ARTICLE IN PRESS Social Networks xxx (2013) xxx xxx

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1 ON-763; No. of Pages 14 ARTICLE IN PRE ocial Networks xxx (2013) xxx xxx Contents lists available at civerse ciencedirect ocial Networks journa l h o me page: A sexual affiliation network of swingers, heterosexuals practicing risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach Anne-Marie Niekamp a,b,, Liesbeth A.G. Mercken c, Christian J.P.A. Hoebe a,b, Nicole H.T.M. Dukers-Muijrers a,b a Department of exual Health, Infectious Diseases and Environmental Health, outh Limburg Public Health ervice, PO Box 2022, 6160 HA Geleen, The Netherlands b Department of Medical Microbiology, chool of Public Health and Primary Care (CAPHRI), Maastricht University Medical Center (MUMC+), PO Box 5800, 6202 AZ Maastricht, The Netherlands c Department of Health Promotion, chool of Public Health and Primary Care (CAPHRI), Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands a r t i c l e i n f o Keywords: exual affiliation networks wingers Exponential random graph models (ERGMs) exually transmitted infections (TIs) Risk behaviour Two-mode methodology a b s t r a c t Using the example of the sexual affiliation networks of swingers, this paper examines how the analysis of sexual affiliation networks can contribute to the development of sexually transmitted infection (TI) prevention strategies. Two-mode network methodology and ERGMs are applied to describe the structural composition of the affiliation network and analyse attribute effects. wingers were found to recruit their sex partners through one large, moderately cohesive network component. wingers who used drugs or had a longer history of swinging tended to frequent websites instead of clubs. This study confirms the relevance of studying sexual affiliation networks and its additional value for TI epidemiology Elsevier B.V. All rights reserved. 1. Introduction exually transmitted infections (TIs) pose a major public health problem worldwide (WHO, 2007). TIs spread primarily through person-to-person sexual contact and, specifically, within so-called high-risk groups. Groups are defined as high-risk when their characteristics (e.g., low socioeconomic status) or behaviours (e.g., frequent changes in sexual partners) are related to high rates of TI transmission (WHO, 2007). To effectively target these high-risk groups is a central concern of TI prevention strategies and epidemiological studies. Research on sexual networks provides additional insight into how TIs spread throughout sexual networks, e.g., who is at highest risk of becoming infected, who is an important spreader of TIs, and how clustering of specific risk behaviours influences the spread of TIs. These insights can have important policy implications for targeted TI prevention strategies (Aral, 1999; Friedman and Aral, 2001; Doherty et al., 2005). wingers, i.e., heterosexual couples who, as a couple, have sex with others, have been identified as a sexual subpopulation with Corresponding author at: Department of exual Health, Infectious Diseases and Environmental Health, outh Limburg Public Health ervice, PO Box 2022, 6160 HA Geleen, The Netherlands. Tel.: ; fax: addresses: anne-marie.niekamp@ggdzl.nl, amniekamp@gmail.com (A-M. Niekamp). a high TI prevalence (10.4% of swingers visiting a Dutch TI clinic were infected with chlamydia and/or gonorrhoea) (Niekamp et al., 2009a,b; Niekamp et al., 2009c; Dukers-Muijrers et al., 2010). Consequently, swingers can be identified as a high-risk group and should be an important target group for prevention and care. However, although the number of swinger websites and clubs suggests that the population of swingers is large, this population is difficult to reach; swingers form a hidden sexual subgroup, and knowledge of their sexual network and sexual behaviour is scarce due to a lack of studies in this field. However, more insight into their sexual networks would enhance TI prevention and care. In the epidemiological and network literature on other highrisk groups, e.g., men having sex with men, there is an increasing body of evidence indicating that the venues where sex partners can meet or recruit other sex partners have an important role in the spread of TIs (De et al., 2004; Klausner et al., 2000; Klovdahl, 1985; Potterat et al., 1985). Interviews with swingers visiting our clinic indicate that swingers extensively affiliate with physical venues, i.e., swingers clubs, and virtual venues, i.e., swinger websites, to meet and recruit sex partners. Therefore, swingers form their sexual network based on their venue affiliations. Thus, our understanding of the hidden sexual networks of swingers can be increased by examining the venues they attend. These venues can be viewed as sexual affiliation networks (Frost, 2007), i.e., two-mode networks formed by two different sets of nodes: one set of nodes representing the swingers and another set of nodes representing the venues they affiliate with. Advanced two-mode network analysis /$ see front matter 2013 Elsevier B.V. All rights reserved. risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

