Felson, M., Andresen, M.A., & Frank, R. (2012). Mobility polygons and the geometry of co-offending. In M.A. Andresen & J.B. Kinney (Eds.), Patterns, prevention, and geometry of crime (pp. 3 – 15). New York, NY: Routledge.
Abstract: The crime mobility triangle summarizes the spatial divergence of three locations: the offender’s residence, the victim’s residence, and the location of the delinquent act itself. The farther these three locations are from one another, the greater the area covered by the mobility triangle. The original mobility triangle was not designed for cases with multiple offenders or multiple victims. Accordingly, the current paper defines the crime mobility polygon, which can include more than three locations when a single incident involves extra offenders or victims. This links the crime mobility and co-offending literatures. We calculate the areas contained within mobility polygons for 4,005 index crime incidents involving two, three, or four offenders. These calculations demonstrate the influence of extra crime participants upon the area an event covers.
Keywords: mobility triangle, geometry, journey to crime, geography of crime, routine activity approach, crime analysis, environmental criminology, co-offending
Scientists often learn to summarize a lot of information with a single scale. The Kelvin temperature scale, the Gini ratio of inequality, life expectancy at birth, the Richter seismic intensity scale, and the Fujita scale of tornado intensity – all of these serve a summary purpose for their respective disciplines. None of these indicators crowds out other research or measures, but each one helps synthesize and focus a good deal of information.1 Our concern in this chapter is to find a general indicator for the spatial analysis of crime events, drawing upon what’s already in the crime analytical literature. We do not declare that we have found a single indicator that does the job – time will tell whether that is true. Nor do we claim first credit – that belongs to Burgess (1925) and more recently to Groff and McEwen (2007). But in this paper we broaden their work and propose a more general scale to summarize a good deal of information about the spatial span for a single crime event. We hope this scale helps compare crime events in their spatial reaches. We demonstrate this comparison using real data on over 4,000 crime events within a single city.
BEGIN WITH THE JOURNEY TO CRIME
The journey to crime is one of the better general indicators that crime analysts have developed to date.2 This journey is a measure of the distance between the offender’s residence and the location of his criminal action. This distance can be zero, and it can be nearly zero, but it also can reflect substantial distances and reveal the use of motorized transport. This indicator can be calculated for individual incidents or for any population of incidents, making possible standard statistical summaries of distances travelled. That allows comparing and contrasting epochs and nations, crime types and offender groupings, on a single quantitative dimension. Thus we can study whether the journey to crime grows as youths age, or as societies develop, or as transit systems are extended, or whether males and females differ. However, the journey to crime does not bring the offender and victim within the same system, since it leaves out the victim’s own journey. Even when the journey to victimization is studied, that is usually separate from the journey taken by the offender. The larger challenge is to assemble a single summary indicator of crime geometry, one that focuses on the criminal event rather than the criminal, taking into account the geometry of the event itself.
BURGESS UNDERSTOOD, BUT DID NOT HAVE MUCH DATA
Among criminologists, Ernest W. Burgess is most famous for introducing the concentric zone summary of the city. He also invented the mobility triangle, (Burgess, 1925). He did so while analyzing the geography of juvenile delinquency in terms of three locations: the residence of the offender, the residence of the victim, and the location where the delinquent act occurred. These three points in space define a triangle. Although Burgess was studying sexual delinquency, and reflected the moral views of its day, the method he devised is useful for summarizing the geometry of diverse criminal behaviors in diverse eras.
Burgess was limited by the data and computation technology of his era. The original crime mobility triangle was not really measured as a triangle at all. The researchers were lucky to have data disaggregating crime or delinquency by local urban tracts,3 and were in no position to calculate the actual distances of journeys taken, or the area covered. As a result, they asked simpler empirical questions. Did all three points lie within the same local urban tract? If so, the illicit act is considered entirely local. If none of these points was located in the same local tract, the illicit act is coded as non-local. Sometimes two of the three points are together but the third is not, requiring an intermediate coding. Figure 1 illustrates the limitations of the original Burgess approach. Although the three points in this triangle are actually quite near, they are defined to be in three separate local tracts, pointing towards a false conclusion that they are non-local. Conversely, a large social area might have all three points dispersed within it but defined as if they are contiguous.
