Exercise 7. Characterizing whole networks

Post date: Mar 03, 2014 2:20:51 AM

For this exercise we will use four datasets:

CAMPNET:

This is a dichotomous adjacency matrix of 18 participants in a qualitative methods class. Ties are directed and represent that the ego indicated that the nominated alter was one of the three people with which s/he spent the most time during the seminar.

KAPTAIL:

This is a stacked dataset containing four dichotomous matrices. There are two adjacency matrices each for social ties (indicating the pair had social interaction) and instrumental ties (indicated the pair had work-related interaction). The two pairs of matrices represent two different points in time. The names of the datasets encode the type of tie in the sixth letter, and the time period in the seventh. Thus, the dataset KAPFTS1 is social ties at time 1 and KAPFTI2 is instrumental ties at time 2, etc.

ZACKAR & ZACHATTR:

ZACKAR is another stacked dataset, containing a dichotomous adjacency matrix, ZACHE, which represents the simple presence or absence of ties between members of a Karate Club, and ZACHC, which contains valued data counting the number of interactions between actors. ZACHATTR is a rectangular matrix with three columns of attributes for each of the actors from the ZACKAR datasets.

EXERCISE:

1) Cohesion using UCINET with CAMPNET

a) Calculate the following measures of cohesion using Network | Cohesion: Density, Geodesic Distances, Maximum Flow, Point Connectivity

b) Compare the point connectivity values and the maximum flow values. (Ignore values on the diagonal.) What is the relationship between them? Why do you think that is? Can you find the edge-independent paths (maximum flow) and node independent paths (point connectivity) between Bill and Pat by visualizing Campnet in NetDraw?

c) The Geodesic Distance procedure used in 1a produces a matrix. Looking at the matrix, what is the diameter of the network? What is the longest distance between any two connected nodes? When is this the diameter and when is it not?

d) Go to Transform | Symmetrize and symmetrize Campnet on the Maximum method. Now run distance again, this time on the symmetrized matrix (called Campnet-Sym by default). No looking at the matrix, and the frequency table above it, what is the diameter of this network?

e) Using your Netdraw visualization, verify a couple entries in the distance, point connectivity, and maximum flow matrices produced.

2) Average Degree & Centralization using KAPTAIL

a) Run Network | Centrality | Degree on KAPTAIL being sure to tell UCINET that the data are symmetric. This will generate results for all four networks (matrices, levels) in the dataset.

b) Compare the results for KAPFTS1 and KAPTFTS2 (the social ties at time 1 and time 2). What happened to average degree? What happened to network centralization? Does this make sense?

c) Compare the results for KAPFTI1 and KAPFTI2 (the instrumental/work ties at time 1 and time 2). What happened to average degree and centralization here? Does this make sense?

d) Why does centralization behave the way it does compared to average degree across the Social and Instrumental ties? (HINT: Look at the maximum and minimum values.)

3) Fragmentation using UCINET and KAPTAIL

a. Using the KAPFTS1 dataset (you may have to unpack KAPTAIL if you have not already done so using Data | Unpack), calculate its fragmentation under Network | Centrality using the default options. This reports both “Fragmentation” and “Distance Weighted Fragmentation.” Why are the numbers different? Which one is more useful for this network? When would you choose to use one or the other?

b. Based on the results from Exercise 2 above, what do you think will happen to each of the fragmentation measures if you run them for KAPFTS2. Run them to check your answers. Were you surprised? By which measure(s)? Why are the results what they are?

4) Core-Periphery using UCINET with KAPTAIL

a. Run Network | Core/Periphery | Categorical on KAPFTS1 and KAPFTS2. How do the results differ? During which time period was there a cleared core/periphery structure to the social ties? What happened to the core between time 1 and time 2?

b. Run Network | Core/Periphery | Continuous on KAPFTS1. Find the line where it recommends how many nodes should be in the core. Does that match the size of the core found from the Categorical procedure? How might you determine which one better captures the core/periphery nature of the data?

Exercise written by Rich DeJordy