Social Network Analysis

Social Networks, Assessment 2
INSTRUCTIONS:
In the 1st summative assessment, you built your own network. In this second assessment, you will continue using your network from assessment 1. You may build a new network for this exercise too (bearing in mind that this may
require extra work for you). If you decide to build a new network, adhere to the constraints given in assessment 1 on how your network should look like (e.g. the network should have at least 10 nodes, the network should be original etc.) Consult Assessment 1 on Moodle for the requirements for your network. Note that you may need to ignore weights, directions, or signs of edges for some of the algorithms you’ll use below. If this turns out to be the case, mention briefly that the algorithm you use ignores (or you choose to ignore) some characteristics of the edges.
Some algorithms you’ll use below may fail to converge. If this happens, report the case, modify the algorithm, the statistical model, of your network until you get a solution.
You will write 1,500 words report. Your report should discuss the items given below. Structure your report in four parts corresponding to the four groups of items below. Each section is equally weighted in the final grade.
A: assortativity and communities
First describe briefly your network (i.e. what are nodes and edges) and how you constructed the network (i.e. how you collected the data). Also provide a plot of your network. The purpose is to remind us your network. If you chose to build a new network for this assessment, you will need give more details here.
1. Divide your network into two or three mutually exclusive subgroups. There may already be natural subgroups in your network (e.g. defensive versus offensive football players, actors from different teams, war lords from different clans, gender, students from different schools or countries etc.). If this is the case, use these natural divisions. If your network does not have such natural subgroups, impose an artificial division yourself and justify your division.
Calculate a modularity statistic using these subgroups and interpret the results. What do the results imply for assortativity in your network?
2. Now study assortativity with respect to a continuous variable. This continuous variable could be degree or any
other variable (e.g. age, income, etc. of a node). Interpret the results. What do your results imply for the level of
assortativity in your network with respect to the continuous variable you study?
3. Ignore now the division you imposed/studied in A-1. Run a community detection algorithm to detect hidden communities. Settle on a final community structure. Compare the communities you find here with those in A-1.
Interpret the results of your community detection algorithm.
B: Small-world and scale-free networks
Discuss briefly what a scale-free network is and what the small-world phenomenon means. Report the degree
distribution in your network and some measures of distance between the nodes in your network. Discuss if your network looks like a scale-free network and exhibits small-world characteristics (Your network will likely be rather
small to discuss these properties which apply to very large networks. But imagine you expand your network by adding many more nodes or by collecting additional data from many other similar networks. Would you expect to
see scale-free or small-world network characteristics?). Briefly discuss the mechanism that may or may not result in a scale-free and a small-world network in your case.
C: Exponential random graph modelling
Discuss briefly what Exponential Random Graph Modelling (ERGM) can tell us about your network that other approaches we treated in this class cannot tell. Formulate at least two or three hypotheses that you can test using an
ERGM. Test these hypotheses by fitting an ERGM with at least two or three independent variables. Interpret the results. Carry out a simulation analysis to assess the goodness-of-fit of your ergm. [NB: not all ERGMs converge.
If non-convergence (R failing to find reasonable solutions) occurs in your case, report this, and try different specifications (e.g. adding geometrically weighted terms, varying the decay parameter of these terms, removing terms, adding alternative terms) until you achieve convergence. If you cannot achieve convergence by this way, try modifying your network by e.g. adding a few new links or removing certain links, expanding your network by adding a few new nodes etc. If nothing works after all these steps, contact the teaching team.]
D: Self-reflection on Social Network Analysis
Based on your personal experience of the analysis of your network in assessment 1 and assessment 2, and comparing it with other social science approaches you have seen during your study discuss in ~350 words: “What are the key features of social network analysis that are different from other approaches in the social sciences?”