School bullying and social networks

School bullying and social networks Master thesis Mónica Vasco Ruiz Supervisor: Jaromír Kovářík Master in Economics: Empirical Applications and Policies 2021/22 University of the Basque Country UPV/EHU School Bullying and Social Networks. M´onica Vasco Ruiz July 29, 2022 Abstract Although school bullying has enormous health, social, and economic consequences that last throughout the entire human life, most bullyingprevention programs are ineffective partially because detecting bullies and their victims is challenging. This study proposes to employ social networks to identify the victims of bullying. To that aim, we elicit friendship and enmity networks and document who suffers bullying in several secondary schools in southern Spain. We show that both friendshipand enmitynetwork measures are relevant and complementary predictors of victimization, independent of classic non-network characteristics employed in the literature. However, how individual positioning and global features of the social organization determine who suffers bullying differs across male and female adolescents. We discuss our results in relation to existing theories of bullying victimization in psychology and sociology. Keywords: Aggression, social networks, school bullying, victimization, friendship, enmity, gender. 1 Introduction Human behavior must be understood in terms of social contexts and groups to which people belong (Moreno, 1934). Not surprisingly, social conditions in childhood and adolescence shape human development. Indeed, there is large evidence that children with positive relationships with their peers have higher levels of emotional well-being, participation, and academic achievement (Wentzel, 2017). In contrast, negative relationships in childhood have adverse effects on many facets of one’s life (Farrington, 1989; Peets et al., 2007; Potirniche and Enache, 2014). Furthermore, such impact on childhood and adolescence peer relationships increases over time (Kaess, 2018). One of the most serious socialization problems in schools is bullying (Olweus, 2013; Juvonen and Graham, 2014). School bullying is defined as repeated and disruptive behavior where one or several classmates intentionally annoy or hurt other 1 classmates, both physically and emotionally. It can take various forms, including physical assault, shoves, teasing, making threats, name-calling, or humiliation (C¸alı¸skan et al., 2019). School bullying is a persistent worldwide phenomenon (UNICEF, 2018; WHO, 2013) and its consequences extend to all domains of bullies’ and victims’ life and span throughout the whole life. More directly, bullying correlates to depression, suicidal and criminal tendencies, drug abuse and violence in both childhood and adulthood (Bernstein and Watson, 1997). However, bullying also has less direct consequences. Individuals involved in bullying have lower education and financial skills (Zych et al., 2015) and higher unemployment rates, lower wealth and income later in life (e.g. Hong and Espelage (2012); Takizawa et al. (2014); Wolke and Lereya (2015); Brimblecombe et al. (2018); Carrell et al. (2018); Sarzosa and Urz´ua (2021)). Although bullying is an understudied topic in economics,1this phenomenon and its consequences have stimulated large literature in other fields. They are of great concern among policymakers (Ortega Ruiz et al., 2013; Baldry and Farrington, 2007; Huang et al., 2019; Olweus and Limber, 2010; Menesini and Salmivalli, 2017; Rigby, 2002).2Motivated by the literature, a considerable number of bullying-prevention programs targeting group-level behavior have been designed and implemented all around the World (see Salmivalli (2010) for a review). However, the meta-analytic studies has concluded that these programs are ineffective (Smith et al., 2004; Merrell et al., 2008; Ttofi and Farrington, 2011; Gaffney et al., 2019; Ferguson et al., 2007). The disappointing results of the existing bullying prevention programs generate several questions. In this study, we answer some of these questions. In particular, we first ask whether victimization is related more to positive or negative relationships or whether positive and negative relationships are two independent predictors of bullying. Second, is bullying a group-wide phenomenon indeed, as suggested by the literature in sociology, or is it only related to local networks, without any relation to more distant network neighborhoods? Lastly, since bullying is a genderspecific phenomenon (Maccoby and Jacklin, 1980; Olweus, 1991; Carbone-Lopez et al., 2010; Silva et al., 2013; Sentse et al., 2015), we pay particular attention to whether how social organization relates to victimization differs across genders. To answer these questions, we exploit the tools of network theory, linking bullying victimization and the patterns of social interactions. To these aims, we first elicit a large dataset on 3,035 students in 11 high schools in Andalusia, the most populated region in Spain. Notably, the data contain an enormous amount of information about all the students, their classes, and schools, including the friendship and enmity networks and selfand other-reported bullying victimization (see Section 3 for details). In our analysis, we explore to what extent the friendship 1See e.g. Brown and Taylor (2008) or Sarzosa and Urz´ua (2021) for exceptions. 2Stop bullying (www.stopbullying.gov) and Beat Bullying (www.coe.int/en/web/edc/beatbullying) are examples of public programs documenting and targeting bullying in the US and European Union, respectively. 2 and/or enmity network information at different levels predict the likelihood of becoming a victim of bullying. Our results indicate that victims occupy peripheral positions in the class friendship networks. However, they are more central in the enmity networks both locally using local measures of centrality and globally using global measures of one’s centrality.3Moreover, both types of relationships are independent predictors of victimization. Network-wide characteristics of the class networks also play a role while explaining victimization, but their impact is quantitatively weaker than that of individual positioning, contradicting the classic approaches to bullying prevention that exclusively target groups rather than individuals. However, since both levels matter differently, the existing programs should target both groups and individuals. Moreover, the positioning of male and female victims differ considerably, suggesting that the reasons why each gender is victimized are different. To the best of our knowledge, the only paper that relates bullying networks is Mouttapa et al. (2004). They analyze a sample of predominantly Latino and Asian schools in the U.S. and correlate bullying with certain features of students’ local networks, such as the number of friends and the likelihood of people having friends engaged in bullying. They find that victims receive fewer friendship nominations from others, but this effect only holds for women. As opposed to Mouttapa et al. (2004), our sample is more extensive and dramatically more representative of the general school population. In addition, we combine both friendship and enmity networks, and our data–particularly the high number of independent networks in our sample–allow us to analyze the role of (not only students’ direct network neighborhoods but also) the entire network architecture in the school. Therefore, our results largely extend their work, provide a more general picture of the role of social organization in bullying, and provide different policy recommendations. The remainder of the paper is structured as follows. Section 2 reviews the literature and presents our research hypotheses. In Section 3, we describe our methodology and the data. Section 4 presents the results. Finally, the last section concludes. 