Figure 1: The Burgess Area-Based “Crime Mobility Triangle” Allocated By Local Tracts Within A City
Although the Burgess method had practical shortcomings, we have to give credit for its innovation – especially taking into account the data available to him at the time. He helped to found crime geography and crime geometry, providing us ideas that we can now use with much greater precision. Thus he set the stage for subsequent work, pointing the way towards a single basic indicator to assist crime analysis.
The theoretical significance of the Burgess crime mobility triangle was brought out in subsequent work by Brantingham and Brantingham (1981). They discussed how offenders move about in space, finding targets and crime sites. They also worked out several alternative offender-target dispersal patterns. These efforts help us to analyze not only the common geometrical patterns for certain types of crime, but also the diverse possibilities that such crimes fill out.
The challenge now is to combine the basic insight offered by Burgess, the theoretical and empirical contributions by the Brantinghams, and more recent research experience on the journey to crime. Groff and McEwen (2007) did just that. Their papers assist our efforts to find a single summary spatial indicator for crime analysts, the problem posed at the start of this paper. The crime mobility triangle does not quite achieve that goal, since it is not designed for multiple offenders. We offer in this paper an extension of the same idea, giving it greater flexibility. But first we briefly review some studies applying the mobility triangle in the intermediate years.
SOME KEY STUDIES USING THE MOBILITY TRIANGLE
Unfortunately, all too few researchers have investigated the crime mobility triangle, considering that the concept has been around for 85 years. This probably reflects the data limitations in the past, and even the present. To calculate a mobility triangle, one needs data for three specific locations on the same incident. In any case, the mobility triangle concept has been applied on occasion to such topics as motor vehicle theft and homicide. The concept has been applied to offenders of different ages. A partial application of Burgess’s idea was Lind’s (1930) analysis of crime in Honolulu. Although lacking information on the victim’s residence, Lind was able to report that delinquency was most localized in low socioeconomic status neighborhoods and during adolescent ages, and that the offender’s geographic span tended to increase with age.
Table 1: Five Types of Mobility Triangle, Robbery, Montreal, Canada, 1968
Mobility triangle type
In the same Local Tract
Percent of robberies
No mobility [*]
Note: Base N = 1722.
We know of no mobility triangle research for the next third of a century. Then in the late 1960s Normandeau (1968) reintroduced the victim into mobility triangle research. In studying robbery in Montreal, he expanded the typology of mobility triangles to five classifications (see Table 1). With this new typology, much more insight into the geometry of crime can be extracted. For instance, combining numbers from column D of Table 1, the same neighborhood is very often shared by
Both offender and victim residences: 14 + 12 = 26 % ,
Both offender residence and crime location: 14 + 19 = 33% ,
Both victim’s residence and crime location: 14 +17 = 32% , and
At least two of these three locations: 14+17+19+12 = 62%.
These Montreal data once more confirm the basic lessons of the mobility triangle: That the friction of distance has an impact on the crime event, but that crime events vary in their degree of urban spread. Indeed, in 38 per cent of cases robberies involve total mobility, with none of the three locations sharing a local neighborhood.
Subsequently, an investigation of rape in Philadelphia (Amir, 1971) found that the offender and victim had residences in the same neighborhood in 82 percent of all cases. In most of these (68 per cent), all three points in the mobility triangle were located within the same neighborhood. The contrast between these studies tells us that robbery spans much more area than rape, justifying further inquiry into mobility triangles.
Rand (1986) extends the previous literature on mobility triangles through an analysis of nine different crime classifications: total crime, homicide, rape, robbery, aggravated assault, burglary, larceny, vehicle theft, and simple assault. Combining these offenses, 31 percent of offenders find their targets within their home census tract. However, disaggregating crime categories leads to interesting contrasts. Localization was as low as 15 percent for larceny, but as high as 53 percent for homicide and rape. Overall, property crimes tend to cover more area, while violent crimes cover less. Although robbery is a violent offense, it fits a property profile. All three studies (reviewed above) confirm the need to disaggregate crime types when studying crime mobility patterns.
