Visualization of Friendship and

Aggression Networks

Tarik Crnovrsanin, Chris W. Muelder, Kwan-Liu Ma, Bob Faris, Diane Felmlee

Bullying is a common occurance in most schools. In order to better understand the frequencies and types of aggression that occur, members of the VIDi group have been working with members of the Sociology department at U. C. Davis along with CNN to visually represent and understand the social networks of students within schools. Here we show some of the results that came from analysis of a survey performed by CNN. In this survey, students were asked to anonymously list friends, bullys, and victims, as well as indentify themselves according to various properties such as race, grade, gender, and many more. Of these properties, we found the strongest patterns correlated to grade and gender.

Visualization of Friendship Networks

  • One of the simplest ways to visualize the friendship network is to plot it in a traditional node-link diagram, where each node is a person and each line indicates a friendship. Here we see that the friendship network naturally forms groups. By color-coding the nodes by grade, we see that these clusters are primarily organized by grade.

  • When we plot the same network and color the nodes by gender, we see that some grades are segregated by gender and others are not. In particular, the 8th and 9th grade clusters are distinctly segregated, whereas higher grades are much less divided, with 12th grade being the most mixed.

  • Using straight lines to represent the connections between people results in a high amount of clutter. By color coding the lines and bundling similar ones together, the structure of the network becomes much more clear, and the grade division is much more apparent.

  • If we then color the students and relationships by gender, the patterns of gender segregation also become much more apparent.

  • To better show the difference betwen relationships within a grade and between grades, we apply a specialized node-link diagram with a radial layout: people are placed around the circle according to some property and ordered by modularity clustering. Connections between like-property nodes are drawn outside the circle, and ones between groups are drawn in bundles through the inside of the circle. Here we show friendships grouped by grade, and note that the outer connections are much denser than those in the circle, confirming the pattern we described earlier. Also, we see that the grades of people with unknown grades (blue) could likely be inferred fairly accurately.

  • When we break up the graph by gender instead of grade in the radial view, we see that there are more same-gender connections than cross-gender ones, but we can also see distinct sub-groups that correspond to grades.

  • If we use the radial layout to group people by grade, and simply color by gender, we can better see how the gender segregation changes with grade. Grades 8 throuh 10 are substantially segregated, while 11 and 12 are much less segregated.

Visualization of Agression Networks

  • We can remove the friendship network, and show aggression instead. Some gender segregation is still visible, but it is apparent that grade still plays a larger role. Also, there are many uninvolved students that can be removed from the plot.

  • Here we re-layout just the agression network, and color it by grade. While it is much sparser than the friendship network, there is still a notable grade division.

  • We can overlay the aggression network on top of the friendship network to view both networks at once, which shows that most of the agression edges are of medium length, and stay within the same grade, as agression occurs more often within the same social circles.

  • While the node-link diagrams are relatively intuitive, it can be difficult to compare them against each other, and it can be difficult to see directionality. In order to compare the friendship and aggression networks, we arrange students vertically and plot the connectivity directionally from left to right, we can see that the aggression network (on the left of the plot) looks very much like the friendship network (on the right of the plot). In both networks, the majority of connections are within a grade level, with relatively very little inter-grade relations.

  • We can apply the same radial techniques to the network of aggression that we did to the friendship network. Here we can see that for the lower grades, the intra-grade aggression substantially outnumbers the inter-grade bullying. Also, the overall amount of bullying trends downward; by the 12th grade the amount of bullying is greatly reduced.

  • When we consider gender instead of grade, the overall results are much more even for males, and skewed for females. Both internal and external agression are comparable for males, but female to female agression is substantially higher, and female to male agression is substantially lower.

A Video Example

  • Here we start with the network of friends colored by grade. The connections fade away, and the nodes turn grey. We then overlay the agression with directionality shown by draw direction. As each agression is drawn, the agressor becomes more red and grows, and the victim becomes more blue. Purple nodes indicate students who were both agressors and victims. As nodes grow, they push others out of the way.