Table 1.
Descriptive Statistics of the Friendship Networks and Bullying Networks Per and Between Time Points (19 Classrooms, 481 Students)
| Friendship networks | Bullying networks | |||||
|---|---|---|---|---|---|---|
| Wave 1 | Wave 2 | Wave 3 | Wave 1 | Wave 2 | Wave 3 | |
| Density indicators | ||||||
| Densitya | 0.22 (0.15 to 0.33) | 0.22 (0.13 to 0.31) | 0.21 (0.12 to 0.30) | 0.09 (0.02 to 0.22) | 0.08 (0.01 to 0.17) | 0.08 (0.01 to 0.18) |
| Number of ties | 135 (108 to 206) | 136 (82 to 226) | 127 (70 to 185) | 52 (14 to 115) | 49 (6 to 100) | 49 (10 to 93) |
| At least one out‐tie | 0.94 (0.80 to 1) | 0.93 (0.73 to 1) | 0.94 (0.69 to 1) | 0.65 (0.37 to 0.95) | 0.64 (0.19 to 0.85) | 0.66 (0.26 to 0.95) |
| At least one in‐tie | 0.95 (0.84 to 1) | 0.94 (0.81 to 1) | 0.93 (0.73 to 1) | 0.47 (0.26 to 0.84) | 0.40 (0.15 to 0.60) | 0.37 (0.17 to 0.58) |
| Average degreeb | 5.3 (4.1 to 7.8) | 5.3 (3.2 to 7.4) | 5.0 (3.0 to 7.2) | 2.1 (0.5 to 4.6) | 2.0 (0.2 to 4.0) | 2.0 (0.4 to 4.0) |
| SD outdegree | 3.9 (2.2 to 6.5) | 3.9 (2.7 to 5.6) | 3.4 (1.9 to 6.1) | 2.1 (0.8 to 4.4) | 2.0 (0.5 to 3.4) | 2.0 (0.8 to 3.6) |
| SD indegree | 2.9 (2.0 to 4.0) | 2.8 (1.5 to 3.9) | 2.7 (1.6 to 3.9) | 2.9 (1.2 to 4.6) | 3.0 (0.7 to 5.5) | 3.4 (0.9 to 5.5) |
| Dyadic indicators | ||||||
| Asymmetrical ties | 122 (80 to 272) | 130 (60 to 252) | 116 (56 to 198) | 88 (24 to 178) | 85 (12 to 158) | 85 (20 to 126) |
| Mutual ties | 74 (44 to 122) | 71 (46 to 100) | 69 (36 to 102) | 8 (0 to 32) | 6 (0 to 26) | 7 (0 to 40) |
| At least one mutual tie | 0.94 (0.80 to 1) | 0.93 (0.73 to 1) | 0.94 (0.69 to 1) | 0.65 (0.37 to 0.95) | 0.64 (0.19 to 0.85) | 0.66 (0.26 to 0.95) |
| Reciprocityc | 0.55 (0.34 to 0.71) | 0.53 (0.41 to 0.63) | 0.55 (0.39 to 0.72) | 0.13 (0.00 to 0.33) | 0.12 (0.00 to 0.26) | 0.10 (0.00 to 0.43) |
| Sex combinations | ||||||
| Boy–boy | 0.35 (0.19 to 0.55) | 0.39 (0.22 to 0.63) | 0.37 (0.22 to 0.56) | 0.33 (0.00 to 0.85) | 0.34 (0.04 to 0.76) | 0.32 (0.00 to 0.78) |
| Girl–girl | 0.44 (0.23 to 0.63) | 0.41 (0.13 to 0.59) | 0.44 (0.18 to 0.65) | 0.20 (0.05 to 0.36) | 0.19 (0.00 to 0.50) | 0.15 (0.00 to 0.38) |
| Boy–girl | 0.10 (0.04 to 0.21) | 0.10 (0.00 to 0.25) | 0.09 (0.02 to 0.27) | 0.34 (0.03 to 0.57) | 0.37 (0.08 to 0.68) | 0.39 (0.08 to 0.79) |
| Girl–boy | 0.11 (0.02 to 0.31) | 0.09 (0.00 to 0.23) | 0.10 (0.00 to 0.22) | 0.14 (0.00 to 0.44) | 0.10 (0.00 to 0.35) | 0.14 (0.00 to 0.32) |
| Triadic indicators | ||||||
| Distance 2 (indirect ties)d | 0.92 (0.72 to 1) | 0.91 (0.62 to 1) | 0.90 (0.58 to 1) | 0.52 (0.16 to 0.95) | 0.49 (0.04 to 0.85) | 0.55 (0.00 to 0.95) |