Another twenty years passed before mobility triangles appeared in the published literature. Tita and Griffiths (2005)4 learned from mobility triangle analysis that homicides bifurcate; that is, they are either very local or very dispersed, but not as likely to show intermediate dispersals. Homicide mobility patterns also vary by participant characteristics, victim-offender relationships, motives, and other event features. Conversant with situational crime prevention (Clarke, 1980), crime mobility triangles are very crime specific, and must be studied accordingly.
THE MOBILITY TRIANGLE AND THE JOURNEY TO CRIME
Groff and McEwen (2007) offer the most advanced and complete research on crime mobility triangles. Previous studies of mobility triangles had used the neighborhood or census tract as the unit of analysis. Groff and McEwen (2007) extended the traditional mobility triangle by defining and analyzing the explanatory power of a new type of mobility triangles based on distances. In other words, they synthesized the journey to crime, journey to victimization, and mobility triangle into a single approach. They examined 2,773 mobility triangles derived from homicide events in Washington, DC. Groff and McEwen demonstrated that distance-based mobility triangles add substantial understanding. Using a one-quarter mile buffer, these offenders found victims in their own neighborhood 46 percent of the time. The distance-based methodology greatly enhances the mobility triangle as a tool for research and analysis.
Although Groff and McEwen added considerably to the conceptualization and detailed understanding of mobility triangles, they were unable to solve one basic problem. A majority of crime at young ages is carried out by more than one cooperating offender. Yet the mobility triangle only includes movements of one offender at a time. It also neglects the movements of plural victims. The purpose of this paper is to define a broader geometric index flexible enough to include co-offending and co-victimization.
THE CO-OFFENDER MOBILITY ISSUE
Nearly a century ago, Breckenridge and Abbott (1912) noted how often young offenders offend together. Since then co-offending has been acknowledged as an important aspect in the etiology of crime, even though it is often difficult to research. Earliest studies found co-offending to be prevalent among youths. Shaw and McKay (1931) found almost 82 percent of youth offending is co-offending in Chicago, Illinois, Gold (1970) found 75 percent in Flint, Michigan, and in a review of eleven studies, Erickson (1971) found that 85 percent of offenses involved co-offending.
These estimates are probably high. Reiss (1988) concludes that co-offending among adolescents takes up roughly half of all incidents (with single counting) and two thirds of all participations (with multiple counting). Andresen and Felson (2010) find that these numbers are highly sensitive to the age composition of the youth population included, since co-offending decelerates rapidly during teenage years.
Accordingly, any study of crime mobility that only includes lone offenders, or that treats co-offenders as if they are lone offenders, will not capture the geographic dynamics of the crime process. Reiss’s review, cited above, concludes that co-offending usually takes place in small groups, namely, of two, three or four. Accordingly we wish to devise a larger category that includes mobility triangles, while also incorporating the geometry of co-offending. We propose to calculate the mobility area for co-offending to allow for more detailed comparisons between and within crime classifications, taking into account different offending patterns. Our challenge is to accomplish this without introducing too much complexity. Our goal is a single summary measure.
THE CRIME MOBILITY POLYGON
Triangles are part of a larger class of geometric figures known as polygons. A polygon is a geometrical figure with three or more sides and angles, derived from the Greek word polugōnon (a figure with many angles). We define the crime mobility polygon that is flexible enough to cover all locations involved in a single crime incident. That includes the location of the incident and the residences of multiple offenders and victims involved. To map the crime mobility polygon, we first plot in space the residence of each of these offenders and victims, plus the scene of the crime that brings them together.5 We then connect these points so as to cover the minimal possible area.
