Social Dynamics of Informa0on Kris0na Lerman USC Informa0on Sciences Ins0tute

Transcription

1 Social Dynamics of Informa0on Kris0na Lerman USC Informa0on Sciences Ins0tute h"p://

2 Social media has changed how people create, share and consume informa:on h"p://blog.socialflow.com/post/ / breaking- bin- laden- visualizing- the- power- of- a- single

3 Social informa0cs

4 Outline 1. A meme is not a virus uncovering the microscopic mechanisms of informa:on spread how psychological factors shape social interac:ons and the diffusion of informa:on 2. Measuring network structure How social interac:ons affect how we measure network structure e.g., iden:fy central nodes and communi:es in the network Explore these ques:ons via empirical studies of social media

5 Social news on Twi;er Users tweet short messages Retweet posts of others Tweets may contain URLs to online content, news Social networks Users follow friends to see Tweets by friends Retweets by friends Dataset sta:s:cs 70K URLs 700K users, 36M edges

6 Social news on Digg Users share news Submit links to news stories Vote on stories of submi"ed by others Social networks Users follow friends to see Stories friends submi"ed Stories friends voted on Dataset sta:s:cs* 3.5K stories 258K users, 1.7M edges *h"p://

7 A meme is not a virus: How is informa0on spead different from an epidemic?

8 Informa0on spread as social contagion A meme is an idea that behaves like a virus that moves through a popula:on, taking hold in each person it infects M. Gladwell infected exposed

9 Informa0on spread as social contagion A meme is an idea that behaves like a virus that moves through a popula:on, taking hold in each person it infects M. Gladwell infected exposed

10 Mechanics of contagion: epidemic threshold How many people are infected in an outbreak? standard model of contagion (independent cascade)

11 Mechanics of contagion: epidemic threshold How many people are infected in an outbreak? standard model of contagion (independent cascade) dies out goes viral epidemic threshold

12 Distribu0on of outbreaks in social media How many people are infected by informa0on? # connected users who share (re- tweet) a post with same URL Digg 3.5K URLs 258K users 1.7M edges Twi;er 70K URLs 700K users 36M edges [Lerman et al. Social Contagion: An Empirical Study of Informa0on Spread on Digg and Twi;er Follower Graphs arxiv: ]

13 Distribu0on of outbreaks in social media Viral outbreaks in social media are rare In most cases, memes reach small frac:on of poten:al audience Why?

14 How do people respond to repeated exposures? Exposure response: probability of infec0on given x infected friends p(infec:on x) Non- monotonic exposure response also observed on Twi"er [Romero et al, 2011] #infected friends [Ver Steeg, Ghosh & Lerman What Stops Social Epidemics? in ICWSM arxiv: ]

15 Failure to respond to repeated exposures limits epidemic size in social media Epidemic threshold unchanged Es:mated transmissibility actual cascades simulated cascades using empirical exposure response [Ver Steeg, Ghosh & Lerman What Stops Social Epidemics? in ICWSM arxiv: ]

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17 A;en0on and the Web Evidence from eye- tracking studies prob. to view post posi:on [Counts & Fisher ICWSM 11] A;en0on limits how far down the page a user navigates

18 Visibility and limited a;en0on new post at top of user s queue post visibility prob. to view post post near the top is highly visible: takes li;le effort to find; user is more likely to see it posi:on

19 Visibility and limited a;en0on some 0me later: newer posts appear at the top post visibility prob. to view post posi:on post is less visible: takes more effort to find; user is less likely to see it

20 Visibility and GUI Twi;er visibility: repost moves it to top posi0on prob. to view post Digg visibility: repost does not change posi0on prob. to view post posi:on posi:on web site GUI affects visibility of reposted memes

21 Users retweet a post when it is most visible Retweet probability vs 0me since exposure by a friend Twi;er (single exposure) Digg Visibility decays as friends add new posts to a user s 0meline: the more friends, the quicker the decay [Hodas & Lerman How Limited Visibility and Divided A;en0on Constrain Social Contagion in SocialCom arxiv: ]