2 ARTICLE IN PRE ON-763; No. of Pages 14 2 A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx techniques can be used to analyse affiliation networks such as the sexual networks of swingers (Frost, 2007). The analysis of sexual affiliation networks can complement conventional epidemiological methodology and make a unique contribution to the knowledge necessary for developing TI prevention strategies. Most empirical studies to date have, however, focused mainly on TI outbreaks in specific venues (De et al., 2004; Klausner et al., 2000; Klovdahl, 1985; Potterat et al., 1985). The existence and role of such venues in the spread of TIs among swingers have never been studied, and to the best of our knowledge, two-mode network methods have not yet been applied to specifically study sexual affiliation networks. In this paper, we focus on the understanding of the sexual affiliation network of swingers to better facilitate the prevention of the spread of TIs among this high-risk group. pecifically, we translate and apply theoretical mechanisms and concepts of one-mode sexual networks to two-mode sexual affiliation networks. We will focus on two aspects of the affiliation network: 1. the structural composition of the affiliation network; 2. the effects of the characteristics of the swingers. 2. Theoretical background Network studies on TIs have focused on the spread of TIs through sexual ties between people. They have tended to examine the sexual network as a one-mode network, i.e., a network containing only one type of node, namely, individual people. tudies of one-mode sexual networks demonstrated that the spread of TIs and the people at highest risk are strongly dependent on both the network structure and the group composition (Doherty et al., 2005; De et al., 2004; Fichtenberg et al., 2009). In the next section, we will first elaborate on the aspects of the network structure, and in ection 2.2, we will elaborate on the importance of individual characteristics tructural composition of the affiliation network and its potential to facilitate TI spread Focusing on the overall network structure, one important question is the extent to which the overall network structure is cohesive. Network cohesion can be defined as the extent to which people in the sexual network are connected to each other. Network cohesion can enhance both the speed of TI spread and the number of people who are infected by TIs. In an analogy to the one-mode sexual network case (Doherty et al., 2005; Ghani et al., 1997; mith et al., 2004), it can be argued that the more cohesive a sexual affiliation network is, the easier TIs will spread throughout the network. Two points are important to consider in this context. First, when the network consists of unconnected groups of people (components in network terms), an outbreak of an TI in one group cannot reach the other groups. The more components there are in a network, the fewer the number of people who will be infected by the TI. Applied to sexual affiliation networks, an increased number of components means that the TI spread will remain limited to one or a few venues and to the people who frequent these venues. econd, when the average distance between people is shorter, the spread of TIs will be faster. The same association applies to sexual affiliation networks, although it is mediated by venues; specifically, if the average distance is shorter, the spread of an TI through the population of swingers will be faster. Although the overall network structure is important for understanding the overall transmission of TIs, from an intervention perspective, targeting specific people is important to prevent the spread of TIs. In this respect, examining to whom people in the network are connected is important, as this relationship can contribute just as much to TI infection as a person s own sexual behaviour (De et al., 2004; Fichtenberg et al., 2009; Bell et al., 1999). Therefore, another important aspect of network structure is centrality, i.e., the position of an individual in the network. Being central in a sexual network, which indicates that a person has many direct and indirect ties to other individuals, enhances not only a person s risk of contracting an TI but also the probability of transmitting it to other people. Therefore, TI prevention should be focused on those central people. In the context of an affiliation network, active individuals (swingers), i.e., individuals who affiliate with many venues, are at higher risk of becoming infected, especially if they frequent high-risk venues. A venue can be labelled high-risk if it is frequented by individuals with a central position in the network. To identify these active individuals, degree centrality will be used. Less active individuals with a less central network position can, however, still have a high risk of TI infection when they are closely connected to other people who are in a central network position (De et al., 2004; Fichtenberg et al., 2009). This can be translated to sexual affiliation networks in the sense that swingers who frequent only one venue can still be at high risk of acquiring an TI if this venue is also frequented by swingers who attend several other venues. Given a core periphery structure, i.e., a high variation in the centrality of members in a network, core members are at a higher risk of becoming infected with an TI, and an TI in the core will spread quickly to other core members and more slowly to peripheral members. To identify who is at higher and lower risk of becoming infected, the coreness of a person in the core periphery structure, i.e., the measure of how near or far a person is located from the core, is important Attribute effects in sexual affiliation networks TI prevention strategies focus on changing the TI-related risk behaviour of those people at highest risk. Therefore, studying attribute effects, such as individual characteristics and the risk behaviours practiced by people, is relevant. Research in The Netherlands has shown that individuals who are younger, have a lower education level, or are of non-european ethnicity are at higher risk of TI infection (Götz et al., 2005). Risk behaviours related to the high transmission rates of TIs include the lack of condom use, men having sex with men, sexual practices such as anal sex, number of sex partners, group sex, and drug use (Götz et al., 2005; Friedman et al., 2011). Furthermore, our interviews with swingers suggested that novice and experienced swingers, as indicated by the number of swinging years, differ in their sexual risk behaviour. The attributes of individuals not only influence the direct risk of becoming infected but can also influence the choice of sex partners, thereby impacting the network