Social network anlaysis has found utility is institutional, classroom and analyses of networked data in socially-based educational games. However, the utility of the method largely rests on being able to ascribe meaning to the structure of the network. Without meaningful interpretation of structure there is no added value to a networked model, you will find more suvccess simply regressing your outcome against student characteristics. Understanding measures of centrality and network structure in SNA are therefore an important, though difficult, aspect of the method. As with all SNA work, the vocabulary can be daunting though the ideas are relatively intuitive.
In this unit we will be working towards building several social network diagrams (graphs/sociograms) of a school classroom and then analyzing both centrality measures and clusters within the network.
We will be using data from:
Representing Classroom Social Structure. Melbourne: Victoria Institute of Secondary Education, M. Vickers and S. Chan, (1981)
Available from the Index of Complex Networks
The data were collected by Vickers & Chan from 29 seventh grade students in a school in Victoria, Australia. Students were asked to nominate their classmates on a number of relations including the following three "layers":
- Who do you get on with in the class?
- Who are your best friends in the class?
- Who would you prefer to work with?
We then have three data set for each of these questions:
best.friends.csv, get.on.with.csv, work.with.csv.
Before we do any further analysis, we would manipulate each of the data sets so that it is suitable for building a social network using iGraph.
We load these three csv data set in table by order as D1, D2, D3.
Then we can use count and select functions to get the edge and vertex for each table.
We can graph the direct connection and visualize each of the graphs and color the nodes according to gender.
Degree centrality means the number of ties that a node has, so it means the same thing for each of networks. If one node has more connections, it will have higher centrality, it will be more important in that case.
Closeness centrality is a way of detecting nodes that are able to spread information very efficiently through a graph. The closeness centrality of a node measures its average farness (inverse distance) to all other nodes. Nodes with a high closeness score have the shortest distances to all other nodes.
Betweenness centrality (or "betweeness centrality") is a measure of centrality in a graph based on shortest paths. Betweenness centrality finds wide application in network theory; it represents the degree to which nodes stand between each other.
All three centrality measures are useful from different aspect, but as same usefullness.
We can count the number of dyads and the number and type of triads using rstudio commands.
The metrics showed the network "get on with" has the most paris of connections. So the network has a good performance for expressing the relationships of different nodes in this dataset.
By some command about cliques, we can have the answer for the following:
What is the size of the largest cliques(s) in each of the three networks?
Which nodes/vertices are in the largest cliques for the three networks? Is there much overlap?
How many maximal cliques are there in each of the networks?
Using the relevant command of articulation_points, we can see the cutpoints for "best friends" and "work with" are 13, and there is no articulation piints for "get on with".
Based on all the information and analysis we did above, 6, 8, 11 are popular in this 7th grade class since they have the highest degree centrality in different networks. 13 is the bridge for connections. Girls tend to have more connection with girls, and so do boys. Based on the analysis, students can be formed as group by gender. Or teacher can let students with different gender form groups so they can have time to know each other. This reflect my experience, I used to play with girls a lot and hardly talked to boys.
Williams, N. (2014). Basics of Social Network Analysis.
Complexity Labs. (2015). Social Network Analysis Overview.
Complexity Labs. (2015). Network Centrality.
Complexity Labs. (2015). Network Clustering & Connectedness.
iGraph. (2016). Get Started with R iGraph