2 Related literature and research hypotheses Our starting hypothesis is that, since bullying is by definition a social phenomenon, the structure of the social organization in schools can stimulate or mitigate bullying. However, the open question is which particular features of social organization matter and how. In this section, we generate several research hypotheses based on the existing theories of bullying victimization in psychology and sociology. To achieve these aims, we focus on analyzing the interaction patterns among peers at school using network data. Social network analysis is a suitable approach to studying links between nodes, how they are connected by existing friendship or enmity, or they are isolated due to lack of these links (Borgatti 3See Section 3 for the different measures employed in this study. 3 et al., 2018; Wasserman et al., 1994). We first discuss whether bullying is a local or group-level phenomenon. Although the literature considers different levels within the socio-cultural structure (Hinde and Stevenson-Hinde, 1987), currently, the dominant theory in the literature that motivates most of the interventions is that bullying is a group-level phenomenon (O’connell et al., 1999; Oldenburg et al., 2018; Lagerspetz et al., 1982; Sutton and Smith, 1999). Therefore, if the group-level norms and organization matter, then network theory predicts that network-wide characteristics (rather than individual positioning) predict the extent of victimization. Hence, we hypothesize the following: H1Global-wide network characteristics predict the extent of bullying victimization. However, the literature does not provide any specific theory regarding which characteristics determine bullying and in which direction. Hence, rather than generating our specific hypotheses, we let the data speak and explore the natural candidates postulated by network theory, such as measures of integration, connectivity, and hierarchy (see Section 3). In contrast to the current theories, the earlier literature has mostly focused on identifying individual risk factors (Juvonen and Graham, 2001, 2014) and the determinants of victimization (Graham, 2016; Olweus, 1997). Hence, we also correlate victimization with individual positioning in friendship and enmity networks. As for friendship networks, Haynie et al. (2001) state that victims exhibit lower self-esteem, feel lonelier, and are less happy at school than their peers. At the same time, it has also been shown that conflict can be reduced with the social influence of referring students and that friendships can provide protection against victimization (Paluck et al., 2016; Paluck and Shepherd, 2012). These claims suggest that victims should have fewer friends or, in network terminology, should have lower connectivity and degree in the friendship networks. In contrast to these claims, Mouttapa et al. (2004) do not find correlations between the number of friends and victimization though. Our second hypothesis is: H2Connectivity/degree in the friendship networks is negatively related to victimization. The role of connectivity (i.e. local centrality) notwithstanding, there are neither theories nor empirical evidence regarding the role of whether the victims would be less central globally. Since our network approach allows us to compute global centrality measures (see Section 3), we test whether being globally central– on top of having many friends–plays a role in victimization but we provide no research hypothesis in this respect. 4 As discussed above, negative interactions might also matter. Moreover, since bullying is a negative social phenomenon by definition, enmity interactions might, in fact, be more important predictors than friendships. It has been documented that negative peer attitudes and hostile school environmental factors can increase the frequency of bullying (Meyer-Adams and Conner, 2008; Pellegrini and Bartini, 2000; Totura et al., 2009; Hong and Espelage, 2012; Rigby, 2005). Therefore, we test whether having many enemies (that is, high local centrality in the enmity network) predict bullying victimization, using the following hypothesis: H3High connectivity in enmity networks predicts bullying victimization. Once again, we have no hypothesis regarding whether less local measures of positioning in the enmity networks matter and how. Finally, there is extensive evidence that bullying is a gender-specific phenomenon in determinants and forms. Girls tend to engage in more indirect bullying (such as gossiping) while boys are more direct (e.g., aggression) (Farrington and Baldry, 2010; Olweus, 1991; Scheithauer et al., 2006; Borg, 1999). Boys are more likely to be involved in bullying than girls, although this effect is less robust across studies (Markkanen et al., 2021). In addition, almost all results in Mouttapa et al. (2004) are gender-specific. Therefore, we hypothesize that: H4Social network positioning and global structure of the class friendship and enmity networks determine bullying victimization differently across genders. Apart from the hypotheses stated above, we test other issues that are not supported or discussed in the literature but which we find of practical relevance. For example, will the local positioning be more, equally, or less important than the network-wide patterns? Is the role of positive and negative relationships complementary predictors of bullying, or do they provide the same information about bullying? These questions are relevant because practical applications of our results should potentially elicit the whole network architectures and both negative and positive relationships. That would require data collection and work that is more complex than eliciting and employing simple individual characteristics. 3 Data and methodology The data for this project have been collected by the authors as a part of the COMPHAS project.4We collected a sample of schools in southern Spain, in which we conducted an extensive in-class survey with 1st - 4th grade students. The survey 4The project called Mapeo de Competencias y Habilidades del Alumnado de Ense˜nanza Secundaria is managed by the Loyola Behavioral LAB (a behavioral economics research center) and the ETEA Foundation at the Universidad Loyola Andaluc´ıa. The project was positively evaluated by the Ethics Committee of the Universidad Loyola Andaluc´ıa. 5 was computerized using an online platform Sand (https://sand.kampal.com), designed for the elicitation of network (and other) data. The survey was conducted between 2021 and 2022 in 11 secondary schools in Andalusia, Spain. All students in the sampled schools were contacted and invited to carry out the survey. Out of the 3,035 students officially enrolled in the schools, 2,521 agreed to start the experiment. We found absenteeism cases, and some students did not finish the online survey. A total of 2,401 students completed the entire survey. In this final sample, 1,210 were men, 1,157 women, 21 reported non-binary gender, and the rest did not answer the gender question. A fraction of 7.4% of students are of migrant origin; this figure is slightly lower than the average of 9.9% in the Spanish non-University education system. The scope of the survey was broad and not only oriented toward the goal of the present study. We elicited a large battery of students’ skills, abilities, behaviors, and attitudes. The survey was designed to provide data on various aspects that play a central role in an adolescent’s daily life. The first part focuses on the sociodemographic characteristics of