Introduction User influence viaCatalana Conclusions

Consensus on Multiplex Networks To CalculateUser Influence in Social Networks

M. Rebollo, E. del Val, C. Carrascosa, A. PalomaresGrupo Tec. Inform.-Inteligencia Artificial

Universitat Politècnica de València

F. PedrocheInst. de Mat. Multidisciplinària

Universitat Politècnica de València

Net-Works 2013

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Problem

User Influence in SNHow users can determine their own influence in an event?

global viewhigh costrecalculated if network changes

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

The Proposal

Consensus over Multiple Networks

decentralizedlocally calculated (bounded rationality)each layer captures a type of interaction

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Consensus

xi(t + 1) = xi(t) + ε∑j∈Ni

[xj(t)− xi(t)]

whereNi are the neighbors of node iε < mini

1|Ni | is a learning rate

converges to the mean of xi(0)

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

User influence

User activity measured through:retweetsrepliesmentions

Each one of these interaction types are stored in a different layer ofa multiplex network.

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Network configuration

nodes are weighted (wi) using its degree in each layerxi(0) is the total number of interactions of each type realizedduring the event

The mean user influence is calculated as the weighted, averagestrength of the node

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Adaption to Weighted Networks

The expression for consensus can be rewritten as

xi(t + 1) = xi(t) +ε

wi

∑j∈Ni

[xj(t)− xi(t)]

that converges to the weighted average of the initial values xi(0)

limt→∞

xi(t) =∑

i wixi(0)∑i wi

∀i

wheneverε < min

i

wi|Ni |

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

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 indifferent 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 UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Event characterization

hashtag tweets n m γ d̄ l g c#tedxValencia 1,803 402 1,142 -1.3318 2.87 2.77 6.0 0.63#seo4seos 2,891 426 1,659 -1.2132 4.11 2.69 6.0 0.73#TAW2013 12,845 2,519 7,817 -1.4650 2.92 3.46 10.0 0.67#kikodeluxe 6,388 2,638 5,030 -1.9191 1.15 3.96 12.0 0.43#nuevosiPhone 16,505 8,546 10,904 -2.2981 1.11 3.57 15.0 0.48#viacatalana 135,668 47,506 129,299 -1.9608 2.20 4.45 14.0 0.28#breakingBad 136,916 71,130 105,344 -1.9500 2.92 6.72 23.0 0.05

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Via Catalana

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Via Catalana

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Via Catalana

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Network Characterization

135,434 ment., d = 5.091,339 retweets , d = 3.36,523 replies, d = 0.2

0 1 2 3 4 5 6−2

0

2

4

6

8

10

12Degree Distribution for #viaCatalana

log(#nodes)

log(d

egre

e)

data

gamma = −1.96081

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

User Influence

tolerance 10−10

2,528 iterationsaverage influence 202.84

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks

Introduction User influence viaCatalana Conclusions

Conclusions

Conclusionsusers can calculate their own influenceconsensus allows decentralized calculations

Limitationsall nodes must follow the algorithmlow convergence speed for some scenarios (for example,normalized weights)one dimensional

@mrebollo UPVConsensus on Multiplex Networks To Calculate User Influence in Social Networks