicted to happen in some vicinity com- mon to both (which, crucially, may have much smaller area than the corresponding radial region). Predicting on the basis of groups of events in this way might there- fore have great potential as a predictive tool, and will be the subject of additional investigation.

Chapter 3

Quantifying the relationship

between street network structure

and burglary risk

The techniques presented in Chapter 2 were concerned with the characterisation of patterns in sets of spatio-temporal crime data, and the use of such techniques to draw inferences regarding criminal behaviour. Although particular crime datasets were considered in the empirical work, however, the technique itself is a general one, applicable to any set of events occurring at known locations in space and time. When using it to examine data, no use is made of contextual information and the analysis remains agnostic to the particular spatial setting. Both theory and empi- orical evidence, however, suggest that the spatial distribution of crime is influenced to a significant extent by environmental factors (see Brantingham & Brantingham, 1981; Andresen, 2014). The aim of this chapter is to examine the influence of one such factor: the structure of urban form, and that of the street network in par- ticular. Previous research (e.g. Beavon et al., 1994; Johnson & Bowers, 2010) has suggested a relationship between street network properties and the distribution of crime; however, many of the network measurements used in those studies do not correspond well to the underlying criminological theory. This chapter examines the use of more sophisticated network properties in accounting for the heterogeneous distribution of crime at street segment level. These properties are used to measure concepts such as usage potential and permeability in an objective and quantitative way, and thereby provide more well-grounded support for related hypotheses.

3.1

Introduction

Several prevailing theories of crime stress the importance of considering contextual factors when analysing the spatial distribution of offences. The general approach of ‘environmental criminology’ (Brantingham & Brantingham, 1981), for example, is based on the notion that crime can be best understood by considering the criminal act itself, and the decision process of which it is the result. Such decision processes take into account the characteristics of potential targets and are also influenced by surroundings, in terms of both the built environment and the activity occurring therein. At an even simpler level, though, for such a decision process to even arise requires that the opportunity in question has become known to the potential of- fender; he or she has, in some sense, encountered it.

Such reasoning implies that understanding the human activity patterns which occur in urban environments is essential to any analysis of the spatio-temporal distribution of crime (Felson, 1987). These affect both the extent to which certain opportuni- ties are encountered and the social forces present when they are (which may affect whether the opportunity is taken). Imbalances in either of these ought to imply heterogeneity in levels of crime occurrence, all else being equal.

In the case of crimes which take place in urban areas - as will be considered here - the routine activities in which people engage, and during which opportunities are encountered, are predominantly those which include movements from place to place within a built environment, often between those which serve particular functions. The way in which the urban space is configured, therefore, shapes these journeys and determines the extent to which inhabitants become aware of the spaces around them (see Brantingham & Brantingham, 1993b). According to this argument, it should be possible to reconcile the criminal character of places with their situation in the urban form.

study is the street network. The street network acts as a ‘skeleton’ for an urban area, in the sense that it is the structure around which all elements of the built environment are arranged. In addition, it acts as a constraint on travel and deter- mines the paths which can be taken in moving between any two locations. On that basis, variations in the level of activity within an urban area can be assessed most appropriately in terms of street network usage.

For crime in particular, it is also the case that many criminal events occur at some location on the street network: as well as being the substrate for movement, it is also the structure on which targets are arranged. This is particularly clear - and analytically expedient - in the case of crimes for which the target is located at a fixed point on the network. Burglary, which will be considered here, is such an example. More generally, analysis based on the street network is well-aligned with the use of small spatial units in geographic criminology, as advocated by several scholars in the field (see, for example, Weisburd et al., 2009); this assumes, of course, that a sufficiently granular network representation is used.

Analysis concerning the street network is also advantageous, and of significant po- tential value, from a practical perspective. The units at which crime reduction activities are implemented are commonly those which can be specified in terms of the street network, e.g. street segments or named roads. Police patrols, which are specified in terms of routes and would themselves involve travel around the network, are an example of this. This is also the case for potential uses of such analysis not directly related to crime reduction: insurance premiums, for example, typically take neighbourhood characteristics into account, often specified at street level.

As would be expected on the basis of these observations, the relationship between crime and the street network has been the subject of several empirical investiga- tions (e.g. Beavon et al., 1994; Hillier, 2004; Johnson & Bowers, 2010). Though these differ in their precise emphases and findings, they demonstrate consistently

the existence of significant relationships between network structure and crime phe- nomena. In most cases, these are then reconciled with theories of offender awareness and decision-making, as well as the role of guardianship.

Nevertheless, these approaches suffer from certain shortcomings related to their mea- surement of the street network. Administrative road classification, for example, is used in many studies, but is not necessarily consistent and, as a categorical variable, suffers from a lack of granularity. Although more explicitly quantitative variables have also been considered, many of those used, such as connection counts, have an association with activity patterns which is somewhat opaque. This is particularly problematic when such findings are used to make inferences about the behaviour of offenders.

The quantitative analysis of street networks, however, has become significantly more advanced in recent years (see Crucitti et al., 2006b), in line with the growth of net- work science more generally. In particular, this has involved the introduction of several metrics which are particularly appropriate to street networks (which have distinctive character, in comparison with networks in general). Moreover, several of these metrics have an immediate interpretation in terms of travel patterns on such a network, relating in particular to the accessibility and likely use of individual places.

Since these concepts are precisely those which are of interest from a criminolog- ical perspective, such metrics provide an opportunity for analysis of crime which is both quantitatively sophisticated and can be related directly to criminological theory. The aim of this chapter is thus to extend understanding of street network effects on crime by employing an explicitly quantitative analytical framework for the study of urban streets, thereby formalising several of the general ideas which have been explored previously. This chapter presents such analysis, considering in particular the relationship between the network metric ‘betweenness’ and levels of burglary. In the process of this, several issues related to street network analysis in

this context will also be discussed, and empirical results concerning network clus- tering more generally will also be presented.

Before presenting the empirical research, a variety of background material will be reviewed. In the first case this will concern the theoretical background from a crim- inological perspective, before moving on to introduce the technical study of street networks and previous work in the field.