# Social Network

**Please turn in a hard copy of your solutions to the TA at the beginning of class. **Your solution should be neat and legible. Remember that collaboration on homework is not permitted. Late assignments will be penalized at the rate of 10% per calendar day.

Q1. Sketch a histogram of the degree distribution of the network below (Y-axis=frequency; X-axis=degree). You can use an Excel graph instead if you prefer. (2 points)

Q2. If you plot this degree distribution on a log-log plot, do you expect to get a straight line? (1 point)

Answer:

Consider our model of the diffusion of a new behavior through a social network. In this network, everyone starts with behavior B, and a threshold q [i.e., b/(a+b)] for switching to a new behavior A (e.g., a new communication app). Any node will switch to A if at least a fraction q of its neighbors have adopted A . If exactly q of its neighbors have adopted A, we assume it adopts A, too. (Same as p>=b/(a+b))

Q3. Let q=1/3, and Lisa is the initial adopter of A. Who will eventually switch to A? (1 point)

Q4. Again let q=1/3, but now Jill is the initial adopter of A. Who will eventually switch to A?(1 point)

Q5. Comment on the effect of the cluster of friends (Mike, Bob, John, Leah, Jill, Emma & Shane) on the probability of cascades that start inside versus outside the cluster. (2 points)

Inside 12/16

Q6. Now let q=1/2. Jill is the initial adopter of A. Will there be a complete cascade? (1 point)

Q7. Again let q=½ and Jill is the initial adopter of A. You can provide an incentive, like a coupon, to make the payoff of A (i.e., “a”) higher when someone uses A with a friend. The person who received your coupon will have q=⅓. What is the minimum number of coupons you need to generate a complete cascade? Explain your answer. (2 points)

Q8. Imagine you are the CEO of a new start-up that sells high-end bedding directly to consumers (https://www.parachutehome.com/). Your sales department reports that your products took off very quickly in some areas but did badly in some others. Your market research team insists that these communities are basically identical and they cannot explain why your products are successful in some areas but not others. Having taken Social Networks, explain, in your own words, to your marketing team what is cumulative advantage in cultural markets, and how it can generate both large inequality in market returns AND unpredictability even the product quality is the same. (2 points)

Q9. Your marketing team is considering (a) distribute 100 coupons to friends and families of your existing customers and (b) distribute 100 coupons to a randomly selected group of people. Which of these two plans will you choose if your product has (i) a high threshold of adoption (e.g., it is expensive, or people are very uncertain about whether it is worth it) and (ii) a low threshold of adoption? Explain your answers concisely. (3 points)

Q10. The graph below is taken from http://graphics.wsj.com/ebola-crisis/

Consider the first 10 patients of Ebola in this graph (hint: the 10th patient is the “Hospital worker”. What is the average number of cases (R_{0}) each of these 10 patients had infected? (2 points) 1.1

Q11. Imagine you were a public health official in the first response team. You were reading the reports about these first 10 patients and whom they infected. Given your answer to Q10, Will you tell your supervisor that an epidemic is (1) unlikely (ii) probable and (iii) almost certain? Explain your answer in 1-2 sentences. (2 points)

Q12. Imagine the first case happened in a city rather than in a small village. Would the chance of an epidemic have increased? Assume infectivity given contact is the same in a city or a village, explain your answer in terms of both average degree and average clustering coefficient of the networks. (2 points)

**Bonus questions (5 points)**

These questions are completely **optional**. It is just to give you a way in addition to the exams to demonstrate your understanding of the materials. It is entirely up to you whether you do them or not. Not all questions require gephi.

-gephi version 0.8.2 data file; works on lab’s computers [here]

-gephi version 0.9.1 data file works with the latest version of gephi 0.9.1, which you can run on your own machine) [here]

An alien spaceship attacks our class and abducted Professor Liu, Emily and Andrew and __three students__. They also take our away our course website’s announcement board etc. so any communication can only go through FB messages (i.e., only students who are FB friends can communicate with each other.)The aliens’ goal is to make communication difficult ( i.e., increases average path length).

HInts: You don’t need gephi to answer some of these questions. But you can experiment with it to help you think through the conceptual issues. To delete nodes, you can select rows under data laboratory and choose delete among the right click options. Rerun the network statistics after deletion will give you the new average path length. Running the “network diameter” statistics generates a column of betweenness centrality in the data laboratory spreadsheet. Any of those columns can be sorted by clicking on the column heading.

B1. You only have limited resources that you can spend on a pre-occupation survey conducted by your alien scouts. Which is less costly to find out: (a) who are the three students with high degree or (b) who are the three students with high betweenness?

B2. From the alien commander’s perspective, what is the advantage of abducting the three classmates with the highest degrees as compared to three randomly selected students?

B3. From the alien ship commander’s perspective, what’s the advantage of choosing students with high betweenness over the the students with the high degrees?

B4. Requires gephi. Referring to the class’s network, which three students will you abduct if you are the alien commander? Relate your explanations to your answers to B2 and B3 (2 points).

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**Category**: Sample Questions