22 Users divide a;en0on over all friends Repost probability vs number of friends user follows (single exposure) Twi;er Digg [Hodas & Lerman How Limited Visibility and Divided A;en0on Constrain Social Contagion in SocialCom arxiv: ]

23 Summary Social contagion is different from viral contagion Due to their limited a"en:on, highly connected people are less suscep:ble to becoming infected Rapidly decaying visibility of posts, combined with limited a"en:on, prevents social epidemics from spreading More info Ver Steeg, Ghosh & Lerman. What Stops Social Epidemics? in ICWSM arxiv: Hodas & Lerman How Limited Visibility and Divided A"en:on Constrain Social Contagion in SocialCom arxiv:

24 Measuring network structure: structure = topology x dynamics

25 Analyzing network structure Central nodes Community structure Strength of :es Zachary, J. Anthro. Research 33 No. 4. (1977)

26 Analyzing network structure Central nodes Network structure is a product of both topology and dynamics Community structure Strength of :es Mathema0cal framework Empirical analysis of data Numerical simula0ons Zachary, J. Anthro. Research 33 No. 4. (1977)

27 Dynamic processes on networks Random walk Epidemics Transi:on rule A"empt to infect one out- neighbor Models Phone calls, web surfing, money exchange, Transi:on rule A"empt to infect all out- neighbors Models Viral contagion, signaling by broadcasts

28 Dynamic processes and centrality A node is central if it is owen visited by the dynamic process random walk dynamics epidemic dynamics steady state distribu:on given by PageRank [Brin & Page, 1998] steady state distribu:on given by Alpha- Centrality [Bonacich, 1987]

29 adjacency matrix A = out- degree matrix D out = D in = in- degree matrix

30 Tangent: Alpha- Centrality (AC) [Bonacich 1987] cr α = A + αa 2 + α 2 A = A(I αa) 1 Measures the number of paths between nodes, each path a"enuated by its length with parameter α Holds while α < 1/λ max, where λ max is largest eigenvalue of A Parameter α sets the length scale of interac:ons α = 0: only neighbors contribute to cr α degree centrality α 1/λ max : more distant nodes contribute, un:l cr α becomes a global metric eigenvector centrality length scale diverges Diverging length scale Cri:cal phenomenon [Ghosh and Lerman, Parameterized Metric for Network Analysis Physical Review E, 2011]

31 What is the cri0cal phenomenon? Epidemic threshold Cri:cal value of transmissibility α c =1/λ max [Wang et al., 2003] For α < α c, epidemic dies out, i.e., reaches vanishing frac:on of nodes For α > α c, epidemic reaches a large frac:on of nodes 1/λ max [Ver Steeg, Ghosh & Lerman, What stops social epidemics? ICWSM, 2011]

32 Limited- a;en0on dynamics Epidemics Limited- a"en:on epidemics Transi:on rule A"empt to infect all out- neighbors Models Viral contagion, signaling by broadcasts Transi:on rule A"empt to infect all out- neighbors Suscep:bility ~ 1/in- degree Models Communica:on in social media

33 Limited- a;en0on Alpha- Centrality (laac) lacr α = AD 1 in + α( 1 AD ) 2 in + α 2 ( 1 AD ) 3 in +... during an epidemic: AC. limited- a;en0on epidemic: laac α=0.14

34 Likelihood of an infec0on random walk w/jump: PageRank (PR) limited- a;en0on random walk w/jumps (lapr) random jump prob.= 0.14

35 Likelihood of an infec0on during an epidemic [AC] limited- a;en0on epidemic [laac] during a random walk w/ restarts [PageRank] limited- a;en0on random walk w/restarts [lapagerank]

36 Choosing appropriate centrality: social media case study follower submitter follower follower

37 Gold standard

38 Which centrality is right for social media? Correla:on between the gold standard and the rankings predicted by Alpha- Centrality and limited- a;en0on AC Digg Twi;er limited- a"en:on Alpha- Centrality best predicts node centrality [Lerman et al., Designing Centrality for Social Media submi"ed to SDM 13]

