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De retibus socialibus et legibus momenti(*) On social networks and the laws of influence

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Picture by photogirl7.1

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Online Social Networks (OSNs): Explosive growth in number of services, volume of users, and published content.

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EVERYBODY OSNs

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users

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brands & companiesusers

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brands & companiesnews media users

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celebrities brands & companiesnews media users

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marketers celebrities brands & companiesnews media users

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marketers celebrities brands & companiesnews media spammers users

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marketers celebrities brands & companiesnews media spammers users researchers

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The holy grail of online social networks?

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influence!

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influence?

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Which one is it ?

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You must choose.

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But choose wisely,for while the true Grailbring you life,the false Grail will takeit from you.

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What the F…

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define:influence

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in·flu·ence /"/the power or capacityof causing an effect inindirect or intangibleways.

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in·flu·ence /"/the power or capacityof causing an effect inindirect or intangible Now, how can iways. measure that?

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influence ≈ attention ≈ clicks Any measure of influence is necessarily a subjective one. However, in this case [Twitter], a good measure of influence should have a high predictive power on how well the URLs mentioned by the influential users attract attention and propagate in the social network. We would expect the URLs that highly influential users propagate to attract a lot of attention and user clicks. Thus, a viable estimator of attention is the number of times a URL has been accessed. Romero, Galuba, Asur & Huberman, “Influence and Passivity in Social Media,” arXiv:1008.1253v1, 2010.

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influence ≈ attention ≈ clicks I’ll rephrase my question…

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influence ≈ attention ≈ clicks How can i measure THat?

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Correlation 101The peanut butter vendor and the three twitterers (plus a statistician)

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A peanut butter vendorwanted to promote his product on Twitter.

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He thought of getting some “influentials” tweeting about hispeanut butter including a URL to his website.

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So, he approached three Twitter users.

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The first one was mostlyknown to nobody and he accepted to tweet about peanut butter for $200.

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The second one was pretty famous in the 1980s and he accepted to tweet about peanut butter for $5,000.Picture by dmason

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Finally, the vendorconvinced Lady Gaga to tweet about peanut butter for $50,000.

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Then, the vendorchecked for the number of website visits each user had attracted.

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The user known tonobody got 20 visits.

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The formerly famoususer got 5,000 visits.

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However, Lady Gaga,got 75,000 visits just on her own.

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The vendor put all of the results on a graph and found this.

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The peanut butter vendor thought: “There exist a positivecorrelation between the promoter’s cachet and the visitors I get.”

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A statistician who was watching the vendornodded in disapproval.“I’m afraid you may be wrong.” –said the statistician.

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“Why?” –replied the vendor.

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“Because you haveforgotten a confounding variable.” –replied the statistician.

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“What the f…, I mean,I beg your pardon?” –said the vendor.

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“How many followershas got the user known to nobody?”–asked the statistician.

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“150 followers.”–answered the vendor.

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“And how many followers has got theformerly famous user?”–asked the statistician.

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“15,000 followers.”–answered the vendor.

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“And Lady Gaga?”–asked the statistician.

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“1,500,000 followers.”–answered the vendor.

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“Then, it’s not thatsurprising that LadyGaga had got much more visits, is it?” –wondered the statistician.

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“If you say so…”–replied the vendor.

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“Let’s note down themoney you have paid foreach user’s follower andthe number of visits yougot from each follower.” –suggested the statistician.

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$200 / 150 followers = 1.33 $ / follower $5,000 / 15,000 followers = 0.33 $ / follower $50,000 / 1,500,000 followers = 0.03 $ / follower 20 clicks / 150 followers = 0.133 clicks / follower 5,000 clicks / 15,000 followers = 0.333 clicks / follower75,000 clicks / 1,500,000 followers = 0.05 clicks / follower

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“You see? There is nosignificant correlation.” –said the statistician.

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“Does this mean itdoesn’t matter who Ihire to promote my peanut butter?”–rhymed the vendor.

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“No.”–replied the statistician–“It means that you don’t know if a user’s cachetallows you to predict thenumber of visits that user is able to attract.”

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“Oh, by the way, I’mlegally obliged to warnyou that correlation is not causation.” –said the statisticianwhile waving goodbye.

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influence ≈ attention ≈ clicks SO. You should measure that.

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influence ≈ attention ≈ clicks AND You should test different metrics for correlation with clicks. The higher the correlation the better the metric could be a proxy for influence…

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influence ≈ attention ≈ clicks PageRank?

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influence ≈ attention ≈ clicks For instance.

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influence ≈ attention ≈ clicks tunkrank?

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influence ≈ attention ≈ clicks For instance.

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influence ≈ attention ≈ clicks Influence- passivity?

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influence ≈ attention ≈ clicks For instance.

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influence ≈ attention ≈ clicks And remember to correct your data for the size of the audience.(*) See last slide for full references.

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new “influence” score Picture by Cayusa

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new “influence” scorephysical metaphor to compute influencebased on dynamic friction and uniformly accelerated linear motion.

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new “influence” scorephysical metaphor to compute influencebased on dynamic friction and uniformly accelerated linear motion. velocity in Twitter = influence acceleration in Twitter = trending (september 2010)

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(october 2010)velocity & acceleration model :( independently proposed very few details disclosed :( different approach?

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anyway...

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Dynamics 101

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Dynamics 101 F mA body of mass m subject to a force F undergoes anacceleration a. The magnitude of a is proportional to F andinversely proportional to m.

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Dynamics 101 F a mA body of mass m subject to a force F undergoes anacceleration a. The magnitude of a is proportional to F andinversely proportional to m.

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Dynamics 101 F mThe smaller the mass the larger the acceleration.