structure. For example, individuals may select partners who exhibit the same risk behaviours, e.g., drug use. When individuals with similar attributes share a relationship, this practice is generally called homophily. Homophily can be caused by social influence and/or the process of social selection (Robins et al., 2007). ocial selection occurs when relationships are formed based on (dis)similarity of the attributes of the actors. In the sexual network literature, it is often referred to as selective mixing (e.g., Boily et al., 2000; Doherty et al., 2005). Dissimilarity, in particular, has been proven to increase the TI risk because individuals at low risk tend to connect with individuals at high risk (Doherty et al., 2005). Homophily can also be caused by social influence, the process in which a person s behaviour is influenced by the behaviour of the people with whom they have relationships (Mercken et al., 2010). With regard to prevention strategies, knowledge about patterns of homophily and the underlying process of social selection can be useful in the development of intervention risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

3 ON-763; No. of Pages 14 ARTICLE IN PRE A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx 3 strategies, e.g., address interventions about condom use to clusters of swingers that do not use condoms. Network interventions to change risk behaviour could be developed using knowledge of the existing patterns of social selection and influence. In the sexual affiliation networks of swingers, homophily is the clustering of swingers with the same attributes at the same venues. If individuals with high-risk behaviour cluster together at specific venues, those venues could be argued to be high-risk locations, and therefore, all the visitors of these venues are at higher risk; thus, swingers who do and do not practice this high-risk behaviour are expected to have a higher risk of TI infection. Prevention strategies can focus on these high-risk venues to prevent TI transmission and venue-related outbreaks of TIs. We will examine the existence and relevance of the attribute effects on the sexual affiliation network structure using two-mode Exponential Random Graph Models (ERGMs) (Wang et al., 2009a; Wang et al., this issue; Wang, 2013). Two-mode ERGM offers the advantage of combining attribute-based aspects with the structural aspects of the network, thereby enabling the examination of whether the described structural characteristics of the network still exist after controlling for the attribute effects. If, for example, a structural characteristic that facilitates TI transmission, such as a person s centrality, is based on a characteristic (e.g., drug use), prevention strategies can focus on people with these characteristics. The current paper aims to map sexual affiliation networks by studying swingers and their venues for sex partner recruitment and to explore the implications for TI epidemiology and prevention by addressing the following study questions: 1. What is the structure of the sexual affiliation networks of swingers, and can it facilitate TI transmission and place individuals at higher risk for TIs? 2. Are any characteristics of swingers associated with the sexual affiliation network structure? 3. Methods 3.1. Data collection The data used in this study were obtained from an open prospective cohort study of swingers, namely, the WAP (wingers World Attitude and Practice) cohort. The purpose of using the WAP cohort was to acquire insight into network-related determinants of the spread of TIs and into swingers sexual behaviour and norms. Medical ethical approval was obtained (2009) from the Medical Ethical Committee of Maastricht University Medical Center. The participants were recruited based on a convenience sample of swingers who attended the TI clinic of the outh Limburg Public Health ervice. Attendees were eligible when they met the definition of a swinger, i.e., being a member of a heterosexual couple that, as a couple, had sex with other couples and/or singles or being a member of a couple or a single who had sex with those heterosexual couples during the past year. This paper presents data from 103 participants from the first wave of the WAP cohort who had been active as swingers during the past 6 months and who provided information about their affiliations with websites or clubs. Following the regular procedures at the TI clinic, participants were tested for the following five major TIs: Chlamydia trachomatis, Neisseria gonorrhoea, Treponema pallidum (syphilis), HIV, and hepatitis B virus. Testing was followed by an extensive self-administered questionnaire assessing actor attributes, including sociodemographics, venues for partner recruitment, swinging history, sexual and drug use behaviours, medical history, perceptions about swinging, and TI and risk behaviours, and information about their partners exual affiliation network data The sexual affiliation network was composed of two sets of nodes: one set consisted of the swingers, and the second set consisted of the venues they frequented. A tie between a swinger and a venue meant that the swinger reported having frequented this venue in the past 6 months. Because ties can only exist between the different node sets, the resulting network is a twomode network. Hereafter, the definition of the two node sets and the computation of attributes for these node sets will be described Definition of venues The questionnaire provided data on participants sexual affiliations by measuring the venues they frequented during the past 6 months. Fixed venue options included lists of the most popular venues in the region, grouped as (i) eight swingers websites where sexual partners can be recruited, (ii) ten swingers clubs where swingers can meet and have sex, and (iii) five erotic parties where people can meet for erotic dancing and occasionally have sex. In addition, respondents had the option to