the school. Additionally, we elicit students’ school achievement, performed risk, and time decision-making tasks, financial literacy, and cognitive reflection tests, etc. Moreover, we elicited students’ selfesteem and personal satisfaction. Importantly, the survey also included questions regarding subjects’ relationships with other students in their school. This included friends and, out of the friends, the best friends, as well as enemies and, out of the enemies, the worst enemies. For that purpose, the appication provided all students with list of all the other students from the same school and year. Hence, each network in our data corresponds to all students from different classes but the same year in one school. Last, participants indicated in the list of other students those who suffered bullying. They were explicitly stated that if they suffered it themselves, they should mark their own name, and if they knew about any other students who suffered bullying, they should mark them. Below, we term self-reported bullying the case when a student included herself in the list of bullied people in the school and other-reported bullying when others indicated someone as a victim. From the friendship and enmity lists, we constructed the networks using the R software and analyzed them. The network data will serve as our primary explanatory variables in Section 4. We performed a nonlinear regression analysis with the statistical package Stata. Our models correlate friendship and enmity network measures with different variables on bullying victimization (see below). 3.1 Dependent variables Our dependent variable reflects whether an individual suffers bullying or not. During the elicitation stage, the survey explicitly included a definition of bullying, 6 complying with the guidelines of the Ethics committee and the Spanish laws. More precisely, the students have been provided with the following information: ”Bullying exists when, repeatedly, several students intentionally annoy a classmate who is unable to stop it. The annoyance can be one or more of the following acts: •Teasing, insults, badmouthing, rejection, negative comments and humiliation (which can also be cyberbullying through Facebook, Whatsapp, Twitter, etc.) •Threats, hits, shoves and the like. If there is bullying in your class group, mark those who are bullied (max. 3). If they do it to you, mark yourself. If there is no bullying, don’t mark anyone.” As mentioned above, apart from this information, the program SAND has provided all students with a list of all the people in the same year in their school, including themselves. They were simply asked to mark those who suffered bullying, including themselves if that was the case according to their opinion. From the reported data, we can distinguish two binary variables indicating whether a student is a victim or not. Firstly, self-reported bullying is the case when a student names himself as a victim, while other-reported bullying refers to cases when a student is named by another as a victim. Both variables take the value of 1 (0) if the participant is (not) a victim. Table 1 summarizes these variables on aggregate and by gender. Although females are more likely to self-report, males are more likely to be named by their peers. In addition, we employ a categorical variable measuring the number of times other classmates have mentioned a student as a victim (labeled No. mentions below). This variable ranges 0 to 8 in our data. Table 1: Fractions of self-reported and other-reported bullying, disaggregated by gender Total Males Females Others N M N M N M N M Self victim-bullying 2,518 0.029 1209 0.026 1157 0.035 152 0.013 Others victim-bullying 3,029 0.094 1210 0.125 1157 0.067 662 0.083 In addition to these variables, we also analyze two other measures, which we label as “intersection” and “union” of selfand other-reported bullying. More precisely, a student is considered bullied using the intersection variable if she selfreport herself as a victim and at least one other individual corroborates it. A student is considered a victim under the union variable if she self-reports herself as a victim or at least one other individual reports that she suffers bullying. Table 2 provides the number of cases in each of the four situations generated by such 7 classification. Table 2: Number of cases of bullying victimization in function of who reports that a students suffer bullying. No others-reported Yes others-reported Total No self-reported 2,237 207 2,244 Yes self-reported 38 36 74 Total 2,269 241 2,518 In total, 2,518 participants answered the question about bullying, among whom 315 individuals are marked either by themselves or by others as bullying victims, representing roughly 12% of the sample. Only 74 (2.9%) students self-reported as victims of bullying, while 241 (9,4%) were reported as victims by other classmates. Their peers corroborate almost 50% of the self-reported cases. These cases correspond to our intersection variable. In contrast, 14% of other reports are corroborated by the victim. In order to analyze the role of the entire network architecture, we consider dependent variables that add up to the victims of bullying in each network. Again we can consider the variables “intersection” and “union” of selfand other-reported bullying. However, of the 30 networks obtained5only 1 does not contain any type of bullying case, as Table 3 shows. Therefore, we focus on the intersection variable for greater reliability. This dependent variable is used in the Section 4.2.2. It counts the cases of bullying reported by the victims and confirmed by their peers in each network. Table 3: Number of networks by classification based on who reports the victim of bullying No others-reported Yes others-reported Total No self-reported 1 2 3 Yes self-reported 0 27 27 Total 1 29 30 3.2 Network variables 3.2.1 Individual positioning The networks were elicited separately for each school-year unit. That is, each network contains people from classes corresponding to the same year in our school. We constructed four different networks from our data: friendship, best-friendship, enmity, and worst-enmity networks (see Section 4.1 for their characteristics). Therefore, each participant has four values for each individual network measure. 5See Section 3.2.2 for networks obtained 8 Table 8: General characteristics of positive and negative networks: Global measurements Friends Best Friends Enemies Worst enemies Number of nodes 3,035 3,035 3,035 3,035 Number of edges 35,784 12,007 13,333 3,122 Density (possible edges) 0.00388 0.00130 0.00144 0.00034 Reciprocity 0.45025 0.38144 0.12360 0.09865 Degree: average 23.58089 7.91235 8.78616 2.05733 (Std. Dev.) (15.88297) (6.74629) (10.75836) (3.78667) Giant component 179 176 180 151 Isolated nodes 30 166 121 1003 Clustering coefficient: total 0.41263 0.31937 0.17001 0.07154 Clustering coefficient: average 0.50461 0.45046 0.30659 0.15787 Degree correlation: 0.17172 0.08361 -0.06212 -0.11370 Diameter 3 6 4 9 Mean distance 2.10301 3.15178 2.40451 3.60126 Assortativity 0.09335 0.04157 -0.15590 -0.16327 Homophily (Gender) 0.29484 0.46091 0.03706 0.08926 Homophily (Class) 0.49239 0.51912 0.23593 0.32718 In contrast, we observe interesting similarities across the friendship and negative structures. Both networks contain giant components of similar sizes and both exhibit typical network hierarchies of social networks. The latter is corroborated by the comparison of the degree distribution in our networks with comparable random graphs in Figures 3 and 4.11 The comparison of the degree distribution of the observed (red) and random (green) networks in Figures 3 and 4 clearly illustrate the typical “fat-tails” of socially generated social networks: too many people are either very peripheral (the left tail of the red degree distributions in Figures 3 and 4) or very connected (the right tail) as compared to the random networks. Hence, important social processes are behind forming friendship and enmity networks. The aim of this study is to test whether such hierarchy is connected with who is bullied in the schools and, therefore, whether the same processes behind the network formation may be driving bullying victimization. 