Consensus on Multiplex Network To Calculate User Influence in Social Networks

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User influence determines how the information is transmitted. Most of the current methods need to consider the complete network and, if it changes, the calculations have to be repeated from the scratch. This work proposes the use of a consensus algorithm to calculate the influence of the participants in a social event through their interactions in Twitter. Retweets, mentions and replies and considered and represented in a multiplex network. The algorithm determines the influence of the users using only local knowledge.
Talk in NetWorks Conference. El Escorial. Dec. 2013

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Consensus on Multiplex Network To Calculate User Influence in Social Networks

  1. 1. Introduction User influence viaCatalana Conclusions Consensus on Multiplex Networks To Calculate User Influence in Social Networks M. Rebollo, E. del Val, C. Carrascosa, A. Palomares Grupo Tec. Inform.-Inteligencia Artificial Universitat Politècnica de València F. Pedroche Inst. de Mat. Multidisciplinària Universitat Politècnica de València Net-Works 2013 @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  2. 2. Introduction User influence viaCatalana Conclusions Problem User Influence in SN How users can determine their own influence in an event? global view high cost recalculated if network changes @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  3. 3. Introduction User influence viaCatalana Conclusions The Proposal Consensus over Multiple Networks decentralized locally calculated (bounded rationality) each layer captures a type of interaction @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  4. 4. Introduction User influence viaCatalana Conclusions Consensus [xj (t) − xi (t)] xi (t + 1) = xi (t) + ε j∈Ni where Ni are the neighbors of node i ε < mini 1 |Ni | is a learning rate converges to the mean of xi (0) @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  5. 5. Introduction User influence viaCatalana Conclusions User influence User activity measured through: retweets replies mentions Each one of these interaction types are stored in a different layer of a multiplex network. @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  6. 6. Introduction User influence viaCatalana Conclusions Network configuration nodes are weighted (wi ) using its degree in each layer xi (0) is the total number of interactions of each type realized during the event The mean user influence is calculated as the weighted, average strength of the node @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  7. 7. Introduction User influence viaCatalana Conclusions Adaption to Weighted Networks The expression for consensus can be rewritten as xi (t + 1) = xi (t) + ε wi [xj (t) − xi (t)] j∈Ni that converges to the weighted average of the initial values xi (0) i lim xi (t) = t→∞ whenever ε < min i wi xi (0) i wi ∀i wi |Ni | @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  8. 8. Introduction User influence viaCatalana Conclusions Events TedXValencia: TED talk. Valencia, June 22th. SEO4SEOS: Professional SEO conference. Alicante, Oct 5th. TAW2013: Twitter Awards 2013, given to celebrities in different categories, 9th and 10th Oct. kikodeluxe: Reality show. Oct 4th. nuevosiPhone: iPhone 5S Apple keynote. Sep 10th. ViaCatalana: Citizen demonstration in Catalonian. Sep 11th. BreakingBad: Comments during the final episode, Sep 29th. @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  9. 9. Introduction User influence viaCatalana Conclusions Event characterization hashtag #tedxValencia #seo4seos #TAW2013 #kikodeluxe #nuevosiPhone #viacatalana #breakingBad tweets 1,803 2,891 12,845 6,388 16,505 135,668 136,916 n 402 426 2,519 2,638 8,546 47,506 71,130 m 1,142 1,659 7,817 5,030 10,904 129,299 105,344 γ -1.3318 -1.2132 -1.4650 -1.9191 -2.2981 -1.9608 -1.9500 @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks ¯ d 2.87 4.11 2.92 1.15 1.11 2.20 2.92 l 2.77 2.69 3.46 3.96 3.57 4.45 6.72 g 6.0 6.0 10.0 12.0 15.0 14.0 23.0 c 0.63 0.73 0.67 0.43 0.48 0.28 0.05 UPV
  10. 10. Introduction User influence viaCatalana Conclusions Via Catalana @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  11. 11. Introduction User influence viaCatalana Conclusions Via Catalana @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  12. 12. Introduction User influence viaCatalana Conclusions Via Catalana @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  13. 13. Introduction User influence viaCatalana Conclusions Network Characterization Degree Distribution for #viaCatalana 12 data gamma = −1.96081 10 91,339 retweets , d = 3.3 6,523 replies, d = 0.2 8 log(degree) 135,434 ment., d = 5.0 6 4 2 0 −2 0 @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks 1 2 3 log(#nodes) 4 5 6 UPV
  14. 14. Introduction User influence viaCatalana Conclusions User Influence tolerance 10−10 2,528 iterations average influence 202.84 @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV
  15. 15. Introduction User influence viaCatalana Conclusions Conclusions Conclusions users can calculate their own influence consensus allows decentralized calculations Limitations all nodes must follow the algorithm low convergence speed for some scenarios (for example, normalized weights) one dimensional @mrebollo Consensus on Multiplex Networks To Calculate User Influence in Social Networks UPV

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