indicate a maximum of three websites, two clubs and two erotic parties that were not listed. For the purpose of our current analysis, only those venues that were specially designed for swingers and were frequented primarily by swingers were included. We excluded general social network sites (e.g., Hyves) that were mentioned by a few swingers and erotic parties, primarily because these venues predominantly serve non-swingers. In total, 39 venues specific to swingers were reported to have been frequented. Of the venues, 33.3% (n = 13) were swinger websites, and 66.7% (n = 26) were swingers clubs; 41.0% (n = 16) of the venues were Dutch, 41.0% (n = 16) were Belgian, 12.8% (n = 5) were German, and 5.1% (n = 2, both websites) were internationally oriented and not associated with any particular country. We did not measure any additional information regarding the venues. Only one venue attribute was used for the current analysis, namely, the type of venue, which could be either a website or a club Definition of swingers and swing units The sample consisted of 103 swingers (median age 43 years). Among this sample, 50.5% (n = 52) were women, 66.0% (n = 68) were Dutch, 31.1% (n = 32) were Belgian, and 2.9% (n = 3) were German. Additionally, 11.7% (n = 12), 63.1% (n = 65), and 25.2% (n = 26) had low, medium, and high education levels, respectively. The population of swingers, almost by default, involves couples composed of one man and one woman who are in a steady relationship with each other and who swing together. This composition is reflected in our sample. Of the respondents, 89.3% (n = 92) were in a steady relationship or marriage and their partner was also part of the sample (forming 46 couples), whereas 5.8% (n = 6) of the respondents were in a steady relationship but their partner did not want to fill in the questionnaire, and only 4.9% (2 women and 3 men) were single at the time of measurement. This composition has important consequences. Because swingers swing together, they make the same choice of venues and, therefore, have exactly the same network ties in the sexual affiliation network; in other words, they are structural equivalents. The structural equivalence of the swingers was measured using the dual projection approach for structural equivalence, as developed by Everett and Borgatti (see their publication in this special issue). In 42 couples, both partners answered the question on venue choice. Of these 42 couples, only 4% were clearly not structural equivalents in their choice of venue. Of the 96% of couples that were almost completely structurally equivalent, one partner reported attending fewer venues in 29% of the couples. This difference is most likely due to recall differences. risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

4 ARTICLE IN PRE ON-763; No. of Pages 14 4 A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx The high frequency of structural equivalence in swingers posed a methodological challenge because it could confound further analysis of the data. As couples appeared to make the same choice of venues, couples were treated as single units, i.e., as one node in the network, in the subsequent analyses. A swing unit represents two individuals in a couple or a single person for those individuals who had no partner or whose partner did not participate in our study. Therefore, a new set of 57 nodes was defined, hereafter called swing units Computation of swing unit attributes In the previous section, we explained why we focus on swing units (couples) as nodes rather than as the individual swingers. Therefore, the attributes for the swing units also needed to be constructed based on the individual attributes of the partners in the swing unit. However, because there may be differences in the demographic data and sexual risk behaviours, both individuals of one swing unit may have different attributes, unfortunately leading to some loss of information in those swing units that consisted of a couple. To assign characteristics to swing units, we accounted for the manner in which the attribute affected TI transmission. Three demographic attributes were used: age, nationality, and level of education. The age of the swing unit was calculated as the mean age of both partners. Of the 46 couples, 81% (37 couples) differed by 5 years or less of age, 17% (8 couples) differed by between 5 and 10 years of age, and only 2% (1 couple) differed by more than 10 years of age. The nationality of a swing unit was defined as Dutch when both partners were Dutch; otherwise, the swing unit was defined as non- Dutch. Only 4% (2 couples) had discrepant nationalities. Regarding the level of education, the highest level of education reported by any partner in a swing unit was used. Differences in the level of education were more pronounced than the other demographic attributes; specifically, in 48% of the couples, one of the partners was more highly educated (difference of 1 level) than the other. In only 4% of the couples, one partner was much more highly educated (difference of 2 levels). The highest level of education is indicative of the socioeconomic position of the swing unit. In most cases, the highest educational level was that of the male partner. Five attributes reflected the TI-related sexual risk behaviours that are known to be correlated with TI transmission: condom use, anal sex practices, men having sex with men (MM), drug use, and group sex. Of the 46 couples, most were similar with regard to drug use, condom use, and group sex (91, 89, and 78%, respectively). A swing unit was considered to be using drugs if at least one partner had used recreational drugs during swinging in the previous 6 months. A swing unit was considered to belong to the category condom use if both partners in the swing unit always used condoms during penetrative (vaginal or anal) sex. A swing unit was considered to belong to the category of group sex in our study if at least one of