| Transitivity indexe | 0.51 (0.37 to 0.70) | 0.55 (0.39 to 0.74) | 0.51 (0.38 to 0.71) | 0.38 (0.00 to 0.79) | 0.45 (0.00 to 0.75) | 0.49 (0.14 to 1) |
| Wave 1 to 2 | Wave 2 to 3 | Wave 1 to 2 | Wave 2 to 3 | |
|---|---|---|---|---|
| Change indicators | ||||
| Creating ties (0 → 1) | 55 (20 to 115) | 46 (15 to 90) | 32 (2 to 86) | 29 (6 to 60) |
| Dissolving ties (1 → 0) | 54 (34 to 112) | 55 (31 to 108) | 35 (10 to 90) | 29 (5 to 81) |
| Stable ties (1 → 1) | 81 (60 to 139) | 81 (46 to 124) | 17 (1 to 41) | 20 (1 to 43) |
| Jaccard indexf | 0.43 (0.32 to 0.52) | 0.45 (0.29 to 0.56) | 0.21 (0.02 to 0.43) | 0.24 (0.03 to 0.54) |
| Friendship × Bullying | Friendship × Victimization | |||||
|---|---|---|---|---|---|---|
| Wave 1 | Wave 2 | Wave 3 | Wave 1 | Wave 2 | Wave 3 | |
| Dependence indicators | ||||||
| Moran’s I autocorrelationg | 0.18 (−0.12 to 0.56) | 0.20 (−0.01 to 0.59) | 0.22 (0.04 to 0.58) | −0.01 (−0.11 to 0.14) | −0.01 (−0.19 to 0.21) | −0.03 (−0.15 to 0.14) |
| Jaccard indexh | 0.06 (0.02 to 0.14) | 0.06 (0.01 to 0.09) | 0.06 (0.01 to 0.12) | — | — | — |
| Shared bullies/victimsi | 0.37 (0.23 to 0.67) | 0.42 (0.26 to 1) | 0.35 (0.17 to 0.57) | 0.23 (0.00 to 0.48) | 0.22 (0.00 to 0.47) | 0.17 (0.04 to 0.36) |
The table shows averages. Minimum and maximum are shown in parentheses.
Density is the number of observed ties divided by the total number of possible ties.
If counted among the victims (referring to students who nominated at least one bully in class), average degree is 4.4 (min = 1.9, max = 8.4) at W1, 4.8 (min = 1.5, max = 8.5) at W2, and 5.2 (min = 2, max = 7.8) at W3, indicating that victims had, on average about 4–5 bullies in class.
Reciprocity was calculated as 2M/(2M + A), where M = mutual ties and A = asymmetric ties.
Distance 2 is the proportion of respondents with ties at two degrees of separation (with at least one connecting intermediary).
Transitivity was calculated as the number of transitive triplets divided by the number of two‐paths (or two‐stars).
Jaccard index is the proportion of stable ties in relation to creating ties and dissolving ties.
Moran’s I autocorrelation indicates the level of similarity (as correlation) between friendship and bullying (outdegrees) or victimization (indegrees).
Jaccard index is the degree (proportion) of dyadic overlap between friendship networks and bullying networks.
Proportion of shared outgoing W‐ties (i and j bully the same victim h) and incoming W‐ties (i and j are victimized by the same bully h) for which there are also outgoing X‐ties (i and j are friends).