Figure 2: The Basic Crime Mobility Polygon For Two Offenders
The basic mobility polygon depicted in Figure 2 illustrates how two offender residences, one victim residence, and one crime location define a quadrangle. This is the easiest example of a mobility polygon because its four points are spread out clearly, forming a rectangle. The area within the rectangle can be treated as an indicator of how widely dispersed the four crime elements are.
However, not all mobility polygons are symmetrical or aesthetically pleasing. Sometimes one of the four points is located within the signature of the other three, producing an irregular polygon of limited spread (Figure 3). Holding the geometric scale constant, these “concave” polygons contain less area within them. This tells us that one of the four points is tucked in rather more closely to the other three, and that the crime incident entails less spatial interaction than in the prior example.
Interestingly, Figure 3 shows that two offenders do not necessarily cover more area than one offender. The “extra” offender in this case resides closer to the victim’s residence and even somewhat closer to the crime incident location. If the first offender alone were plotted in a crime triangle, more area would be covered. And so it becomes an empirical question how much area multiple offenders cover.
The mobility polygon is defined for each criminal incident. In particular, the area within the polygon can be calculated as an indicator of the “spread” that each criminal incident covers. If two roommates attack a third in their own room, the crime incident covers minimal area, perhaps even zero. And so the mobility polygon offers a general measure. Moreover, it incorporates crime triangles for single offender incidents. It can also be expanded to include multiple victims, and a version could even be developed for serial or sequential crimes.
Figure 3: Examples Of A Concave Crime Mobility Polygon For Two Offenders
Most importantly, the area covered by mobility polygons can be summed up statistically to provide general indicators. This makes it possible to compare and contrast different epochs and nations, crime types and offender groupings, on a single quantitative dimension, regardless of the number of offenders or victims per incident. One can study whether the mobility polygon grows as youths age, or as societies develop, or as transit systems are extended. One can study whether drug dependency widens the mobility triangle or not. One can exclude or include those living in the same building or the same apartment or house. In short, the mobility polygon is quite flexible as a summary measure for crime geometry.
Brantingham and Brantingham (1981) defined the search areas of offenders in comparison to their targets. They differentiated eight models of offender search behaviour, beginning with the two most basic forms. In case 1, an individual offender searches for crime targets within one basic area. In case 2, multiple offenders search for crime targets within one basic search area. They do not specify that multiple offenders necessarily act simultaneously as co-offenders. But their model allows for a cluster of offenders living in a single district and finding targets in roughly the same locations nearby.6 Within this form, one can expect co-offenders to live only small distances from one another and to find targets rather near. This means that the involvement of multiple offenders, even as co-offenders, does not necessarily require substantial travel. It is an empirical question how much space crime participants cover, for any given incident or for a population of incidents. The crime mobility polygon is an excellent tool for addressing this empirical question.
DATA SOURCE FOR THE CURRENT STUDY
To demonstrate the potential of mobility polygons, we have selected Surrey, British Columbia, part of the Vancouver metropolis with good data and moderate metropolitan density. Surrey includes a population of about 400,000. It includes six town centers, including Fleetwood, Whalley, Guildford, Newton, Cloverdale and South Surrey. Surrey is an area of urban sprawl, light industry, strip development and malls, including apartments and single family dwellings. Its crime rates are not as high as Vancouver itself, but still noteworthy. The current study is based on several thousand mobility polygons. These polygons require known offenders with known addresses, along with the ability to locate victims and crime scenes. Thus they are drawn upon a much larger file of crime data.
Those data are relatively coherent, given that Canada has a single criminal code and that Surrey is policed by a single agency, the Royal Canadian Mounted Police. The incident-based data are extracted from the RCMP Police Information Retrieval System (PIRS) for 48 months, from August 1, 2002 through July 31, 2006. We begin with 5,101 mobility polygons. However, some of these lack necessary geographic reference points or otherwise produce invalid polygons. We focus on 4,005 valid polygons for incidents with a single victim and four or fewer offenders.
