复旦大学：《网络科学导论 Introduction to Network Science》教学成果_学生翻转课堂展示4 Group Report

Group report Presenter: Jingwei han haifan Zhang canrong lou

Group Report Presenter: Jingwei Han, Haifan Zhang, Canrong Lou

Outline 01 02 03 04 Centrality Friendship Math proof Analysis of an arvar d paradox Simulationexperiment

01 Centrality 02 Friendship paradox 03 Math proof and Simulation 04 Analysis of Harvard experiment Outline

Central node Definition angles Closeness centrality Degree centrality (1 When calculating the average ) Generally the degree of the length of the shortest path central node is the highest between the node and all other ② Randomly choose one node move to a linked one that nodes, the central node is has higher degree, repeating the always the smallest step, finally we always reach the central nod

Central node Definition angles 02 Degree centrality ①Generally the degree of the central node is the highest. ②Randomly choose one node ,move to a linked one that has higher degree, repeating the step , finally we always reach the central node. 01 Closeness centrality ①When calculating the average length of the shortest path between the node and all other nodes ，the central node is always the smallest

B

friendship paradox: Your Friends Have More Friends Than You do 01. Randomly sampling in cases/links 02. Randomly sampling in people/nodes It is to see the probability that It is to see the proba bility that one of your friend has more most of ones friends have more friends than you do friends than he does (whose degree is higher, he is (whose degree is higher, he is compared with others less than he compared with others more often should have been as one of others friend

friendship paradox: Your Friends Have More Friends Than You Do. 01. Randomly sampling in cases/links 02. Randomly sampling in people/nodes It is to see the probability that one of your friend has more friends than you do. (whose degree is higher, he is compared with others less than he should have been. ) It is to see the probability that most of one ʼ s friends have more friends than he does. (whose degree is higher, he is compared with others more often as one of others ʼ friend. )

Math analysis Mean number of friends of friends= 2d 2/2d) Denote Than =2d/N 2d12)/(2d) 02=2(d1-1)2/ ∑(d12-2ud1+p2)/N =C2d12/N)(2d/N ∑d2/N-2u2+u2 (2+02)/u ∑d12N-2 =+02/u

Math analysis Mean number of friends of friends = (Σdi ²)/(Σdi ) Denote: μ = Σdi / N σ2 = Σ(di - μ)2/N = Σ(di ² - 2μdi + μ2)/N = Σdi 2/N - 2μ2 + μ2 = Σdi 2/N - μ2 Than: (Σdi ²)/(Σdi ) = (Σdi ²/N)/(Σdi /N) =(μ2 + σ2)/μ =μ + σ2/μ

Simulation 1 Let's verify the mathematical proof above and test the friendship paradox on different network structure

Simulation 1: Let’s verify the mathematical proof above and test the friendship paradox on different network structure

Harvard experiment introduction ACHIEVEMENT By monitoring the friends METHOD group, 16 days advance C warning is got of an have the random group impending epidemic in nominate their friends this human population those friends would be more central

Harvard experiment introduction ACHIEVEMENT By monitoring the friends group, 16 days advance warning is got of an impending epidemic in this human population METHOD have the random group nominate their friends, those friends would be more central

Harvard experiment analysis Observed Differences in Epidemic Curves u乙uozu23 Friend Group DAYS SINCE SEPTEMBER 1 DAYS SINCE SEPTEMBER 1

Harvard experiment analysis

Harvard experiment analysis Network PEOPLE &FRIENDS

Harvard experiment analysis