Skip to main content

Part of the book series: Springer Theses ((Springer Theses))

  • 882 Accesses

Abstract

The works of this thesis fall into the broad field of research on social networks which has been studied, in different communities at various times, for many decades. A general definition of a social network is a system which contains a set of social actors (the actor may be an individual or an organisation) that interact according to a set of social relationships or interconnections. Social network analysis is the study of variables of interest in the network, e.g. the actors’ opinions on a given topic, and how these variables may be determined or may be changed due to the interactions.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Other works may assume the opinion is a discrete variable. An interpretation of an opinion as a real number is provided in Chap. 2.

  2. 2.

    This condition implies that for any two individuals i and j, i can directly or indirectly (via a path on the graph) influence j’s opinion. The reader is referred to Chap. 2 for details.

References

  • Abelson RP (1964) Mathematical models of the distribution of attitudes under controversy. Contrib Math Psychol 14:1–160

    Google Scholar 

  • Altafini C (2013) Consensus problems on networks with antagonistic interactions. IEEE Trans Autom Control 58:935–946

    Article  MathSciNet  Google Scholar 

  • Anderson BDO, Yu C, Fidan B, Hendrickx JM (2008) Rigid graph control architectures for autonomous formations. Control Syst 28:48–63

    Article  Google Scholar 

  • Asch SE (1951) Groups, leadership, and men. Carnegie Press, Pittsburgh, pp 222–236. chapter Effects of Group Pressure Upon the Modification and Distortion of Judgments

    Google Scholar 

  • Becker J, Brackbill D, Centola D (2017) Network dynamics of social influence in the wisdom of crowds. Proc Natl Acad Sci 114:E5070–E5076

    Article  Google Scholar 

  • Blondel VD, Hendrickx JM, Tsitsiklis JN (2009) On Krause’s multi-agent consensus model with state-dependent connectivity. IEEE Trans Autom Control 54:2586–2597

    Article  MathSciNet  Google Scholar 

  • Boyd S, Ghosh A, Prabhakar B, Shah D (2006) Randomized gossip algorithms. IEEE Trans Inf Theory 52:2508–2530

    Article  MathSciNet  Google Scholar 

  • Brockmann D, Helbing D (2013) The hidden geometry of complex, network-driven contagion phenomena. Science 342:1337–1342

    Article  Google Scholar 

  • Cai K, Ishii H (2012) Average consensus on general strongly connected digraphs. Automatica 48:2750–2761

    Article  MathSciNet  Google Scholar 

  • Cao M, Morse AS, Anderson BDO (2008) Reaching a consensus in a dynamically changing environment: a graphical approach. SIAM J Control Optim 47:575–600

    Article  MathSciNet  Google Scholar 

  • Cao Y, Ren W, Egerstedt M (2012) Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks. Automatica 48:1586–1597

    Article  MathSciNet  Google Scholar 

  • Chandrasekhar AG, Larreguy H, Xandri JP (2012) Testing models of social learning on networks: Evidence from a framed field experiment. Work. Pap., Mass. Inst. Technol., Cambridge, MA

    Google Scholar 

  • Chopra N (2012) Output synchronization on strongly connected graphs. IEEE Trans Autom Control 57:2896–2901

    Article  MathSciNet  Google Scholar 

  • Dandekar P, Goel A, Lee DT (2013) Biased assimilation, homophily, and the dynamics of polarization. Proc Natl Acad Sci 110:5791–5796

    Article  MathSciNet  Google Scholar 

  • DeGroot MH (1974) Reaching a consensus. J Am Stat Assoc 69:118–121

    Article  Google Scholar 

  • Del Vicario M, Bessi A, Zollo F, Petroni F, Scala A, Caldarelli G, Stanley HE, Quattrociocchi W (2016) The spreading of misinformation online. Proc Natl Acad Sci 113:554–559

    Article  Google Scholar 

  • Duggins P (2017) A psychologically-motivated model of opinion change with applications to american politics. J Artif Soc Soc Simul 20:1–13

    Article  Google Scholar 

  • Etesami SR, BaĹźar T (2015) Game-theoretic analysis of the hegselmann-krause model for opinion dynamics in finite dimensions. IEEE Trans Autom Control 60:1886–1897

    Article  MathSciNet  Google Scholar 

  • Flache A, Mäs M, Feliciani T, Chattoe-Brown E, Deffuant G, Huet S, Lorenz J (2017) Models of social influence: towards the next Frontiers. J Artif Soc Soc Simul 20

    Google Scholar 

  • French JRP (1956) A formal theory of social power. Psychol Rev 63:181–194

    Article  Google Scholar 

  • Friedkin NE (2015) The problem of social control and coordination of complex systems in sociology: a look at the community cleavage problem. IEEE Control Syst Mag 35:40–51

    MathSciNet  Google Scholar 

  • Friedkin NE, Bullo F (2017) How truth wins in opinion dynamics along issue sequences. Proc Natl Acad Sci 114:11380–11385

    Article  Google Scholar 

  • Friedkin NE, Johnsen EC (1990) Social influence and opinions. J Math Sociol 15:193–206