COMPARING MOBILITY POLYGONS WITH DIFFERENT NUMBERS OF OFFENDERS
Our 4,005 polygons include 3,319 lone offender incidents. These polygons are nothing more than the mobility triangles studied by Groff and McEwen. However, the data also provide us with 528 polygons with two co-offenders, 132 with three co-offenders, and 26 with four co-offenders. We begin by comparing these offending group sizes.
Table 2 presents summary statistics for these polygons combining a dozen major offenses, but disaggregating by offender group size. We avoid using means and standard deviations because they are highly sensitive to extreme values. In some cases offenders or victims of crime include tourists or others who have travelled long distances. In many cases, they travel no distance at all. The medians reduce the impact of extreme values by cutting the sample into low and high halves. The first and third quartile points cuts the halves into quarters, and the interquartile range subtracts these to give a measure of dispersion unmolested by extreme values. On the other hand, these statistics do reflect large numbers of zeros or other small numbers that tell us some crimes are entirely local.
Table 2: Crime Mobility Polygons For One Victim And One, Two, Three, Or Four Offenders. Descriptive Statistics For Twelve Crime Types, Combined. Surrey, British Columbia, Canada, August 1, 2002 Through July 31, 2006, Square Kilometers
Source: RCMP Information Retrieval System (PIRS).
Lone offender incidents cover about 2 square kilometres. When two co-offenders are involved, the area covered more than doubles to 4.4 square kilometres, as indicated by the median. Interestingly, three co-offenders only widen the area to a small degree, to a median of 5.16. But four co-offenders have a great impact in this sample, almost tripling the area covered by paired offenders to 12.7 square kilometres. Although the latter number is based on only 26 cases, it suggests a future inquiry into whether co-offending groups of four are fundamentally different in their spatial character from pairs and trios. This point is amplified by the first quartile statistics. The first quartile covers less than a square kilometre for one, two, or three offender incidents. But incidents with four co-offenders have a first quartile point of 2.75 square kilometres, indicating that they operate on a wider spatial scale.
For all group sizes, Table 2 indicates a substantial interquartile range. Thus the higher end cases cover a good number of square kilometres, even for lone offenders. Clearly, criminal acts have a great deal of variation in the space they covered, even when the impact of extreme distances is neutralized. We now turn to a more detailed analysis for different types of crime.
ANALYSIS BY CRIME TYPE
With lone and two co-offenders, we have sufficient cases to disaggregate crime polygons for several types of crime. Table 3 offers descriptive statistics for each of 12 offense types for lone offenders. Non-violent offense types are on top of the Table, with an equal number of offense types involving violence below. Within these two categories, offenses are ordered from lowest to highest medians, in square kilometres. Residential burglary “covers” a very small area, with a median of 0.17.7 At the other extreme, theft of motor vehicle by a single offender produces mobility polygons (in this case a triangle) with a median exceeding five square kilometres.
Table 3 indicates that the geometry of crime polygons transcends the nonviolent-violent crime divide. Each category includes some crimes that cover little space and some that cover much more. Assaults and aggravated assaults have medians just over one square kilometre. Sexual assaults have medians of about four square kilometres. Armed robberies have a median of 3.2, more than any property crime except theft of a motor vehicle. These data indicate that certain distinctions among crime types can be geometrically important. Thus theft from motor vehicles tends to cover less space than theft of motor vehicles. Armed robbery appears to cover more space than unarmed robbery. Although homicide and aggravated assault are very similar in other respects, homicide appears to have a wider geometric pattern, with a median of 2.72 square kilometres.
Table 3: Mobility Polygons For Lone Offenders, Lone Victims: Quartile Distribution Statistics, Disaggregated Or Twelve Crime Types, Surrey, British Columbia, Canada, August 1, 2002 Through July 31, 2006, Square Kilometers
a. Residential Burglary
b. Commercial Burglary
c. Other Burglary
e. Theft from Motor Vehicle
f. Theft of Motor Vehicle
Offenses involving violence
h. Aggravated Assault
i. Armed Robbery
l. Sexual Assault
Source: RCMP Information Retrieval System (PIRS). Note that the mobility polygons in this table are equivalent to mobility triangles.