the partners in the swing unit not only swapped partners but also had sex with more than two individuals at the same moment in time. This definition of group sex is narrower than that used in other recent studies addressing group sex (e.g., Friedman et al., 2011) because, by their definition, all swingers practice group sex. A swing unit was considered to belong to the category anal sex if at least one of the partners in the swing unit practiced penetrative anal sex. MM couples were inherently dissimilar because women cannot practice MM. If same-sex sexual practices were reported for a male, the swing unit was categorised as MM. All sexual behaviours were reported over the past 6 months. Two attributes were related to swinging history and behaviour: number of swinging years and number of swinging sex partners in the last 6 months. A total of 17% of the couples had a difference of at least one year in the number of swinging years, indicating that they did not start swinging together. The number of swinging years was defined as the mean number of years for which individuals in the swing unit had practiced swinging. Couples were very dissimilar with regard to the number of sex partners. In many cases, the women had twice as many sex partners as the men because women in general had sex with both men and women during swinging, whereas most men only had sex with women. The number of sex partners in the swing units was calculated as the mean number of sex partners of both individuals Analysis procedure Analysis of the structural composition of the network: cohesion and centrality The structural composition of the network was described and visualised using UCINET (Borgatti et al., 2002) and Netdraw version (Borgatti, 2002). Two cohesion measures were computed directly from the two-mode data: fragmentation and average geodesic distance. Fragmentation was calculated as the proportion of pairs of nodes that are unreachable from each other. Fragmentation is zero when the network consists of one component and all nodes are interconnected. The average geodesic distance measures the average of the shortest distances between a pair of nodes. Thus, the cohesion of a network increases when the average geodesic distance decreases (Borgatti and Halgin, 2011). To identify the position of specific swing units and venues, both degree centrality and coreness were calculated. In the sexual affiliation network, the swing unit can only be directly connected via venues and not by other swing units. Therefore, for the measurement of centrality, a different method and interpretation are used than those used in one-mode network analysis (Borgatti, 2009; Borgatti and Everett, 1997; Borgatti and Halgin, 2011). The degree and standardised degree of the swing units reflect the level of activity of the swing units (i.e., the number of different venues frequented). For venues, the degree measures reflect the level of the popularity of the venues. To calculate the degree in UCINET (Borgatti et al., 2002), the two-mode matrix was transformed into a bipartite one-mode representation, while normalised degree was obtained via the two-mode data procedure in UCINET (Borgatti et al., 2002). The existence of a core periphery structure and the associated coreness scores were tested following the dual projection approach for two-mode networks (Everett and Borgatti, in this issue). The coreness score measures the distance of a node to the core. The higher the coreness score, the closer the node is to the core of the affiliation network Analysis of attribute effects In a subsequent step, statistical analyses were conducted to assess the importance of swing unit attributes and venue type on the network structure. To explore associations between the swing unit attributes and the number and type of venues, epidemiological analyses, including non-parametric and chi-square tests, were conducted. These analyses were performed with P package version 17.0 (P Inc., Chicago, UA). Two-mode ERGMs (Wasserman and Pattison, 1996; nijders et al., 2006; Robins et al., 2007; Wang et al., 2009a; Wang et al., this issue; Wang, 2013) provide a method for modelling the structure of complex affiliation networks and testing for attribute effects (e.g., patterns of homophily and social selection) on the network structure. In the example presented here, in the ERGM, we only included attributes that were significantly associated, based on the epidemiological analysis, with the number and types of venues frequented. The statistical analysis of the ERGMs was conducted with BPNet (Wang et al., 2006), a program used for the estimation and risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

5 ON-763; No. of Pages 14 ARTICLE IN PRE A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx 5 simulation of two-mode networks using Markov Chain Monte Carlo Maximum Likelihood estimation techniques. For a further introduction to ERGMs and two-mode ERGMs and for technical details about fitting ERGMs with BPNet, we refer the reader to nijders et al. (2006), Robins et al. (2007), Wang et al. (2009a,b), Harrigan (2009), Wang et al. (this issue), Wang (2013), Robins and Lusher (2013a,b), and Koskinen and Daraganova (2013). An ERGM was deemed acceptable for interpretation if it converged (t-ratios for all parameters <0.1), had a good goodness of fit (GOF), and was easy to interpret, according to Wang et al. (2009a). To obtain convergence, the graph density was fixed (nijders et al., 2006). Models without a fixed density did not result in good convergence. 