11Comparable random networks are networks with the same number of nodes and connections in which the links are distributed randomly in the population. 15 Figure 3: Comparison of the degree distribution of the friendship network. Red=True network; green=random network Figure 4: Comparison of the degree distribution of the enmity network. Red=True network; green=random network 4.2 Networks and Bullying In this section, we analyze to what extent we can identify individuals who are being bullied using the information about the social networks summarized in the previous section. We illustrate the idea using Figures 5 - 8 that plot the friendship, bestfriendship, enmity, and worst-enmity networks, respectively. This time, we color the network members according to their victimization status. The majority of the nodes are white because most people do not suffer bullying. Blue nodes represent adolescents who self-report being bullied at school but are not named as victims by others. Yellow nodes correspond to students whom their classmates name as victims, but they do not self-report that.12 Last, green nodes are cases of people who both self-report themselves and are reported by others as victims (corresponding to our variable intersection). A close look at the four networks reveals a clear pattern: the victims tend to occupy peripheral positions in the friendship networks, while they find themselves in the center of the graphs in the enmity networks. In the case of negative and positive networks, these features are more evident when the links are stronger (i.e. in the best-friendship and worst-enmity networks). 12There are no such cases in Figures 5 - 8. 16 Figure 5: Friendship network in one school colored by bullying victimization. White = no bullying; blue = Selfreported; green = Intersection Figure 6: Best-friendship network in one school colored by bullying victimization. Colors defined as in Figure 5. Figure 7: Enmity network in one school colored by bullying victimization. Colors defined as in Figure 5. Figure 8: Worst-enmity network in one school colored by bullying victimization. Colors defined as in Figure 5. In the following section, we formally test the observations using regression analysis. We mostly employ logistic regressions to predict whether a student is a victim of bullying, using the different network measures as predictors and other socioeconomic characteristics as control variables. 17 4.2.1 Bullying and individual positioning In this section, we illustrate step by step the prediction ability of the positive networks only, followed by the negative networks only and finally, we incorporate both types into the statistical models. In the main part of the analysis, we focus on our bullying intersection as the dependent variable to save on space. The results for the other variables are qualitatively similar and we only report our results for the other dependent variables in Section 4.2.4, where we present our selected model. As a starting point, we replicate the analysis presented by Mouttapa et al. (2004) who only use local variables and friendship networks. In this exercise, we obtain similar estimates but ours tend to be more significant, probably due to the greater statistical power of our sample size. We confirm that victims of bullying receive fewer friendship nominations and their friends are also more likely to be victims of bullying, but, as opposed to Mouttapa et al. (2004), our results are statistically strong. Using the enmity networks instead or combining both shows that the negative networks in a model Mouttapa et al. (2004) to Mouttapa et al. (2004) reveals that negative relationships deliver important and independent information from friendship networks while detecting the victims of bullying (see Appendix A.1 for details). Since our main models reported below extend the analysis of Mouttapa et al. (2004) considerably, we relegate the results of this replication analysis to Appendix A.1. Table 9 reports the results of a more general model using the bullying intersection variable defined in Section 3, in which one is labeled as a victim if both she and others report her as such. We employ the logistic regressions and the different models differ as follows: model (1) only includes the friendship networks but, in contrast to Mouttapa et al. (2004), we introduce the density of students’ network neighbourhoods (to analyze the effect of social cohesion) and global-centrality measures of each individual (to test whether the effect of centrality goes beyond one’s immediate network neighborhood). Model (2) repeats this analysis replacing the friendship network with the enmity one; the remaining models combine both network types, but model (4) adds controls to the network variables and model (5) clusters the errors at the level of the network to account for possible correlations in the data. Table 9 also report McFadden’s pseudo R2as measure of goodness of fit (McFadden, 1973); McFadden (1977) claims that a model has a good fit if the pseudo R2>0.2 (see also Lee (2013)). Table 9 reveals that the friendship and enmity networks each separately explain 4-7% of the variability of the dependent variables. Since this number increases to over 10% in model (3), the information provided by each network type does not overlap much. If we include the traditional determinants considered in the literature, the predictability of our model rises to almost 30%.13 The likelihood ratio chi-square tests illustrate that all our models clearly outperform a model without regressors. Furthermore, no model suffers from collinearity as the Variance Inflation Factor (VIF) is always 13All control variables are introduced in Section 3.3. Gender dummy never results significant, but, in line with the literature, the migrant dummy is a robust predictor of victimization. 18 well below 10. As for the network variables, several centrality measures are significant predictors of bullying in the friendship network. In contrast, only the in-degree and the fraction of reciprocated enmities are significant in the model. In Section 4.2.4, we discuss the role of the individual variables in more detail. Table 9: Results of regression of bullying and individual positioning. Logistic regression and individual-level analysis. (1) (2) (3) (4) (5) VARIABLES Intersection Intersection Intersection Intersection Intersection Out degree (+) 0.042** 0.039** 0.035 0.035 In degree (+) -0.141*** -0.141*** -0.208*** -0.208*** Betweenness (+) 0.000 0.000 0.002 0.002* Eigenvector (+) -3.870 -3.962 -4.712 -4.712** Closeness (+) -1.007 -0.765 -1.495 -1.495 Clustering (+) 0.768 0.588 0.860 0.860 Reciprocal degree (+) -0.360 -0.273 0.744 0.744 Friend victims 2.549*** 2.097*** 0.848 0.848 Out degree (-) 0.013 0.008 0.006 0.006 In degree (-) 0.099*** 0.079*** 0.076** 0.076** Betweenness (-) 0.000 0.000 -0.000 -0.000 Eigenvector (-) 0.167 0.408 -2.331 -2.331 Closeness (-) -1.088 -1.259 -0.709 -0.709 Clustering (-) -0.743 -0.663 -0.849 -0.849 Reciprocal degree (-) -0.065 -0.028 0.675 0.675* Enemy victims 0.485 0.301 -0.530 -0.530 Constant -3.952*** -4.870*** -4.199*** -0.219 -0.219 Observations 3,035 3,035 3,035 2,241 2,241 Pseudo R20.0750 0.0404 0.107 0.298 0.298 Prob< χ20.0000 0.0000 0.0000 0.0000 VIF 3.58 1.61 2.91 4.91 4.91 Controls No No No Yes Yes Cluster-Robust S.E. No No No No Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Probability of obtaining the χ2statistic, testing the overall model Variance Inflation Factor, VIF<10 if no multicollinearity Control variables described in Section 3.3 Robust standard errors clustered at network level (30 clusters) Table 10 repeats the analysis from for models (4-5) in Table 9 for each gender separately. The analysis clearly reveals that who is bullied is clearly genderspecific. First of all, different network characteristics predict bullying victimization among men and women. Most importantly though, the ability to predict bullying (as illustrated by pseudo R2) increases considerably with respect to the pooled regressions in Table 9. If predicted by gender separately, we can explain roughly 41% and 36% of the variability of the dependent variable in the case of men and women, respectively. Hence, predicting bullying victimization using networks should consider men and women separately. 