(7) Based on the graph below, answer the questions that follow. 6 H Question 2 (30 points) The graph below depicts a social network of nine individuals in which edges represent friendships. It may look familiar to some of you. (a) What is the average path length between node A and the seven other nodes in the graph above? (If it helps clarify things, the path length between node A and node C is 2.) Show your work briefly. (b) If you could add one edge between any pair of nodes in the graph, towards making the average path length from node A computed above as low as possible, which pair of nodes would you connect? Provide a clear explanation for why your choice is correct. In a survey, individuals 1, 2, 3 and 4 indicate that they consume alcohol recreationally, while 5, 6, 7, 8, and 9 indicate that they do not consume alcohol recreationally. Let's say everyone is being truthful. (a) Is there an edge in this graph which is a local bridge but is not a bridge? If so, identify at least one such edge. If not, provide a couple of sentences explaining your answer, and provide an example of an edge you could add that would satisfy the property of being a local bridge but not a bridge? (b) Would you expect the edge connecting node 3 and node 5 to be a strong tie or a weak tie? Why? (c) A local expert asserts that the social network above displays assortative mixing in the behavior of recreational alcohol consumption. Explain what this expert means, and why they are correct. (d) Provide a clear explanation of how the assortative mixing observed in this social network may have arisen (i) because of selection; (ii) due to influence, and (iii) due to homophily or exogenous factors. When answering this question, it is not sufficient for you to simply define the terms selection, influence and so on in an abstract way. You must situate each idea in the example given, and provide a 1-2 sentence of a scenario illustrating each of the three ideas. B For example, referring back to our class discussion of high school grades, a candidate answer in that context would be "Students who are more intelligent are likely to form friendships with other students who are intelligent. Additionally, a student who is intelligent is more likely to get high grades. The social network of high school students may thus display assortative mixing by grades because of " (where the word in the blank would be selection, influence, or homophily/exogenous factors). 2 1 Question 3 (35 points, 2-3 sentences for each part) B E strong tie weak tie H The graph below illustrates a portion of a social network. The solid lines represent strong ties, and the dashed lines represent weak ties. (a) Does node A satisfy the Strong Triadic Closure property? Explain clearly why or why not. (b) Does node B satisfy the Strong Triadic Closure property? Explain clearly why or why not. (c) Does node F satisfy the Strong Triadic Closure property? Explain clearly why or why not. (d) In your opinion, which node is likely to have more social capital, node A or node F? Explain your reasoning based on what you have learned in this course. (e) Which relationship is likely to be more trusting the relationship between B and E, or the relationship between C and E? Explain your reasoning based on what you have learned in this course. (f) We have discussed a few methods for community detection in the course. Choose one such method that you might use to identify two distinct communities within this social network. Outline the method you have chosen very briefly, and why you chose it. (You don't have to provide any mathematical details in your answer.) Question 4 (15 points, about a page) - submit as a separate PDF file Pick your favorite large networked data set. (An example of a networked data set would be Instagram's social graph. Another example would be a network of employees created based on their email exchange. Another would be the network of cities connected by direct flights. Another would be a network of corporations where two corporations are connected if they share a board member. You don't have to use any of these examples, these are just for illustration of scope.) That's it! Apply some of the concepts you have learned in this course towards describing how you would use this data set to gain a better understanding of a social or economic question of your choosing. (This is a broad and open-ended question, so interpret "social or economic question" in any way you'd like to.) 3