    Article  Google Scholar 

  • Friedkin NE, Johnsen EC (2011) Social influence network theory: a sociological examination of small group dynamics, vol 33. Cambridge University Press, Cambridge

    Google Scholar 

  • Friedkin NE, Jia P, Bullo F (2016a) A theory of the evolution of social power: natural trajectories of interpersonal influence systems along issue sequences. Sociol Sci 3:444–472

    Article  Google Scholar 

  • Friedkin NE, Proskurnikov AV, Tempo R, Parsegov SE (2016b) Network science on belief system dynamics under logic constraints. Science 354:321–326

    Article  MathSciNet  Google Scholar 

  • Harary F (1959) Studies in social power. Ann. Arbor, University of Michigan Press, Michigan, pp 182–198. chapter A criterion for unanimity in French’s theory of social power

    Google Scholar 

  • Harary F, Norman RZ, Cartwright D (1965) Structural models: an introduction to the theory of directed graphs. Wiley, New York

    Google Scholar 

  • Hegselmann R, Krause U (2002) Opinion dynamics and bounded confidence models, analysis, and simulation. J Artif Soc Soc Simul 5

    Google Scholar 

  • Jadbabaie A, Lin J, Morse AS (2003) Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans Autom Control 48:988–1001

    Article  MathSciNet  Google Scholar 

  • Jia P, MirTabatabaei A, Friedkin NE, Bullo F (2015) Opinion dynamics and the evolution of social power in influence networks. SIAM Rev 57:367–397

    Article  MathSciNet  Google Scholar 

  • Kempe D, Kleinberg J, Tardos E (2003) Maximizing the spread of influence through a social network. In: Proceedings of the 9th ACM SIGKDD international conference on knowledge discovery and data mining, pp 137–146

    Google Scholar 

  • Krick L, Broucke ME, Francis BA (2009) Stabilisation of infinitesimally rigid formations of multi-robot networks. Int J Control 82:423–439

    Article  MathSciNet  Google Scholar 

  • Kuran T (1997) Private truths, public lies: the social consequences of preference falsification. Harvard University Press, Harvard

    Google Scholar 

  • Liu BJ, Mou S, Morse AS, Anderson B, Yu C (2011) Deterministic gossiping. Proc IEEE 99:1505–1524

    Article  Google Scholar 

  • Liu J, Chen X, BaĹźar T, Belabbas MA (2017a) Exponential convergence of the discrete- and continuous-time altafini models. IEEE Trans Autom Control 62:6168–6182

    Article  MathSciNet  Google Scholar 

  • Liu Q, Ye M, Qin J, Yu C (2016) Event-based leader-follower consensus for multiple Euler-Lagrange systems with parametric uncertainties. In: Proceedings of IEEE 55th annual conference on decision and control (CDC). Las Vegas, USA, pp 2240–2246

    Google Scholar 

  • Liu Q, Ye M, Qin J, Yu C (2017b) Event-triggered algorithms for leader-follower consensus of networked euler-lagrange agents. IEEE Trans Syst, Man, Cybern: Syst. https://doi.org/10.1109/TSMC.2017.2772820, arXiv:1703.03166

  • Liu Q, Ye M, Sun Z, Qin J, Yu C (2017c) Coverage control of unicycle agents under constant speed constraints. In: Proceedings of the 20th IFAC world congress. Toulouse, France, pp 2526–2531

    Google Scholar 

  • Lorenz J (2007) Continuous opinion dynamics under bounded confidence: a survey. Int J Mod Phys C 18:1819–1838

    Article  Google Scholar 

  • Mäs M, Flache A, Kitts JA (2014) Cultural integration and differentiation in groups and organizations. In: Perspectives on culture and agent-based simulations, pp 71–90

    Google Scholar 

  • Mei W, Mohagheghi S, Zampieri S, Bullo F (2017) On the dynamics of deterministic epidemic propagation over networks. Ann Rev Control

    Google Scholar 

  • Mellon J, Yoder J, Evans D (2016) Undermining and strengthening social networks through network modification. Sci Rep 6:34613

    Article  Google Scholar 

  • Mirtabatabaei A, Bullo F (2012) Opinion dynamics in heterogeneous networks: convergence conjectures and theorems. SIAM J Control Optim 50:2763–2785

    Article  MathSciNet  Google Scholar 

  • Nedić A, Liu J (2017) On convergence rate of weighted-averaging dynamics for consensus problems. IEEE Trans Autom Control 62:766–781

    Article  MathSciNet  Google Scholar 

  • O’Gorman HJ (1975) Pluralistic ignorance and white estimates of white support for racial segregation. Public Opin Q 39:313–330

    Article  Google Scholar 

  • Olfati-Saber R, Fax J, Murray R (2007) Consensus and cooperation in networked multi-agent systems. Proc IEEE 95:215–233

    Article  Google Scholar 

  • Parsegov SE, Proskurnikov AV, Tempo R, Friedkin NE (2017) Novel multidimensional models of opinion dynamics in social networks. IEEE Trans Autom Control 62:2270–2285