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Dynamics 101 F a mThe smaller the mass the larger the acceleration.

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Dynamics 101F mThe larger the mass the smaller the acceleration.

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Dynamics 101F a mThe larger the mass the smaller the acceleration.

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Dynamics 101 Fa m FfThe force of kinetic friction Ff oposes movement and finallystops an object if no force Fa is applied.

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Dynamics 101 Fa W Ff N 1 for horizontalFf  ·m·g·cos( ) plane

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Dynamics 101 F Fa  Ff Fa  ·m·g·cos( )a   m m m

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Dynamics 101 Faa  ·g·cos( ) m

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Dynamics 101 Faa  ·g·cos( ) m

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Dynamics 101 Faa  ·g·cos( ) m

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Dynamics 101 Faa  ·g·cos( ) m

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Dynamics 101 Faa  ·g·cos( ) m damping constant z (decay factor for the acceleration of those users not receiving mentions) 0  z  1

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Dynamics 101 Fa a z m Fa Favt  vt 1 vt  vt 1  a  tz1   z a  v m m

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Dynamics 101 number of @ mentions in Fa the last hour a z mvelocity in theprevious hour Fa Fa vt  vt 1 vt  vt 1  a  tz1   z a  v m m

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Dynamics 101velocity is a good Fa influence score a  z(better than PageRank m and TunkRank) Fa Fa vt  vt 1 vt  vt 1  a  tz1   z a  v m m

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Dynamics 101velocity is a good Why? Fa influence score a  z(better than PageRank m and TunkRank) Fa Fa vt  vt 1 vt  vt 1  a  tz1   z a  v m m

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Dynamics 101velocity is a good Fa influence score a  z(better than PageRank m and TunkRank) Fa vt  vt 1  a  vt 1   z m

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Dynamics 101 Fa a z macceleration detects trending users Fa Fa vt  vt 1 vt  vt 1  a  tz1   z a  v m m

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Dynamics 101 Fa how? a z macceleration detects trending users Fa Fa vt  vt 1 vt  vt 1  a  tz1   z a  v m m

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Dynamics 101 Fa a z macceleration detects trending users Fa vt  vt 1  a  vt 1   z m

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Dynamics 101 Fa a z macceleration detects trending users Fa vt  vt 1  a  vt 1   z m Any example?

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Lance Armstrong (7-time Tour de France winner) a.k.a. @lancearmstrong

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@lancearmstrong velocity frommarch 2009 to august 2009

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absolute increases in velocity

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a zoom of that...

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these spikescorrespond to 2009 Tour de France,Armstrong’s comebak

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huge isolated spikearound the 4th week of march! relevant event?

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good luck get well soonmost frequent phrases in the best wishes anti-doping tweets mentioning hope ok@lancearmstrong around the recovery just luck surgery 4th week of march 2009 broken clavicle

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good luckOn March 17, 2009 Lance Armstrong was get well soonrequired by French anti-doping agency to best wishesprovide a hair sample. anti-dopingOn March 23, 2009 Lance Armstrong broke hope okhis collarbone in a crash during a race in recovery justSpain and had to face surgery. luck surgery broken clavicle

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just anecdotal evidencebut seems promising :)

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just anecdotal evidencebut seems promising :)

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ReferencesE. Bakshy et al. “Identifying Influencers on Twitter,” Proceedings of the fourth ACM International Conference on Web Searchand Data Mining, 2011.d. boyd et al. “Tweet, Tweet, Retweet: Conversational Aspects of Retweeting on Twitter,” Proceedings of the Hawaii InternationalConference on System Sciences, 2010.W. Galuba et al. “Outtweeting the Twitterers - Predicting Information Cascades in Microblogs,” Proceedings of the 3rdconference on Online social networks, 2010.D. Gayo-Avello. Nepotistic Relationships in Twitter and their Impact on Rank Prestige Algorithms. Arxiv preprint.arXiv:1004.0816, 2010.D. Gayo-Avello et al., De retibus socialibus et legibus momenti. Arxiv preprint. arXiv:1012.2057v1, 2010.B.A. Huberman et al. “Social networks that matter: Twitter under the microscope,” First Monday, vol. 14, no. 1--5, 2009.J.M. Kleinberg, “Authoritative sources in a hyperlinked environment,” Proceedings of the ninth annual ACM-SIAM symposiumon Discrete algorithms, 1998, pp. 668--677.C. Lee et al. “Finding Influentials from Temporal Order of Information Adoption in Twitter,” Proceedings of 19th World-WideWeb (WWW) Conference (Poster), 2010.L. Page et al. The PageRank Citation Ranking: Bringing Order to the Web, 1998, Available at:http://dbpubs.stanford.edu/pub/1999-66A. Pal & S. Counts. “Identifying Topical Authorities in Microblogs,” Proceedings of the fourth ACM International Conference onWeb Search and Data Mining, 2011.D.M. Romero et al. Influence and Passivity in Social Media. Arxiv preprint. arXiv:1008.1253v1, 2010.E.I. Schwartz, A New Model for Predicting Social-Media Impact, 2010. Available at:http://www.technologyreview.com/business/26438/D. Tunkelang. A Twitter Analog to PageRank, 2009. Available at: http://thenoisychannel.com/2009/01/13/a-twitter-analog-to-pagerank/J. Weng et al. “TwitterRank: Finding Topic-sensitive Influential Twitterers,” Proceedings of the third ACM internationalconference on Web Search and Data Mining, 2010, pp. 261--270.J. West et al. Big Macs and Eigenfactor Scores: Dont Let Correlation Coefficients Fool You. Arxiv preprint. arXiv:0911.1807v2,2010.