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Probabilistic models of network diffusion How cascades spread in real life: Viral marketing Blogs GGroup membership b hi Last 20 minutes: mid‐term mid term course evaluation 10/27/2009 Jure Leskovec, <strong>Stanford</strong> CS322: Network Analysis 2
How do viruses/rumors propagate? Will a flu‐like virus linger, or will it become extinct? (Virus) birth rate β: probability than an infected neighbor attacks (Virus) death rate δ: probability that an infected node heals 10/27/2009 N 1 Infected Prob. β Prob. δ N N 2 Healthy Jure Leskovec, <strong>Stanford</strong> CS322: Network Analysis 3 N 3
Page 1: CS 322: (Social and Information) Ne
Page 5 and 6: Number of noodes time Susceptible I
Page 7 and 8: Number N of nodes n time SSusceptib
Page 9 and 10: What should t depend on? avg. degr
Page 11 and 12: N umber off Infectedd Nodes 500 400
Page 13 and 14: [Leskovec et al., SDM ’07] Blogg
Page 15 and 16: [Leskovec et al., TWEB ’07] Send
Page 17 and 18: Prob. Prob of adoption depends on t
Page 19 and 20: LiveJournal community membership Pr
Page 21 and 22: For viral marketing: We see that n
Page 23 and 24: Competing sociological theories x y
Page 25 and 26: Large anonymous online retailer (Ju
Page 27 and 28: There are relatively few DVD titles
Page 29 and 30: Some products are easier to recomme
Page 31 and 32: What is the effectiveness of subseq
Page 33 and 34: 47,000 47 000 customers responsible
Page 35 and 36: 94% of users make first recommendat
Page 37 and 38: How big are cascades? What are the
Page 39 and 40: is the most common cascade subgraph
Page 41 and 42: Coount 10 6 10 4 10 2 10 0 10 0 = 1
Page 43 and 44: The pprobability yof observing g a
Page 45 and 46: 1) Randomly pick blog to infect, in
Page 47: Blogs - information epidemics Whic

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