Although we tried very hard to reduce the impact of extreme values, we still cannot escape the importance of large numbers. The third quartile point is always much greater than the median, but the median is not always much greater than the first quartile point. In the case of theft, the bottom quartile of cases covers from zero to 0.41 square kilometres. The next quartile reaches up to about 2 square kilometres. The third quartile reaches up to 11. Thus some thefts cover a good deal of space. Theft of motor vehicle as well as sexual assault can cover a good deal of space, with third quartile points of 18.7 and 20.6 square kilometres, respectively.
Table 4 explores mobility polygons when there are two co-offenders, for ten crime types. We lacked sufficient cases to analyze (b) commercial burglary or (k) homicide for two co-offenders. However, the other ten offenses indicate that co-offending does not simply mimic the spatial coverage for lone offending. For example, the median area covered by robbery for co-offenders in robbery is 7 square kilometres, much greater than for lone offenders. Theft from motor vehicles is also much more expansive for co-offenders than for lone offenders. In contrast, ordinary theft for co-offenders and lone offenders cover similar expanses. Although the data are limited, they do indicate that groups of co-offenders behave rather differently from lone offenders. This conclusion is even more evident when examining third quartile points. The upper quartile of co-offenders cover 25 square kilometres for theft from motor vehicles and for robbery, as well as over 40 square kilometres for “other burglary.”
We did not have enough cases to disaggregate crime types when there are three or four co-offenders. But we feel fairly confident from those mobility polygons we were able to examine and summarize that this is an area worthy of further inquiry.
Table 4: Mobility Polygons For Two Co-Offenders, Lone Victims: Quartile Distribution Statistics, Disaggregated For Ten Crime Types, Surrey, British Columbia, Canada, August 1, 2002 Through July 31, 2006, Square Kilometers
a. Residential Burglary
c. Other Burglary
e. Theft from Motor Vehicle
f. Theft of Motor Vehicle
Offenses involving violence
h. Aggravated Assault
i. Armed Robbery
l. Sexual Assault
Note: This Table excludes (b) 6 commercial burglaries and (k) 8 homicides, since these are too few cases for analysis.
Source: RCMP’s Information Retrieval System (PIRS).
Our purpose in this paper is not to replace but rather to supplement the diverse measures of crime geometry that are increasingly being developed and applied to data. We have argued that mobility polygons are a general category that subsumes crime triangles, while providing additional ways to look at how crime spreads out over space. Each criminal act has a variety of spatial features, and several of these are summed up by the mobility polygon. This concept is expandable to include sequential crimes, the journey after crime, and other interesting feature of crime geography. We can see that mobility polygons vary greatly in size for any one crime type, while displaying systematic variations among crime types. We can see that the number of offenders has a major impact on these polygons, but the impact is not automatic or smooth. We see that these polygons vary among nonviolent crime types as well as among crime types, crosscutting the two. We also see that the upper reaches of mobility can be quite significant, even when extreme cases are neutralized.
We view offenders as making three key decisions: selecting their group, selecting their journey, and selecting their crimes. Some will first select their group, with the journeys and crimes emerging later. Others will select their journeys first. Still others may have a particular crime in mind, subsuming the group and journey decisions to the crime itself. Still others get into a crime situation with no journey at all. We suggest that these patterns are reflected in the crime mobility polygon and the area it covers. We suspect that, for a majority of offenses, decisions about groups and journeys precede and largely set the stage for criminal acts that were either unplanned or only planned in a rudimentary way.
Address correspondence to: Martin A. Andresen: [email protected]
Acknowledgements: We would like to thank Michael Maxfield and Peter Carrington for helpful comments on an earlier draft of this chapter. We would also like to thank Paul J. Brantingham for unknowingly commenting on one of the contributions in this volume dedicated to his work.
The social indicators movement sought to find measures and summaries of society’s conditions (Land, 2000). However, no single measure of society’s “condition” was accepted.
For a review of the journey to crime literature, see Wiles and Costello (2000), Costello and Wiles (2001), and Snook (2004).