39 Community detec0on Divide the network into group such that nodes within a group are more similar to each other than to other nodes [Zachary An Informa0on Flow Model for Conflict and Fission in Small Groups. J. Anthro. Research 33 No. 4. (1977)]

40 Dynamics of synchroniza0on in networks ater a long 0me Hierarchical community structure revealed en route to synchroniza0on [Arenas et al. Synchroniza0on Reveals Topological Scales in Complex Networks, Phys. Rev. LeE. 96 (2006)]

41 Mathema0cs of synchroniza0on Random walks Kuramoto model of coupled oscillators nodes are coupled via diffusive interac:ons (random walk- like) Linear model: Laplacian

42 Mathema0cs of synchroniza0on Random walks Kuramoto model of coupled oscillators nodes are coupled via diffusive interac:ons (random walk- like) Epidemics Non- conserva:ve model of coupled oscillators nodes are coupled through epidemic- like interac:ons Linear model: Laplacian Linear model: Replicator

43 Network structure via the eigenvalue spectrum Eigenvalue spectrum characterizes graph structure Number of null eigvals of L # disconnected components Time to reach steady state smallest posi:ve eigval (Cheeger bound) Gaps between consecu:ve eigvals rela:ve difference of :me scales

44 Network structure via simulated dynamics Simulate different synchroniza:on models (L vs R) star:ng from a random ini:al configura:on Measure similarity (degree of synchroniza:on) between nodes awer a period of :me Cluster nodes by their similarity i.e., nodes in the same cluster are more synchronized with each other than with nodes in other clusters

45 Network structure via simulated dynamics Degree of synchroniza:on of pairs of nodes in the Karate Club network over :me More synchronized Less synchronized

46 Community structure of karate club

47 Community structure of Digg social network Whiskers Core

48 Community structure of Digg social network is preserved at 0ghter resolu0on scales Whiskers Core

49 Community structure of Digg social network is preserved at 0ghter resolu0on scales Whiskers Core

50 Community structure of Digg social network is preserved at 0ghter resolu0on scales Whiskers

51 Dynamics reveals different views of network structure core of Digg small communi:es (whiskers) Li"le overlap between the cores discovered by the two models 40K nodes 360K edges total 3.7K users in small communi:es 450 users in small communi:es [Ghosh & Lerman, Role of Dynamic Interac:ons in Mul:- scale Analysis of Community Structure arxiv preprint]

52 Dynamics reveals different views of network structure Quality of small communi:es Quality is measured by co- ac:vity of pairs of community members Anomalous communi:es discovered by conserva:ve model in the center of the network (scale =1) A 13- core group of 26 users with 300 co- votes on average A 4- core group of 9 users with 600 co- votes on average [Ghosh & Lerman, Role of Dynamic Interac:ons in Mul:- scale Analysis of Community Structure arxiv proprint]

53 also for Facebook social network core of AU network small communi:es (whiskers) Li"le overlap between the cores discovered by the two models 6.4K nodes 200K edges total 1.3K users in small communi:es 32 users in small communi:es [Ghosh & Lerman, Role of Dynamic Interac:ons in Mul:- scale Analysis of Community Structure arxiv preprint]

54 Summary Informa:on diffusion in social media What stops social epidemics? in ICWSM- 11 How limited visibility and divided a"en:on constrain social contagion, in Social Compu:ng 2012 Dynamics and network structure Centrality Rethinking centrality: the role of dynamical processes in social network analysis, arxiv: Communi:es Network structure, topology & dynamics in synchroniza:on, Phys. Rev E. 2012, arxiv: Social :es Using proximity to predict ac:vity in social networks, arxiv:

55 Acknowledgments Collaborators Rumi Ghosh (USC Ph.D., 2012) Nathan Hodas Greg Ver Steeg Jeon- Hyung Kang Tad Hogg Sponsors