Mobility triangle research investigates the spatial proximity of the offender's residence, the victim's residence, and the crime location, assuming that the residences of the offender and victim are the starting points of their journey to crime and victimization, respectively. As reviewed below, the mobility triangle research categorizes crime triangles based on their relative localities: all are in the same neighbourhood, all are in different neighbourhoods, and so on.
The mobility triangle literature has largely ignored the mobility patterns of co-offenders and co-victims, despite its importance in understanding the aetiology of crime. For nearly a century, since Breckenridge and Abbott (1912) noted the frequency of young offenders offending together, co-offending has been acknowledged as an important aspect in the aetiology of crime. Early studies of co-offending found that co-offending is substantial for youth offending: Shaw and McKay (1931) found almost 82% of youth offending was co-offending in Chicago, Illinois; Gold (1970) found 75% in Flint, Michigan; and in a review of 11 studies, Erickson (1971) found that 85% of offences involved co-offending, Though some recent research has questioned the extent of co-offending (Carrington 2002; Stolzenberg and D'Alessio 2008), there is still substantial evidence that offending, particularly youth offending, is a group (co-offending) phenomenon. Moreover, some scholars have found that, even though co-offenders make similar criminal decisions for target selection as do solo-offenders (Bernasco 2006), co-offenders commit criminal offences more frequently and commit more serious offences (Hindelang 1976; Sarnecki 2001), "early starters" that co-offend commit more crimes later (McCord and Conway 2002), and exposure to violent crimes through co-offending leads to more violent crimes later in a criminal career (Conway and McCord 2002). Lastly, Felson (2003) argues that co-offending causes more harm to youth, ethnic minorities, and cities. Needless to say, there is substantial evidence for the incorporation of co-offending into any criminological analysis.
In this paper, we investigate the impact of increasing the number of offenders/victims on the area covered by different crime classifications. Mobility triangles, by definition, involve only one offender and one victim, so we extend mobility triangle research to examine the mobility polygon. Our primary research question is as follows: what is the relationship between the area covered by crime and the number of offenders/victims, by crime classification? The mobility triangle research uses categories to classify the triangle. To identify the nuances in the area covered for a crime, these traditional categories are too crude. Consequently, rather than the traditional categories used to describe mobility triangles, we calculate the mobility area.
2 The geometry of offending and victimization
Mobility triangles are a geometrical representation of the relations between the offender's residence, the victim's residence, and the location of the criminal incident, each of which is a vertex of the triangle. First developed by Burgess (1925), mobility triangles provide a typology for describing the geometry of crime. Burgess (1925) describes three types of mobility triangles: (2) delinquency (neighbourhood) triangles (offenders' residence, victim's residence, and crime location all in the same neighbourhood/community), (offense) mobility triangles (offender's and victim's residence in the same neighbourhood, but the crime location is elsewhere), and promiscuity (total mobility) triangles (all points are in different neighbourhoods). Once classified, offender-victim movement patterns can be mapped and compared across different social groups, gender, and crime classifications.
The first known research to apply Burgess's (1925) mobility triangle typology to crime was Lind's (1930) analysis of crime in Honolulu. Lind's (1930) focus, however, did not include the location of the victim's residence. Rather, Lind (1930) was concerned with the residences of offenders, with regard to mobility triangles. Lind (1930) found that the delinquency triangle most often occurred within low socio-economic status neighbourhoods and that the mobility of offenders increased with age (delinquency [right arrow] mobility [right arrow] promiscuity triangles).
Normandeau (1968), studying various forms of robbery, introduced the victim into mobility triangle research but only considered solo-offenders. Perhaps more significantly, Normandeau (1968) expanded the typology of mobility triangles to five classifications. With this new typology, much more insight into the geometry of crime may be extracted: the offender and the victim reside in the same neighbourhood 26% of the time, the offender's residence and the crime location are in the same neighbourhood 33% of the time, and the victim's residence and the crime location are in the same neighbourhood 32% of the time. Therefore, there is a strong geographical bias in the commission of crime, whether that bias is finding targets close to the offender's home, or finding targets close to the victim's home.
Investigating rape in Philadelphia, Amir (1971) found that, most often (68% of the time), the crime neighbourhood triangle was present; in 82% of all cases, the offender and victim had residences in the same neighbourhood. Moreover, when comparing robbery and rape, it is clear that these two different crime classifications have very different dominating mobility-triangle types.
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. She finds that 31% of offenders find their targets in their home neighbourhood (census tract); however, there is a substantial range depending on the crime classification: the percentage is as low as 15% (larceny) and as high as 53% (homicide and rape). Overall, the total mobility triangle is the most common (45%), and the offence mobility triangle is the least common (5%). Furthermore, property crimes tend to be total mobility triangle and violent crimes tend to be neighbourhood triangles. Rand's (1986) results confirm the importance of analysing detailed crime classifications similar to the work of Amir (1971) and of Normandeau (1968).
Tita and Griffiths (2005) analysed mobility triangles for homicide. In their research, they employed a 5-classification typology that is the same as that of Normandeau (1968) but uses different naming conventions. They found that homicides tend to be either total mobility triangles (28%) or crime neighbourhood triangles (27%). Their primary contribution to this literature is...