We selected the word “local tract” for an international audience. The words “district” has different meanings across nations, while census enumeration tracts have different names in different nations and languages. “Local tract” is a rather neutral choice of words, implying something less than a square kilometer, and often a few square blocks. Sometimes we use the word, “neighborhood” in reviewing other authors.
In their research, they employed a 5 classification typology that is the same as Normandeau (1968), but uses different naming conventions.
If the victim’s property is attacked in her absence, it is still mapped as the crime location. For example, a stolen car’s location when stolen is the crime location.
Brantingham and Brantingham (1981) allowed for complex search areas, as well as dynamic search areas, with multiple offenders potentially involved in both. Many of their ideas and applications are beyond the scope of the current chapter.
A burglary of one’s own home already collapses a triangle to zero area. But some victims of burglary may own apartments that others occupy, or may have sublet their own homes.
Amir, M. (1971). Patterns of forcible rape. Chicago, IL: University of Chicago Press.
Andresen, M.A., & Felson, M. (2010). The impact of co-offending. British Journal of
Criminology, 50, 66 - 81.
Brantingham, P.L., & Brantingham, P.J. (1981). Notes on the geometry of crime. In P.J.
Brantingham and P.L. Brantingham (Eds.), Environmental criminology (pp. 27 – 53).
Beverly Hills, CA: Sage Publications.
Breckenridge, S.P., & Abbott, E. (1912). The delinquent child and the home. New York, NY:
Russell Sage Foundation Charities Publication Committee.
Burgess, E.W. (1925). Can neighborhood work have a scientific basis? In R.E. Park, E.W.
Burgess, and R.D. McKenzie (Eds.), The city: Suggestions for investigation of human
behaviors in the urban environment (pp. 142 – 155). Chicago, IL: University of Chicago
Clarke, R.V.G. (1980). Situational crime prevention: theory and practice. British Journal of
Criminology, 20, 136 – 147.
Costello, A., & Wiles, P. (2001). GIS and the journey to crime: An analysis of patterns in South
Yorkshire. In A. Hirschfield, & K. Bowers (Eds.), Mapping and analysing crime data:
lessons from research and practice (pp. 27–60). London: Taylor and Francis.
Erickson, M. (1971). The group context of delinquent behavior. Social Problems, 19, 114 – 129.
Gold, M. (1970). Delinquent behavior in an American city. Belmont, CA: Brooks/Cole.
Groff, E.R., & McEwen, T. (2007). Integrating distance into mobility triangle typologies. Social
Science Computer Review, 25, 210 – 238.
Land, K.C. (2000). Social indicators. In E.F. Borgatta and R.V. Montgomery (Eds.),
Encyclopedia of sociology, revised edition (pp. 2682 – 2690). New York, NY: Macmillan
Lind, A.W. (1930). Some ecological patterns of community disorganization in Honolulu.
American Journal of Sociology, 36, 206 – 220.
Normandeau, A. (1968) Patterns in robbery. Criminology, 6, 2 – 16.
Rand. A. (1986). Mobility triangles. In R.M. Figlio, S. Hakim, and G.F. Rengert (Eds.),
Metropolitan crime patterns (pp. 117 – 126). Monsey, NY: Criminal Justice Press.
Reiss, A.J., Jr. (1988). Co-offending and criminal careers. Crime and Justice, 10, 117 – 170.
Shaw, C.T., & McKay, H.D. (1931). Report on the causes of crime, volume II. Washington,
DC: Government Printing Office.
Snook, B. (2004). Individual differences in distance travelled by serial burglars. Journal of
Investigative Psychology and Offender Profiling, 1, 53-66.
Tita, G., & Griffiths, E. (2005). Traveling to violence: the case for a mobility-based spatial
typology of homicide. Journal of Research in Crime and Delinquency, 42, 275 – 308.
Wiles, P., & Costello, A. (2000). The ‘road to nowhere’: The evidence for travelling criminals.
Home Office Research Study 207. London: Research, Development and Statistics
Directorate, Home Office.