    Article  MathSciNet  Google Scholar 

  • Proskurnikov A, Matveev A, Cao M (2016) Opinion dynamics in social networks with hostile camps: consensus versus polarization. IEEE Trans Autom Control 61:1524–1536

    Article  Google Scholar 

  • Proskurnikov AV, Tempo R (2017) A tutorial on modeling and analysis of dynamic social networks. Part I. Ann Rev Control 43:65–79

    Article  Google Scholar 

  • Qin J, Yu C (2013) Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica 49:2898–2905

    Article  MathSciNet  Google Scholar 

  • Ramazi P, Riehl J, Cao M (2016) Networks of conforming or nonconforming individuals tend to reach satisfactory decisions. Proc Natl Acad Sci 113:12985–12990

    Article  Google Scholar 

  • Ravazzi C, Frasca P, Tempo R, Ishii H (2015) Ergodic randomized algorithms and dynamics over networks. IEEE Trans Control Netw Syst 2:78–87

    Article  MathSciNet  Google Scholar 

  • Ren W, Beard RW (2005) Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans Autom Control 50:655–661

    Article  MathSciNet  Google Scholar 

  • Russell J, Ye M, Anderson BDO, Hmam H, Sarunic P (2017) Cooperative localisation of a GPS-denied UAV in 3-dimensional space using direction of arrival measurements. In: Proceedings of the 20th IFAC world congress. Toulouse, France, pp 8291–8296

    Google Scholar 

  • Shi G, Johansson KH (2013) The role of persistent graphs in the agreement seeking of social networks. IEEE J Sel Areas Commun 31:595–606

    Article  Google Scholar 

  • Smaldino PE, Epstein JM (2015) Social conformity despite individual preferences for distinctiveness. R Soc Open Sci 2:140437

    Article  MathSciNet  Google Scholar 

  • Spong MW, Hutchinson S, Vidyasagar M (2006) Robot modeling and control, vol 3. Wiley, New York

    Google Scholar 

  • Su W, Chen G, Hong Y (2017) Noise leads to quasi-consensus of hegselmann-krause opinion dynamics. Automatica 85:448–454

    Article  MathSciNet  Google Scholar 

  • Taylor M (1968) Towards a mathematical theory of influence and attitude change. Hum Relat 21:121–139

    Article  Google Scholar 

  • Trinh MH, Ye M, Ahn HS, Anderson BDO (2017) Matrix-weighted consensus with leader-following topologies. In: 11th asian control conference (ASCC). IEEE, pp 1795–1800

    Google Scholar 

  • Waters NL, Hans VP (2009) A jury of one: opinion formation, conformity, and dissent on juries. J Empir Leg Stud 6:513–540

    Article  Google Scholar 

  • Wu Y, Su H, Shi P, Lu R, Wu ZG (2017) Output synchronization of nonidentical linear multiagent systems. IEEE Trans Cybern 47:130–141

    Article  Google Scholar 

  • Ye M, Anderson BDO, Yu C (2016a) A variable gain model-independent algorithm for rendezvous of euler-lagrange agents on directed networks. Australian control conference. Newcastle, Australia, pp 153–158

    Google Scholar 

  • Ye M, Anderson BDO, Yu C (2016b) Model-independent trajectory tracking of euler–lagrange agents on directed networks. In: Proceedings of IEEE 55th annual conference on decision and control (CDC). Las Vegas, USA, pp 6921–6927

    Google Scholar 

  • Ye M, Anderson BDO, Yu C (2017a) Bearing-only measurement self-localization, velocity consensus and formation control. IEEE Trans Aerosp Electron Syst 53:575–586

    Article  Google Scholar 

  • Ye M, Anderson BDO, Yu C (2017b) Distributed model-independent consensus of Euler-Lagrange agents on directed networks. Int J Robust Nonlinear Control 27:2428–2450

    Article  MathSciNet  Google Scholar 

  • Ye M, Anderson BDO, Yu C (2018) Leader tracking of euler-lagrange agents on directed switching networks using a model-independent algorithm. IEEE Trans Control Netw Syst. https://doi.org/10.1109/TCNS.2018.2856298. early Access

  • Ye M, Yu C, Anderson BDO (2015) Model-independent Rendezvous of Euler-Lagrange agents on directed networks. In: Proceedings of IEEE 54th annual conference on decision and control. Osaka, Japan, pp 3499–3505

    Google Scholar 

  • Yu C, Anderson BDO, Mou S, Liu J, He F, Morse AS (2017) Distributed averaging using periodic gossiping. IEEE Trans Autom Control 62:4282–4289

    Article  MathSciNet  Google Scholar 

  • Zhang L, Ye M, Anderson BDO, Sarunic P, Hmam H (2016) Cooperative localisation of UAVs in a GPS-denied environment using bearing-only measurements. In: Proceedings of IEEE 55th annual conference on decision and control (CDC). Las Vegas, USA, pp 4320–4326

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mengbin Ye .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ye, M. (2019). Introduction. In: Opinion Dynamics and the Evolution of Social Power in Social Networks. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-10606-5_1

Download citation

Publish with us

Policies and ethics