Social Media Intelligence Test
WESTERN SYDNEY UNIVERSITY Sample Exam – Autumn Session 2016 School of Computing, Engineering and Mathematics STUDENT DETAILS Complete your details in this section when instructed by the Exam Supervisor at the start of the exam. You should also complete your details on any answer booklets provided. STUDENT SURNAME: STUDENT FIRST NAME: STUDENT ID: EXAM INSTRUCTIONS Read all the information below and follow any instructions carefully before proceeding. You must comply with all directions given by Exam Supervisors. You may begin writing when instructed by the Exam Supervisor at the start of the exam. Clearly indicate which question you are answering on any Examination Answer Booklets used. Unit Name: Social Median Intelligence Unit Number: 301116 Number of Questions: 6 Total Number of Pages: 4 Value of Questions: Exam questions are worth 8 marks, giving a total of 48 marks. Answering Questions: Answer all questions in the Examination Answer Booklet provided. Unit Coordinator: Laurence Park Time Allowed: 2 hours (includes reading time) RESOURCES ALLOWED Only the resources listed below are allowed in this exam. All printed materials, books, handwritten or printed notes, and calculators are allowed. Any calculator which has the primary function of a calculator is allowed. For example, calculators on mobile phones or similar electronic devices are not allowed. DO NOT TAKE THIS PAPER FROM THE EXAMINATION ROOM Question: 1 2 3 4 5 6 Total Points: 8 8 8 8 8 8 48 Score: 301116 Social Media Intelligence Sample Exam Question 1 (8 marks) The following questions refer to the following graph. ● ● ●● ● ● ● ● A B CD E F G H (a) (2 marks) Compute the embeddedness of the edge between nodes A and B (b) (2 marks) Compute the neighbourhood overlap between nodes A and B (c) (2 marks) Given that the graph satisfies the strong triadic closure property, identify the most likely strength of the edge between A and E (either strong or weak) and explain your reasoning. (d) (2 marks) Identify a node in the graph that has high social capital and explain why its position in the graph gives it high social capital. Question 2 (8 marks) The following questions refer to the following signed graph. + − + − − + + − + − ● ● ● ● ● A B C D E Question 2 continues. . . Page 1 of 4 301116 Social Media Intelligence Sample Exam (a) (2 marks) What changes must be made to the network for it to be structurally balanced. (b) (2 marks) Show how the structurally balanced graph can be represented as a bipartite graph. (c) (2 marks) The edges A−C, A−D, B −E, C −D were removed to produce the following graph. + − − + + − ● ● ● ● ● A B E C D Show how to merge the set of nodes into supernodes. (d) (2 marks) Use the supernodes, identify if the graph is weakly balanced. Question 3 (8 marks) Using the following payoff matrix: Player B X Y Player A X 3, 2 1, 1 Y 0, 1 2, 3 (a) (2 marks) Determine if player A have a strictly dominant strategy and explain why or why not. (b) (2 marks) State if a pure strategy Nash Equilibrium exists and state why or why not. (c) (2 marks) State which strategies are Pareto Optimal, and state why. (d) (2 marks) Give an example of a game (showing the payoff for each player using each strat- egy) that has no pure strategy Nash equilibrium. Question 4 (8 marks) The plot below contains a log-log plot of the count of the number of twitter followers for each twitter user. Use the information in this plot to answer the following questions. Question 4 continues. . . Page 2 of 4 301116 Social Media Intelligence Sample Exam 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 2 4 6 8 10 log(Number of Followers) lo g( F re qu en cy ) (a) (2 marks) Show that a linear log-log plot of the distribution implies that the distribution follows a power law model. (b) (2 marks) Using the plot, estimate the two coefficients of the power law distribution. (c) (2 marks) Given the previous model coefficients, if we were to simulate the twitter followers network using the Simple Power Law model, what value would p (the probability of following someone Uniformly at random) selecting be set to? (d) (2 marks) Is it expected that the number of twitter followers follows a power law distribu- tion? Given the nature of Twitter, explain why this is a valid assumption. Question 5 (8 marks) (a) (2 marks) If the world wide friend network does not contain triadic closure and everyone has the same number of friends, how many friends would each of us need to ensure that we are no more than 6 hops from the world population of 7 billion people? (b) (2 marks) The Watts-Strogatz model connects all nodes to their neighbours and connects each node to a set of randomly chosen nodes (random edges). What do the randomly chosen edges model in a social network? (c) (2 marks) The Generalised Watts-Strogatz model requires that all people be uniformly spread across the landscape, to use the optimal clustering exponent q = 2. How do we adjust the model when modelling a real world friend network, where people are not uni- formly spread? (d) (2 marks) Given the social group {A,B,C}, {A,B}, {A,B,D}, {G,E, F}, {A,G,E, F} in the above graph, compute the social distance from A to B and A to F . Question 6 (8 marks) (a) (2 marks) Are the following set of pairwise preferences complete and transitive? Explain why or why not. A ≻ B A ≻ C C ≻ B Question 6 continues. . . Page 3 of 4 301116 Social Media Intelligence Sample Exam (b) (2 marks) Construct a ranking that satisfies the following pairwise preferences: A ≻ B A ≻ D D ≻ C (c) (2 marks) Arrow’s theorem examines the conditions 1) Unanimity, 2) IIA, and 3) non- dictatorship. Which of the three conditions does Borda Count satisfy? Explain your answer. (d) (2 marks) Provide a set of rankings of items X, Y and Z that exhibit the Condorcet Para- dox. END OF EXAM Page 4 of 4