19 Table 10: Results of regression of bullying and individual positioning by gender. Logistic regression and individual-level analysis. Males Females (1) (2) (3) (4) VARIABLES Intersection Intersection Intersection Intersection Out degree (+) -0.005 -0.005 0.088** 0.088** In-degree (+) -0.029 -0.029 -0.381*** -0.381*** Betweenness (+) 0.003* 0.003** 0.000 0.000 Eigenvector (+) -3.203 -3.203 -158.432*** -158.432*** Closeness (+) 1.655 1.655 -1.894 -1.894 Clustering (+) -1.316 -1.316 0.101 0.101 Reciprocal degree (+) -3.012* -3.012* 3.162*** 3.162*** Friend victims 0.618 0.618 0.457 0.457 Out degree (-) 0.014 0.014 -0.002 -0.002 In degree (-) 0.070 0.070 0.110** 0.110** Betweenness (-) 0.001 0.001 -0.000 -0.000 Eigenvector (-) -948.680** -948.680** -0.309 -0.309 Closeness (-) 0.898 0.898 -10.701 -10.701 Clustering (-) 2.103* 2.103** -1.374 -1.374 Reciprocal degree (-) 0.552 0.552 0.725 0.725 Enemy victims -0.992 -0.992 -0.908 -0.908 Constant 5.877* 5.877* -1.863 -1.863 Observations 840 840 1,072 1,072 Pseudo R20.415 0.415 0.358 0.358 Prob< χ20 0 VIF 5.46 5.46 5.07 5.07 Controls Yes Yes Yes Yes Cluster-Robust S.E. No Yes No Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Probability of obtaining the χ2statistic, testing the overall model Control variables described in Section 3.3 Clustered Standard Errors by network (30 clusters) 4.2.2 Bullying and network-wide characteristics In this section, we verify whether global network measures can predict bullying victimization at the network level. Our dependent variable is the number of bullying victims in each network (that is, year-school unit) and the explanatory variables are network-wide characteristics. Hence, each regression is conducted with 30 observations. Since the global measures are highly correlated (see Appendix A.3 for correlation matrices), Table 11 presents numerous simple linear regressions, in which each model considers one unique global network characteristic but the same for both the friendship and enmity network (as well as controls). Therefore, models (1 - 9) in Table 11 only differ in the regressors listed in the first column of the table. We estimate that the density of the enmity network is correlated with the in20 stances of bullying in the network (model (1)), but this is not the case of friendship networks. Similarly, higher reciprocity of enmities and their higher homophily increases bullying (models (2) and (7)). Model (3) reveals a negative relationship between the average in-degree and bullying in the friendship network: more friendships decrease bullying. In contrast, in model (6), the relationship observed with the friendship network in the standard deviation of clustering is positive. The remaining global measures are never significant. All in all, certain network architectures might stimulate or mitigate bullying. We investigate this claim in the following section combining individual positioning and global network measures. Table 11: Results of linear regression of bullying and network-wide characteristics (1) (2) (3) (4) (5) (6) (7) (8) (9) VARIABLES Intersection Intersection Intersection Intersection Intersection Intersection Intersection Intersection Intersection Density (+) -1.030 Density (-) 13.057* Global reciprocity (+) -3.199 Global reciprocity (-) 8.802*** Average in degree (+) -0.136** Average in degree (-) -0.033 SD in degree (+) -0.258 SD in degree (-) -0.221 Global clustering (+) -1.120 Global clustering (-) -1.675 SD clustering (+) 12.600* SD clustering (-) 2.762 Group homophily (+) -0.009 Group homophily (-) 1.500* Modularity (+) -0.450 Modularity (-) -0.857 No. communities (+) 0.021 No. communities (-) -0.019 Constant -0.706 0.022 2.477** 2.299** 1.868 -1.490 -0.088 0.933 0.730 Observations 30 30 30 30 30 30 30 30 30 R20.360 0.471 0.359 0.354 0.285 0.366 0.418 0.282 0.284 Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes Cluster-Robust S.E. Yes Yes Yes Yes Yes Yes Yes Yes Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Control variables described in Section 3.3 Clustered Standard Errors by network (30 clusters) 4.2.3 Both individual positioning and global characteristics as predictors of bullying In this section, we test whether individual positioning combined with global network measures can predict individual-level victimization. Table 12 presents nine logistic regressions. The benchmark model is a regression (5) from Table 9; we complement this model with the global network-wide measures one by one (as in Table 12 above). We observe that in-degree is a robust predictor of victimization both in the friendship and enmity networks. In addition, global centrality measures, namely eigenvector or betweenness, in the friendship network also remain significant, suggesting the centrality protects from bullying beyond the effect of local in-degree. Victims tend to be less central in positive networks locally and globally. Centrality beyond the local neighborhood in enmity networks does not seem to contribute to bullying. Regarding the global measures, the results mimic those in Table 11. Victims of 21 bullying tend to belong to networks with fewer enmities where their reciprocity is higher. Low hierarchy (low standard deviation of degrees) in the enmity network prevents bullying. Moreover, a higher number of network subcommunities (reflected in both modularity and number of communities) stimulates victimization. Overall, these results confirm that networks matter, but friendship and enmity networks on the one hand and different network features at the individual and global level, on the other, affect bullying differently. Table 12: Results of regressions of bullying and individual positioning and global characteristics. Logistic regression and individual-level analysis. (1) (2) (3) (4) (5) (6) (7) (8) (9) VARIABLES Intersection Intersection Intersection Intersection Intersection Intersection Intersection Intersection Intersection Out degree (+) 0.028 0.031 0.040 0.033 0.027 0.037 0.040 0.029 0.034 In degree (+) -0.206*** -0.193*** -0.178*** -0.189*** -0.203*** -0.206*** -0.166*** -0.209*** -0.215*** Betweenness (+) 0.002* 0.002* 0.001 0.002 0.002* 0.002 0.001 0.002** 0.002* Eigenvector (+) -5.083** -5.265*** -3.356 -2.982 -4.336** -4.998*** -4.719** -6.846*** -4.401** Clustering (+) 0.292 0.214 0.919 0.410 0.427 0.842 0.718 0.550 0.713 Closeness (+) -3.971 -6.683 -1.514 -2.403 -2.141 -1.447 -4.225 -2.883* -1.055 Reciprocal degree (+) 0.598 0.552 0.621 0.615 0.650 0.811 0.469 0.673 0.791 Friend victims 0.189 0.262 0.673 0.771 0.888 0.924 0.015 0.408 0.730 Out degree (-) 0.002 0.004 0.014 0.011 0.012 0.006 0.007 