4. Results 4.1. tructural composition of the network The final sexual affiliation network consisted of 57 swing units and 39 venues. All swing units formed affiliations with at least one venue (see Fig. 1). Of the 57 swing units, 59.6% (n = 34) frequented both websites and clubs, 36.8% (n = 21) frequented only websites, and only two swing units (3.5%) frequented clubs only. The network formed a single component (which corresponds to a fragmentation of 0). Therefore, all swing units and venues in the network were interconnected with each other through the network. Thus, in principle, an TI can spread throughout the entire network. However, the speed of spread may depend on the distance between the nodes. The average distance between two nodes in the affiliation network was 3.1, indicating that the overall structure of the component was moderately interconnected. Because the network consisted of one moderately interconnected component, an TI outbreak at one venue, e.g., a club, will most likely not remain restricted to this venue but also extend to other venues. With respect to the units that are central in the network and therefore should be targeted in an intervention, we next consider both the degree centrality and the coreness of the swing units and venues (Table 1). The activity (degree) of the swing units varied between the attendance of 1 and 12 different venues (normalised degree, ). The popularity (degree) of the venues varied between 1 and 33 for websites (normalised degree, ) and between 1 and 10 for clubs (normalised degree, ). Moreover, the sexual affiliation network had a clear core periphery structure, with a core of highly connected swing units (n = 16) and venues (n = 7) (Fig. 2). This core has a density of 0.607, whereas the periphery has a density of Although the network consists of one component, both the range for the degree centrality and the core periphery structure indicate a high level of centralisation, i.e., the extent to which some swingers and events are more central than others. The coreness scores for swingers and venues are provided in Table 1. The coreness scores varied between and for swing units and between and for venues. In Fig. 1, these coreness scores are represented by different node sizes. Table 1 and Fig. 1 both show that the venues in the core of the affiliation network are all websites. The 7 websites and 16 swing units in the centre of the graph in Fig. 1 form the core of the affiliation network. The highly connected core enables an TI in one core member to spread quickly to the other core members and, shortly thereafter (but with a slower speed), to the periphery. Because core members have a higher risk of becoming infected with an TI and spreading that TI, targeting TI prevention strategies at core members could therefore be more effective than targeting them at peripheral members. Because all core venues turned out to be websites, interventions should especially focus on visitors to these websites. Table 1 Centrality measures of swing units and venues, sorted in descending sequence of coreness score. Top 16 swing units and top 7 venues (all websites) form the core of the affiliation network. wing unit Degree Normalised degree Coreness score Core Periphery Venue (C = club, W = website) Degree Normalised degree Coreness score Core W W W W W W W risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

6 ARTICLE IN PRE ON-763; No. of Pages 14 6 A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx Table 1 (continued ). wing unit Degree Normalised degree Coreness score Periphery C W C C W W C C C C C C C C C C C C C W C C C C C C C C C W W C drug use. wing units that reported a longer history of swinging, had group sex, or used drugs visited more websites than those who did not report these behaviours. This association can also be visualised in Fig. 3. In addition, core members appeared to use drugs and practice group sex more often than peripheral members. Although these results appear to indicate that coreness was related to these attributes, we did not further test for this relationship. Furthermore, no relationship was observed between drug use and the number of clubs frequented. winging years, group sex, and drug use were not significantly interrelated in multiple bivariate analyses ERGM results To further assess the importance of attribute effects to risk behaviour, we fitted several ERGMs to the affiliation network. All models presented below converged and had a good goodness of fit (Robins and Lusher, 2013b). A list of the parameter effects that were used, including their graph configurations and descriptions, is given in Tables 3 and 4. The list is based on earlier work by Agneessens et al. (2004), Agneessens and Roose (2008), and Wang et al. (2009a), Wang et al. (this issue). The models included parameters for both structural (Table 3) and attribute (Table 4) effects. The parameter estimates and standard errors for the different models are presented in Table 5. A parameter effect is significant (with an alpha of 0.05) when the estimate is at least twice its standard error, or greater, in absolute value. A large positive parameter estimate suggests that the effect tends to occur more than expected by chance (given the other effects in the model), and a large negative parameter indicates that the effect tends to occur less than expected (Lusher and Robins, 2013) Attribute effects To examine the importance of the attributes of the swing units, we first explored the associations between swing unit attributes and the number and types of venues frequented (Table 2). wing unit attributes were generally not significantly associated with the number of websites or clubs frequented, except for the following three characteristics: number of swinging years, group sex, and Baseline model First, a baseline model was tested with only structural effects, as shown in Table 3. The parameters in the model are related to the structural network characteristics that we found to be important during the descriptive network analysis: the edges (density) and three-path parameter are used to capture cohesion, star parameters are used to represent the level of centralisation and the core periphery structure, and clustering and sharing parameters are used to test for clustering effects. Fig. 1. Affiliation network of swing units and venues graph, size of nodes is based on coreness score. The websites and swing units in the centre form the core of the affiliation network. risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

