03-small_world_annot

03-small_world_annot -...

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CS224W: Social and Information Network Analysis Jure Leskovec, Stanford University http://cs224w.stanford.edu
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Due in 1 week: Oct 4 in class! The idea of the reaction papers is: To familiarize yourselves more in depth with the material covered in class Do reading beyond what was covered. You should be thinking beyond what you just read, and not just take other people's work for granted. an be done in groups of 2 students Can be done in groups of 2 3 students Read at least 3 papers: Anything from course website, last year’s website nything from Easley leinberg Anything from Easley Kleinberg How to submit: File: PDF or DOC with SUNetIds of team members: g if 2 members then: < UNetId NnetId df E.g., if 2 members then: <SUNetId> <SUNnetId>.pdf Upload to Dropbox folder at http://coursework.stanford.edu 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 2
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On 3 5 pages answer the following questions: page: Summary 1 page: Summary What is main technical content of the papers? How do they fit in the field, and what you have learned in class so far? hat is the connection between the papers you are discussing? What is the connection between the papers you are discussing? 1 page: Critique Why is it interesting in relation to the corresponding section of the urse? course? What were the authors missing? Was anything particularly unrealistic? 1 page: Brainstorming pg g What are promising further research questions in the direction of the papers? How could they be pursued? An idea of a better model for something? A better algorithm ? A test of a model or algorithm on a dataset or simulated data? 9/28/2010 Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu 3
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rdos enyi andom Graph model dos enyi ‘60] Erdos Renyi Random Graph model [Erdos Renyi, 60] aka.: Poisson/Bernoulli random graphs ot perfect model but interesting calculations Not perfect model but interesting calculations Two variants: G p : undirected graph on n nodes and each n,p gp edge (u,v) appears i.i.d. with probability p So a graph with m edges appears with prob.: (M choose m) p m (1-p) M-m , where M=n(n-1)/2 is the max number of edges G n,m : undirected graph with n nodes, m uniformly at random picked edges Jure Leskovec, Stanford CS224W: Social and Information Network Analysis, http://cs224w.stanford.edu What kinds of networks does such model produce? 9/28/2010 4
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What is expected degree of a node? Let X v be a random var. measuring the degree of the node v (# of incident edges): E[X v ]= j jP(X v =j) Linearity of expectation: For any random variables Y 1 ,Y 2 ,…,Y k If Y=Y 1 +Y 2 +…Y k , then E[Y]= i E[Y i ] asier way: ecompose = X +X 2 +…+ Easier way: decompose X v in X v X v1 X v2 X vn where X vu is a {0,1} random variable which tells if edge (v,u) exists or not. So: [X = [ =p(n- ) E[X v ] u E[X vu ] p (n 1) How to think about it: Prob. of node u linking to node v is
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03-small_world_annot -...

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