0.010 0.002 In degree (-) 0.071** 0.081** 0.121*** 0.120*** 0.097** 0.081** 0.099** 0.089** 0.078** Betweenness (-) 0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 Eigenvector (-) -1.786 -1.382 -1.981 -1.617 -1.322 -2.615 -0.088 -2.386 -2.220 Clustering (-) -1.086 -0.881 -0.011 -0.146 0.098 -0.910 -0.238 -0.449 -0.782 Closeness (-) -0.626 -0.752 -1.124 -1.143 -0.975 -0.814 -0.960 -0.889 -0.631 Reciprocal degree (-) 0.579 0.555 0.425 0.377 0.515 0.648 0.462 0.534 0.644 Enemy victims -1.362 -1.467 -0.799 -0.875 -0.664 -0.494 -1.598* -0.959 -0.445 Density (+) 0.434 Density (-) 15.287 Global reciprocity (+) -0.201 Global reciprocity (-) 7.883** Average in degree (+) -0.141 Average in degree (-) -0.360*** SD in degree (+) -0.131 SD in degree (-) -0.722*** Global clustering (+) 5.327** Global clustering (-) -12.461* SD clustering (+) 1.764 SD clustering (-) 3.438 Group homophily (+) 1.920 Group homophily (-) 2.356* Modularity (+) -5.957* Modularity (-) 0.669 No. communities (+) -0.190** No. communities (-) 0.040 Constant -1.451 -1.691 2.632 2.813 -0.533 -1.134 -3.231 1.279 0.076 Observations 2,241 2,241 2,241 2,241 2,241 2,241 2,241 2,241 2,241 Pseudo R20.313 0.322 0.318 0.325 0.314 0.299 0.329 0.311 0.307 VIF 5.62 6.90 6.59 7.39 7.26 8.26 5.61 6.31 5.24 Controls Yes Yes Yes Yes Yes Yes Yes Yes Yes Cluster-Robust S.E. Yes Yes Yes Yes Yes Yes Yes Yes Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Control variables described in Section 3.3 Clustered Standard Errors by network (30 clusters) 4.2.4 Selecting final models Since many variables in Table 12 are never significant, this section presents models in which we only restrict attention to dependent network variables that result significant in at least one regression. Since this leads to one unique model, Table 13 includes the selected model for each of the dependent variables introduced in Section 3: bullying intersection (model (1)), bullying union (2), self-reported bullying (3), other-reported bullying (4), and the number of times one is mentioned as a victim by others (5). 22 Being bullied is robustly related to the number of times one is named as a friend (popularity) positively and the number of times one is named as an enemy negatively. Moreover, global centrality in the friendship network consistently predicts bullying. Moreover, the higher the fraction of victims’ enemies, the less likely she is a victim herself. At the network-wide level, segregation–measured by the number of communities and homophily on classroom–stimulates bullying. The best fitting model is (1), where the dependent variable is the intersection; it explains 34%. Our models predict much less of the other dependent variables. However, if we select our models separately for each gender, the fit increases substantially. For example, Table 14 reports the intersection variable’s case and shows that our model’s predictive ability increases by 44.1% and 10.6% for males and females, respectively. Hence, once again, the gender-specific analysis is more suitable predicting victimization than the pooled analysis. Table 13: Result of final logistic regression and individual-level analysis. (1) (2) (3) (4) (5) VARIABLES Intersection Union Self-R Others-R No. others-R Out degree (+) 0.052* 0.008 0.021 0.009 0.003** In degree (+) -0.136*** -0.088*** -0.062** -0.099*** -0.016*** Eigenvector (+) -7.271*** -0.546 -5.630*** -0.095 0.062 In degree (-) 0.111*** 0.125*** 0.054** 0.140*** 0.030*** Enemy victims -1.686* -0.416 -0.717 -0.456* -0.090** N. isolates (+) -0.952*** 0.096 -0.149 0.061 0.024 N. communities (+) 0.542* -0.120* 0.053 -0.098 -0.024 Group homophily (-) 3.776*** 1.200*** 1.501*** 1.407*** 0.353*** Constant -3.971** 0.637 -0.009 -0.234 0.653*** Observations 2,241 2,241 2,241 2,241 2,241 VIF 7.34 7.34 7.34 7.34 (Pseudo) R20.340 0.141 0.174 0.165 0.0972 Controls Yes Yes Yes Yes Yes Cluster-Robust S.E. Yes Yes Yes Yes Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Control variables described in Section 3.3 Clustered Standard Errors by network (30 clusters) 23 Table 14: Result of final logistic regression and individual-level analysis by gender. Males Females (1) (2) VARIABLES Intersection Intersection Out degree (+) 0.072** In degree (+) -0.317*** Eigenvector (+) -5.169*** -151.192*** Betweenness (+) 0.003*** Reciprocity (+) -4.235*** 2.567* In degree (-) 0.148** 0.141** Gender homophily (+) -4.926*** Group homophily (+) 3.103*** N. important communities (+) 0.587*** Density (-) 60.246*** Assortativity (-) 9.411** SD in degree (-) -1.225*** Group homophily (-) 4.464*** Constant -9.209** -0.744 Observations 858 1,077 Pseudo R20.490 0.376 Controls Yes Yes Cluster-Robust S.E. Yes Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Control variables described in Section 3.3 Clustered Standard Errors by network (30 clusters) 5 Conclusions and Discussion Since school bullying is by definition a social phenomenon, we ask to what extent friendship and enmity networks at school serve to identify the victims of bullying. Our results show that social organization as described by these networks provides a piece of quantitatively important and independent information about who suffers bullying in our data. We particularly observe that (i) both individual network positioning and network-wide organization play a role while predicting victimization, but different characteristics play a role at the individual vs. global level, and individual positioning seems to be somewhat more relevant than the global architecture; (ii) friendship and enmity networks play an orthogonal role in predicting victimization; and (iii) the way the network predict victimization differs considerably across both sexes. Before we discuss the implications of our results for different theories of bullying in psychology and sociology, we would like to emphasize that our analysis is purely correlational. We do not claim that - nor does our data allow us to prove whether - specific network positioning leads to bullying or whether being a victim of bullying leads to specific network positions. In fact, we believe that both phenomena evolve hand in hand and none of them “causes” the other. We insist that our analysis is a simple fitting exercise which tests whether we use network data in order to predict who can suffer from bullying because observing who is bullied directly is for many reasons challenging. 24 Salmivalli, C. and Isaacs, J. (2005). Prospective relations among victimization, rejection, friendlessness, and children’s self-and peer-perceptions. Child development, 76(6):1161–1171. Sarzosa, M. and Urz´ua, S. (2021). Bullying among adolescents: The role of skills. Quantitative Economics, 12(3):945–980. Scheithauer, H., Hayer, T., Petermann, F., and Jugert, G. (2006). Physical, verbal, and relational forms of bullying among german students: Age trends, gender differences, and correlates. Aggressive Behavior: Official Journal of the International Society for Research on Aggression, 32(3):261–275. Sentse, M., Kretschmer, T., and Salmivalli, C. (2015). The longitudinal interplay between bullying, victimization, and social status: Age-related and gender differences. 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Systematic review of theoretical studies on bullying and cyberbullying: Facts, knowledge, prevention, and intervention. Aggression and violent behavior, 23:1–21. 