7 ON-763; No. of Pages 14 ARTICLE IN PRE A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx 7 Fig. 2. Core periphery structure of the affiliation network. The numbers are referring to the swing units. To find the best baseline model, both models with lower order and higher order ERGM effects were tested (nijders et al., 2006; Wang et al., 2009a). Models with only lower order effects did not converge, whereas models with only higher order effects had problems associated with the degree distribution, most likely because the observed network did not include any isolates. Not disallowing isolates in the estimation of the model is going to adversely affect many of the other structural features of the network (especially alternating degree parameters, as these placed very strict functional restrictions on the number of isolates) (nijders et al., 2006). A solution would be to constrain the degree distribution in the sense that it is only possible to sample graphs in which every node has at least a degree of one (Wang, 2013). This option was not available in any statistical package, e.g., BPNet, at the time of analysis. To partially take this problem into account, we include lower order degree distribution effects (2-stars and 3-stars) in combination with higher order degree distribution effects (alternating stars) in the baseline model. However, models that combine lower and higher order degree distribution effects need to be interpreted with caution because these effects can interact with each other (nijders et al., 2006). In the baseline model (Table 5, model I), significant structural ERGM effects were found that could explain the observed affiliation network. The positive 2-star effects for swing units and venues indicate that there were some active swing units and some popular venues in the network, and the negative alternating star effects suggest that there was little variation in the degree distribution for the less popular nodes (Wang, 2013). Combining the results of the 2-star and alternating star effects confirms the core periphery structure found in the descriptive analysis of the structural composition of the network (Robins and Lusher, 2013b). However, the degree-based effects have to be interpreted with some caution because of the described limitations of the software regarding the estimation of networks without isolates. The significant negative three path effect was weak but indicated a tendency of active swing units to not frequent popular venues (Agneessens and Roose, 2008). risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

8 ARTICLE IN PRE ON-763; No. of Pages 14 8 A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx Table 2 Associations between swing unit attributes and venue attributes tested with non-parametric and Chi-square tests. U attribute U attribute distribution % (n) Websites Clubs Visited a % (n) Median number [IQR] Visited % (n) Median number [IQR] All swing units (n = 57) 100[57] 96.5 [55] 2[2 3] (range 1 10) 63.2 [36] 2[1 3] (range 1 5) Age (U mean) < [34] 96.7 [33] 3[2 4] 64.7 [22] 2[1 3] [23] 95.7 [22] 2[1 3] 60.9 [14] 2[1 2] Nationality All U Dutch 59.6 [34] 94.7 [36] 2[1 4] 65.8 [25] 2[1 3] Non Dutch 40.4 [23] 100[19] 3[2 3] 57.9 [11] 2[1 3] Education (U highest) Low/middle 61.4 [35] 97.1 [34] 3[2 4] 57.1 [20] 2[1 3] High 38.6 [22] 95.5 [21] 2[2 3] 72.7 [16] 2[1 2] Years swinging (U mean) * < [28] 92.9 [26] 2[1 3] 71.4 [20] 2[1 3] [29] 100[29] 3[2 5] 55.2 [16] 3[1 3] No. of partners b (U mean) < [30] 96.7 [29] 2[2 3] 56.7 [17] 2[1 3] [27] 96.3 [26] 3[2 4] 70.4 [19] 2[1 2] Male-male sex b No 77.2 [44] 95.5 [42] 2[2 3] 65.9 [29] 2[1 3] Yes 22.8 [13] 100[13] 3[2 5] 53.8 [7] 1[1 3] Always condom use b No 56.1 [32] 96.9 [31] 3[1 4] 65.6 [21] 2[1 3] Yes 43.9 [25] 96.0 [24] 2[2 3] 60.0 [15] 2[1 3] Anal sex b No 59.6 [34] 97.1 [33] 3[2 4] 67.6 [23] 2[1 3] Yes 40.4 [23] 95.7 [22] 2[2 3] 56.5 [13] 2[1 2] Group sex b * No 33.3 [19] 100[15] 2[1 3] 68.4 [13] 2[2 3] Yes 66.7 [38] 94.7 [36] 3[2 4] 60.5 [23] 2[1 3] Drug use b * * No 29.8 [17] 88.2 [15] 2[1 2] 88.2 [14] 2[1 3] Yes 70.2 [40] 100[40] 3[2 4] 55.0 [22] 2[1 3] IQR, interquartile range; U, swing unit; n, number of swing units. * ignificant (p < 0.05). a Difference in proportions not calculated because of high prevalence of frequenting website. b Reported over the past 6 months during swinging. Fig. 3. Affiliation network graphs with swing unit attributes for drug use, group sex and swinging years, size of nodes is based on coreness score. risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

9 ON-763; No. of Pages 14 ARTICLE IN PRE A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx 9 Table 3 Baseline structural effects for ERG models. tructural effect BPNet code Description positive (+) and negative ( ) effect Graph configuration wing unit 2-star A2 Lower and higher order effects for variance in swing unit degree-distribution: wing unit 3-star A3 (+) Tendency of some swing units to be more active (frequent more venues) and others to be less active ( ) Tendency of swing units to be more equal in activity wing unit alt-star A-A Venue 2-star B2 Lower and higher order effects for variance in venue degree-distribution: Venue 3-star B3 (+) Tendency of some venues to be more popular (frequented by more swing units) and others to be less popular ( ) Tendency of venues to be equal in popularity (lower order degree distribution effect) Venue alt-star A-B Three path L3 (+) Tendency of active swing units to frequent popular venues ( ) Tendency of active swing units not to frequent popular venues Clustering C4 (+) Given that a swing unit already shares a venue with another swing unit, the tendency for both swing units to share another venue to form ( ) Given that a swing unit already shares a venue with another swing unit, the tendency not to select another venue tied to this swing unit wing unit sharing A2P-A (+) Tendency for venues to share multiple swing units ( ) Tendency against venues to share multiple swing units Venue sharing A2P-B (+) Tendency for swing units to share multiple venues ( ) Tendency against swing units to share multiple venues, swing units;, affiliation. risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),

