Independent variables

3.5.1. Network measures

The primary network measure used in this study is Freeman’s betweenness centrality. Betweenness centrality is defined as the extent to which an actor is found on the shortest path between unconnected actors (Freeman, 1977). Individuals with high betweenness centrality score are able to control the flow of information between unconnected individuals and are able to reach different regions of the overall network.

Social capital in networks has often been measured using Burt’s structural holes measures. However, Borgatti, Jones and Everett (1998) maintain that when information

about the entire network is available, centrality measures such as betweenness centrality are richer measures than structural hole measures (e.g., effective size, constraint). Betweenness centrality measures a node’s position in the network by considering every node in the network, whereas structural hole measures are based on ego-networks (Borgatti et al., 1998).

Secondary analyses consider four additional network measures: 1) degree centrality, 2) effective size, 3) constraint, and 4) coreness. Degree centrality simply refers to the size of an ego’s network. High centrality in a network indicates “where the action is” (Wasserman, & Faust, 1994, p.179). In other words, high degree centrality indicates high visibility in the network.

While having many contacts in a network may be reflective of one’s importance, redundancy of ties greatly limits the access to unique information and the ability of an ego to control information flow in a network (Burt, 1992). Differential access to social capital implies positional advantages in a network (Bourdieu, 1986; Burt, 2000).

According to Burt (1992; 2004), positional advantages appear when one is taking advantages of structural holes. Structural holes are found in a network whenever two individuals or groups are not connected to one another (Burt, 1992). Bridging this gap confers positional advantages to the individual occupying this structural hole, as it grants access to different information and opportunities (Burt, 2004). Social capital, created by proximity to structural holes, is thus acquired by this mechanism known as “brokerage”

(Burt, 1992; 2004; 2005). Brokerage reflects social capital in the sense that “networks that span structural holes provide broad and early access to, and entrepreneurial control over, information” (Burt, 2000, p. 347).

Two measures were used to measure access to structural holes. Effective size of a network refers to degree centrality minus the redundancy of ties (Burt, 1992). In other words, effective size refers to an ego’s access to alters that are not connected to one another. Morselli and Tremblay (2004) argued that effective size of a network was more important that the simple size of this network in predicting criminal achievement. A related measure that was proposed by Burt (1992) is network constraint. While similar to effective size in that it is a measure of network redundancy, constraint considers the

“network time”³ invested in constrained individuals (Burt, 1992, p.55). Network constraint differs from effective size in that it is less related to degree centrality, and more related to network efficiency. In other words, low constraint indicates that a larger proportion of an ego’s alters are themselves low on constraint. Since network constraint is a proportion, changes in alters’ constraints will be less impacted in larger networks (i.e. because each alter is has smaller weight), than it will be in smaller ego-networks. Still, egos with small or large networks will receive similar low constraint scores if all their ties are themselves low on constraints. Comparatively, given that small networks can never achieve an effective size larger than their degree centrality, it is likely that larger networks will be associated with larger effective sizes as well.

Constraint is thus more reflective of strategic access to opportunities from structural perspective, whereas effective size reflects access to opportunities through the sheer volume of contacts.

The final measure used is the measure of coreness. Coreness measures the extent to which an individual is found at the core of a network rather than on its periphery (Borgatti & Everett, 1999), a measure that is especially suitable for research on gang networks (Bouchard & Konarski, in press). The measure estimates the coreness values for all pairs of nodes in a network and gives high values when most ties of an ego are found close to the center of the network, and low values when most ties are found in the periphery. This measure indicates to what extent an individual is in the “thick of things”.

Individuals close to the core of the network are thus crucial to the structure of the overall network.

All measures were computed using UCINET version 6.392 (Borgatti, Everett, &

Freeman, 2002).

3.5.2. Control variables

The main analysis includes three control variables. First, age was used as a control in regression models. Given the cross-sectional nature of the data, age was

3 In a non-valued network, network time simply refers to the proportion of all ego’s contacts an alter represents

coded as a gang member’s age at the end of the study period (2008). The relationship between age and criminal involvement is well known in criminology. Furthermore, given the inclusion of gang members from a wide age range, it was crucial to control for this effect. Second, further analyses revealed a quadratic effect of age on versatility.

Regression models thus included age squared in order to control for this effect.

Third, total arrests were entered as a control in the models. The relationship between offending frequency and versatility has been a source of concern for critiques of the use of the versatility index (Sullivan et al., 2009). The following chapter looks at the relationship in detail. However it is important to note that this variable does not necessarily refer to the number of arrests used to compute the versatility score. As will be demonstrated in the following chapter, some offences were excluded for the purpose of measuring versatility. Total arrests include all arrests recorded for an offender between 2001 and 2008. It is important to control for the total official contacts with police in this study as it may have an influence on offender’s networks. A gang member arrested frequently will most likely draw more attention from law enforcement, even if those arrests are minor probation violations.

An additional measure was used in secondary analyses. The proportion of arrests was used to measure the extent to which contacts with police were through official arrests or informal contacts. It was measured by dividing the total number of arrests by the total number of contacts (arrests and informal contacts). A high value on this measure indicates that most contacts between a gang member and law enforcement were made through formal arrests.