32 A Appendices A.1 First appendix We replicated the Mouttapa et al. (2004) analysis. In this analysis, we only focus on friendship networks. Four logistic regression models are estimated to explain the binary variables of bullying and just one linear regression in the last place. Table 15 contains the coefficients. Table 15: Results of logistic regression of victims variables: positive network (1) (2) (3) (4) (5) VARIABLES Intersection Union Self-R Others-R No. others-R Out degree 0.035** 0.008 0.008 0.012 0.003* (0.017) (0.009) (0.015) (0.009) (0.002) In degree -0.185*** -0.088*** -0.085*** -0.101*** -0.016*** (0.045) (0.017) (0.028) (0.018) (0.003) Reciprocal degree 1.167 0.224 0.347 0.316 0.039 (0.769) (0.314) (0.509) (0.343) (0.062) Friend victims 1.413* 2.792*** 1.643*** 2.770*** 0.685*** (0.741) (0.422) (0.611) (0.437) (0.140) Migrant 0.038** 0.024*** 0.026** 0.026*** 0.004 (0.015) (0.009) (0.013) (0.009) (0.002) Constant -3.601*** -1.563*** -2.982*** -1.719*** 0.247*** (0.473) (0.202) (0.340) (0.217) (0.040) Observations 2,368 2,368 2,363 2,368 2,368 (Pseudo) R20.0836 0.0644 0.0356 0.0701 0.046 Prob >F (χ2) 0.0000 0.0000 0.0001 0.0000 0.0000 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Hence, it is confirmed that victims of bullying receive fewer nominations, regardless of whether they have self-reported or have been reported by other peers. Furthermore, the count of friends who are bullied is also significant. Victims have more friends who are also victims of bullying. Moreover, considering model (1)14, which reflects the intersection, the measure out degree is also significant. This same model is estimated by gender, presenting the results in Table 16. In degree is significant in all four models, while the attributes of friends are only significant in the union. However, it is noteworthy that there are differences regarding gender. Model (3) indicates that women included in the intersection cases, who suffer bullying, tend to mention more friends and noticeably have more reciprocal friends. 14It is verified that the model does not present multicollinearity problems, it has an average VIF of 3.18 33 Table 16: Results of logistic regression of victims variables by gender Males Females (1) (2) (3) (4) VARIABLES Intersection Union Intersection Union Out degree 0.020 0.004 0.064** 0.011 (0.022) (0.012) (0.027) (0.014) In degree -0.107* -0.099*** -0.289*** -0.085*** (0.060) (0.020) (0.074) (0.030) Reciprocity -0.807 0.182 2.688*** 0.480 (1.515) (0.418) (0.941) (0.507) Friend victims 2.020 2.949*** 0.797 2.521*** (1.501) (0.639) (0.936) (0.589) Migrant -0.010 0.020* 0.052*** 0.028** (0.017) (0.011) (0.018) (0.014) Constant -3.465*** -1.117*** -3.668*** -2.052*** (0.730) (0.298) (0.634) (0.296) Observations 1,137 1,137 1,089 1,089 Pseudo R20.0552 0.0808 0.145 0.0545 Prob< χ20.0110 0.0000 0.0003 0.0000 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Similarly, an analysis of negative networks is performed. In this case, instead of including the count of friends who are bullied, we take into account the enemies who are bullied. Table 17: Results of logistic regression of victims variables: negative network (1) (2) (3) (4) (5) VARIABLES Intersection Union Self-R Others-R No. others-R Out degree 0.017** 0.005 0.019*** -0.002 0.002 (0.008) (0.007) (0.006) (0.009) (0.002) In degree 0.092*** 0.111*** 0.063*** 0.120*** 0.026*** (0.019) (0.013) (0.017) (0.013) (0.005) Reciprocity 0.555 -0.089 -0.230 0.036 0.047* (0.398) (0.177) (0.277) (0.193) (0.029) Victim enemies 0.315 0.289 0.043 0.350 0.049 (0.560) (0.242) (0.396) (0.259) (0.041) Migrant 0.032*** 0.022** 0.025** 0.024** 0.003 (0.010) (0.010) (0.011) (0.010) (0.002) Constant -5.178*** -2.697*** -3.868*** -2.945*** 0.007 (0.334) (0.137) (0.213) (0.151) (0.026) Observations 2,368 2,368 2,368 2,368 2,368 (Pseudo) R20.0477 0.0487 0.0272 0.0567 0.035 Prob >F (χ2) 0.0000 0.0000 0.0000 0.0000 0.0000 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 The results obtained with the negative network are similar to those with the positive network. Mentions received as enemies are significant in all models. However, except for in degree, no other variable is significant in all models. In models (1) and (3), mentions made stand out. The more enemies mentioned, the more 34 likely it is to be bullied and self-report it. Table 18 shows the model by gender. In the case of men, the mentions received as enemies are significant as in the previous model. On the contrary, in the female model (3), the degree of reciprocity also stands out, the victims tend to have more bad reciprocal relationships. Table 18: Results of regression: negative network by gender Males Females (1) (2) (3) (4) VARIABLES Intersection Union Intersection Union Out degree 0.017 -0.002 0.016* 0.016* (0.012) (0.010) (0.009) (0.008) In degree 0.120*** 0.150*** 0.075*** 0.095*** (0.034) (0.019) (0.026) (0.018) Reciprocity -0.178 -0.261 0.957** -0.045 (0.799) (0.233) (0.440) (0.288) Victim enemies 0.478 -0.014 0.201 0.855** (0.904) (0.312) (0.748) (0.407) Migrant -0.006 0.021 0.040*** 0.023* (0.015) (0.014) (0.012) (0.014) Constant -5.254*** -2.441*** -5.031*** -3.152*** (0.537) (0.184) (0.423) (0.222) Observations 1,137 1,137 1,089 1,089 Pseudo R20.0477 0.0680 0.0628 0.0557 Prob > χ20.0002 0.0000 0.0410 0.0000 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 19: Results of regression: positive network (Best friends) (1) (2) (3) (4) (5) VARIABLES bullying intersection bullying union self bullying others bullying n others bullying Out degree 0.016 0.023** -0.003 0.030*** 0.008*** (0.013) (0.009) (0.021) (0.010) (0.003) In degree -0.269*** -0.198*** -0.172*** -0.209*** -0.031*** (0.099) (0.033) (0.066) (0.036) (0.005) Reciprocity 0.063 0.275 -0.499 0.484** 0.108*** (0.523) (0.202) (0.395) (0.213) (0.039) Best friend victims 1.440*** 2.369*** 1.551*** 2.328*** 0.519*** (0.536) (0.297) (0.439) (0.299) (0.106) Migrant -0.005 0.028*** -0.151 0.030*** 0.004* (0.012) (0.010) (0.486) (0.010) (0.002) Constant -3.624*** -1.819*** -2.822*** -2.079*** 0.166*** (0.364) (0.153) (0.284) (0.162) (0.027) Observations 2,368 2,368 2,363 2,368 2,368 R20.041 Pseudo R20.0470 0.0717 0.0428 0.0734 Prob > χ20.0005 0.0000 0.0000 0.0000 Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 35 A.2 Second appendix Table 20: Positive and Negative Network Regression Results: Out degree (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES Intersection Intersection Intersection Intersection Intersection Intersection Intersection Intersection Out degree (+) 0.012 0.003 0.007 0.019 0.019 0.018 0.019 0.001 Out degreee (-) 0.018*** 0.020*** 0.021*** 0.012 0.011 0.010 0.010 0.012 Reciprocity (+) -1.203** -1.161** -1.137* -1.167** -1.220** -1.125* -0.714 Reciprocity (-) 0.285 0.313 0.330 0.233 0.246 0.416 1.223*** Eigenvector (+) -5.561 -6.021 -6.065 -5.980 -5.613 -6.465 Eigenvector (-) 0.521 0.586 0.557 0.610 0.258 -2.507 Betweenness (+) -0.001 -0.001 -0.001 -0.001 0.001 Betweenness (-) 0.000*** 0.000*** 0.000*** 0.000*** 0.000 Closeness (+) -1.053 -1.067 -0.924 -2.077 Closeness (-) -1.205 -1.184 -1.007 -0.167 Clustering (+) 0.275 0.210 0.306 Clustering (-) -0.208 -0.324 -0.763 Friend victims 2.715*** 1.223 Enemy victims 0.399 -0.120 Constant -4.675*** -4.054*** -4.102*** -4.182*** -4.055*** -4.121*** -4.553*** -0.116 Observations 3,035 3,035 3,035 3,035 3,035 3,035 3,035 2,241 Pseudo R20.00877 0.0185 0.0263 0.0338 0.0362 0.0366 0.0557 0.235 Prob< χ20.0010 0.0003 0.0004 0.0011 0.0042 0.0025 0.0000 0.0000 Controls No No No No No No No Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Control variables described in Section 3.3 Table 21: Positive and Negative Network Regression Results: In degree (1) (2) (3) (4) (5) (6) (7) (8) VARIABLES Intersection Intersection Intersection Intersection Intersection Intersection Intersection Intersection In degree (+) -0.102*** -0.104*** -0.096*** -0.115*** -0.117*** -0.123*** -0.120*** -0.195*** In degree (-) 0.102*** 0.101*** 0.102*** 0.094*** 0.094*** 0.094*** 0.084*** 0.072** Reciprocity (+) -0.781 -0.837 -0.658 -0.681 -0.752 -0.758 0.337 Reciprocity (-) -0.264 -0.246 -0.198 -0.309 -0.266 -0.094 0.648 Eigenvector (+) -4.607 -4.140 -4.287 -3.917 -3.521 -3.754 Eigenvector (-) 0.546 0.781 0.683 0.883 0.763 -2.320 Betweenness (+) 0.001 0.001 0.001 0.001 0.003*** Betweenness (-) 0.000 0.000 0.000 0.000 0.000 Closeness (+) -1.226** -1.164* -1.109* -1.783 Closeness (-) -1.473 -1.429 -1.295 -0.715 Clustering (+) 0.580 0.477 0.789 Clustering (-) -0.791 -0.814 -0.974 Friend victims 2.054*** 0.815 Enemy victims 0.316 -0.525 Constant -3.975*** -3.401*** -3.427*** -3.519*** -3.369*** -3.399*** -3.660*** 0.363 Observations 3,035 3,035 3,035 3,035 3,035 3,035 3,035 2,241 Pseudo R20.0607 0.0701 0.0732 0.0783 0.0821 0.0855 0.0977 0.294 Prob< χ20.