10 ARTICLE IN PRE ON-763; No. of Pages A-M. Niekamp et al. / ocial Networks xxx (2013) xxx xxx Table 4 Binary attribute effects for ERG models. BPNet code Description positive (+) and negative ( ) effects Graph configurations wing unit attribute effect wing unit attribute density Attr-RA (+) Higher tendency of swing units with attribute to frequent venues, compared to swing units without attribute ( ) Lower tendency of swing units with attribute to frequent venues wing unit attribute 2-star Attr-TOA2 (+) Tendency of swing units with the same attribute to share the same venues ( ) Tendency of swing units with different attributes to share the same venues Venue attribute effects Venue attribute density Attr-RB (+) Higher tendency of venues with attribute to attract swing units compared to venues without attribute ( ) Lower tendency of venues with attribute to attract swing units compared to venues without attribute Venue attribute 2-star Attr-TOB2 (+) Tendency for swing units to frequent venues with the same attribute ( ) Tendency against swing units to frequent venues with the same attribute Combined attribute effects Combined swing unit and venue attribute density Attr-RAB (+) Tendency of swing units with attribute to frequent venues with attribute ( ) Tendency of swing units with attribute not to frequent venues with attribute, venues with or without attribute;, venues with attribute;, swingunits with or without attribute;, swingunits with attribute;, affiliation. The significant negative parameter for swing unit sharing combined with the significant positive-venue 2-star parameter suggested a tendency of venues to not share swing units and therefore a tendency to not cluster. Thus, two venues that are frequented by the same swing unit are less likely to be both frequented by other swing units. This pattern could explain the lack of fragmentation and the moderate geodesic distance in the affiliation network, and it increases the probability of the spread of an TI throughout the network ingle attribute models econd, we tested single attribute models, where the baseline model was extended for each attribute separately with the corresponding attribute effects (attribute density and attribute 2-star) as described in Table 4. We only included swing unit attributes that were significantly associated with the number of venues frequented in the earlier epidemiological analysis: drug use, group sex, and number of swinging years (Table 2). In the four single attribute models, a significant but weak attribute effect was found only for the drug use 2-star (Table 5, model II), indicating homophily based on drug use, i.e., some venues attract drug-using swing units and others attract non-drug-using swing units. For the other swing unit attributes, i.e., group sex (Table 5, model III) and number of swinging years (Table 5, model IV), no significant attribute effects were found. The venue attribute website effects (Table 5, model V) were also not significant, indicating that there was no difference in the tendency of websites and clubs to attract swing units Combined attribute models In the combined attribute models, we specifically examined the relationship between swing unit attributes and venue attributes (i.e., whether swing units with a particular attribute have a higher tendency to frequent a venue with a particular attribute) by adding combined attribute effects. For each of the swing unit attributes, the model was extended by including the two venue attribute effects (density and 2-star effect) and a combined attribute density effect for the swing unit attribute and venue attribute together. In the combined attribute model for drug use (Table 5, model VI), both drug use density and website density had significant negative effects, indicating that drug users had a lower tendency to frequent venues and that websites had a lower tendency to attract swing units. There was a significant positive effect for the combined density of drug use and websites; specifically, drug users had a stronger tendency to visit websites than non-drug users. Interestingly, the significant drug use 2-star effect became non-significant, indicating that the segmentation of venues into those that are attended by those that use drugs and other venues that predominantly attract non-users appears to be explained away by the types of venues that drug users and non-users choose. Interventions that focus on the prevention of drug use and related risk behaviours could therefore better be directed to visitors of websites instead of club visitors. With regard to group sex (Table 5, model VII), there were no significant attribute effects in the combined model. Thus, there was no difference in the type of venue preferred between swing units that practice group sex and those that do not practice group sex. The combined attribute model for the number of swinging years (Table 5, model VIII) showed a significant positive effect for the combined density of swinging years and websites. wing units that have swung longer have a strong tendency to frequent websites. Therefore, prevention strategies that focus on this group of swingers should preferably be directed at websites Final model Lastly, we fitted a final model that included all attribute effects to examine the effects of the attributes controlling for all other attributes. In the final model (Table 5, model IX), the same effects risk behaviours that potentiate the spread of sexually transmitted infections: A two-mode approach. oc. Netw. (2013),