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 Controls No No No No No No No Yes *** p<0.01, ** p<0.05, * p<0.1 Friendship network (+), enmity network (-) Control variables described in Section 3.3 36 Table 22: correlation coefficients local measures Variables (1) (2) (3) (4) (1) Out degree (+) 1.000 (2) Out degree (-) 0.095 1.000 (0.000) (3) In degree (+) 0.410 0.045 1.000 (0.000) (0.013) (4) In degree (-) -0.009 0.107 -0.013 1.000 (0.635) (0.000) (0.487) A.3 Third appendix Table 23: Correlation coefficients global measures (positive network) Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (1) Num nodes (+) 1.000 (2) Num edges (+) 0.847 1.000 (0.000) (3) Density (+) -0.826 -0.547 1.000 (0.000) (0.000) (4) Global reciprocity (+) -0.751 -0.560 0.774 1.000 (0.000) (0.000) (0.000) (5) Assortativity (+) 0.237 0.011 -0.389 -0.151 1.000 (0.000) (0.528) (0.000) (0.000) (6) Average in degree (+) -0.017 0.475 0.383 0.184 -0.391 1.000 (0.337) (0.000) (0.000) (0.000) (0.000) (7) Average degree (+) -0.017 0.475 0.383 0.184 -0.391 1.000 1.000 (0.337) (0.000) (0.000) (0.000) (0.000) (0.000) (8) SD degree (+) 0.698 0.913 -0.372 -0.434 -0.053 0.589 0.589 1.000 (0.000) (0.000) (0.000) (0.000) (0.003) (0.000) (0.000) (9) SD in degree (+) 0.588 0.793 -0.258 -0.268 -0.075 0.588 0.588 0.867 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (10) Global clustering (+) -0.874 -0.655 0.941 0.848 -0.219 0.270 0.270 -0.475 -0.323 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (11) Average clustering (+) -0.853 -0.603 0.930 0.805 -0.369 0.313 0.313 -0.403 -0.346 0.958 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (12) SD clustering (+) 0.399 -0.035 -0.572 -0.266 0.525 -0.744 -0.744 -0.074 -0.120 -0.446 -0.468 1.000 (0.000) (0.053) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (13) G. component (+) 0.997 0.860 -0.829 -0.763 0.222 0.003 0.003 0.709 0.585 -0.880 -0.847 0.372 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.851) (0.851) (0.000) (0.000) (0.000) (0.000) (0.000) (14) No. isolates (+) 0.456 0.194 -0.319 -0.178 0.278 -0.272 -0.272 0.153 0.286 -0.291 -0.430 0.512 0.391 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (15) Mean distance (+) 0.637 0.249 -0.858 -0.618 0.406 -0.599 -0.599 0.048 0.082 -0.749 -0.804 0.647 0.629 0.360 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.008) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (16) Diameter (+) 0.503 0.173 -0.721 -0.562 0.270 -0.537 -0.537 0.030 0.049 -0.660 -0.726 0.493 0.497 0.285 0.864 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.100) (0.007) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (17) Gender homophily (+) 0.309 0.041 -0.516 -0.354 0.308 -0.445 -0.445 0.033 0.026 -0.457 -0.445 0.534 0.306 0.195 0.428 0.326 1.000 (0.000) (0.023) (0.000) (0.000) (0.000) (0.000) (0.000) (0.066) (0.152) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (18) Group homophily (+) -0.382 -0.361 0.210 0.495 0.157 -0.211 -0.211 -0.468 -0.516 0.290 0.261 0.042 -0.386 -0.115 -0.184 -0.222 -0.279 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.021) (0.000) (0.000) (0.000) (0.000) (0.000) (19) Modularity (+) 0.361 0.004 -0.699 -0.306 0.333 -0.568 -0.568 -0.204 -0.227 -0.492 -0.510 0.560 0.358 0.185 0.759 0.578 0.387 0.179 1.000 (0.000) (0.820) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (20) No. communities (+) 0.642 0.373 -0.476 -0.344 0.328 -0.257 -0.257 0.318 0.398 -0.467 -0.581 0.566 0.587 0.958 0.466 0.377 0.259 -0.230 0.212 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (21) No. important comm. (+) 0.833 0.670 -0.686 -0.721 0.266 -0.085 -0.085 0.586 0.453 -0.778 -0.735 0.369 0.841 0.267 0.497 0.434 0.299 -0.495 0.150 0.505 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) 37 Table 24: Correlation coefficients global measures (negative network) Variables (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (1) No. nodes (-) 1.000 (2) No. edges (-) 0.610 1.000 (0.000) (3) Density (-) -0.778 -0.183 1.000 (0.000) (0.000) (4) Global reciprocity (-) -0.541 -0.207 0.783 1.000 (0.000) (0.000) (0.000) (5) Assortativity (-) -0.003 -0.259 -0.172 -0.153 1.000 (0.863) (0.000) (0.000) (0.000) (6) Average in degree (-) -0.096 0.700 0.490 0.216 -0.284 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (7) Average degree (-) -0.096 0.700 0.490 0.216 -0.284 1.000 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (8) SD degree (-) 0.234 0.837 0.095 -0.158 -0.409 0.830 0.830 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (9) SD in degree (-) 0.026 0.714 0.384 0.187 -0.242 0.903 0.903 0.732 1.000 (0.155) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (10) Global clustering (-) -0.622 0.113 0.791 0.533 -0.079 0.699 0.699 0.349 0.670 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (11) Average clustering (-) -0.121 0.537 0.367 0.054 -0.463 0.772 0.772 0.858 0.662 0.588 1.000 (0.000) (0.000) (0.000) (0.003) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (12) SD clustering (-) 0.326 0.263 -0.309 -0.315 -0.259 -0.022 -0.022 0.426 -0.032 -0.147 0.506 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.235) (0.235) (0.000) (0.082) (0.000) (0.000) (13) G. component (-) 0.990 0.687 -0.728 -0.509 -0.043 0.005 0.005 0.337 0.105 -0.563 -0.016 0.364 1.000 (0.000) (0.000) (0.000) (0.000) (0.019) (0.789) (0.789) (0.000) (0.000) (0.000) (0.370) (0.000) (14) No. isolates (-) 0.316 -0.358 -0.528 -0.364 0.253 -0.692 -0.692 -0.620 -0.531 -0.549 -0.724 -0.156 0.177 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (15) Mean distance (-) 0.578 -0.007 -0.615 -0.473 0.257 -0.461 -0.461 -0.352 -0.303 -0.563 -0.545 -0.157 0.501 0.640 1.000 (0.000) (0.700) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (16) Diameter (-) 0.476 -0.052 -0.531 -0.440 0.355 -0.433 -0.433 -0.383 -0.273 -0.517 -0.570 -0.303 0.399 0.605 0.917 1.000 (0.000) (0.004) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (17) Gender homophily (-) 0.461 0.243 -0.413 -0.351 -0.046 -0.134 -0.134 0.122 -0.001 -0.293 0.064 0.440 0.434 0.281 0.357 0.302 1.000 (0.000) (0.000) (0.000) (0.000) (0.011) (0.000) (0.000) (0.000) (0.963) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (18) Group homophily (-) -0.105 -0.324 0.280 0.478 0.264 -0.238 -0.238 -0.485 -0.156 0.036 -0.354 -0.350 -0.136 0.168 0.125 0.225 -0.088 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.049) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (19) Modularity (-) 0.446 -0.301 -0.673 -0.342 0.342 -0.708 -0.708 -0.648 -0.544 -0.649 -0.749 -0.172 0.339 0.803 0.675 0.652 0.228 0.265 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (20) No. communities (-) 0.442 -0.278 -0.623 -0.405 0.254 -0.710 -0.710 -0.583 -0.522 -0.635 -0.712 -0.075 0.310 0.976 0.701 0.663 0.376 0.150 0.826 1.000 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (21) No. important comm (-) 0.599 0.004 -0.765 -0.597 0.091 -0.533 -0.533 -0.210 -0.454 -0.774 -0.375 0.207 0.552 0.447 0.550 0.574 0.473 -0.078 0.589 0.572 1.000 (0.000) (0.826) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) 38