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Dynamical Social Networks

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Encyclopedia of Systems and Control

Abstract

The classical field of social network analysis (SNA) considers societies and social groups as networks, assembled of social actors (individuals, groups or organizations) and relationships among them, or social ties. From the systems and control perspective, a social network may be considered as a complex dynamical system where an actor’s attitudes, beliefs, and behaviors related to them evolve under the influence of the other actors. As a result of these local interactions, complex dynamical behaviors arise that depend on both individual characteristics of actors and the structural properties of a network. This entry provides basic concepts and theoretical tools elaborated to study dynamical social networks. We focus on (a) structural properties of networks and (b) dynamical processes over them, e.g., dynamics of opinion formation.

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Notes

  1. 1.

    A n × n matrix W is (row-)stochastic if all its entries are nonnegative w ij ≥ 0, and each row sums up to 1, i.e., \(\sum _{j=1}^nw_{ij}=1\) for each i = 1, …, n.

  2. 2.

    stochastic matrices satisfying this property are known as fully regular or SIA (stochastic indecomposable aperiodic) matrices; such a matrix serves as a transition matrix of some regular (ergodic) Markov chains (Proskurnikov and Tempo 2017). The vector p is nonnegative in view of the Perron-Frobenius theorem and stands for the unique stationary distribution of the corresponding Markov chain.

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Author information

Authors and Affiliations

  1. Institute of Electronics, Computer and Telecommunication Engineering (IEIIT), National Research Council of Italy (CNR), Turin, TO, Italy

    Chiara Ravazzi

  2. Department of Electronics and Telecommunications, Politecnico di Torino, Turin, TO, Italy

    Anton Proskurnikov

  3. Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia

    Anton Proskurnikov

Authors
  1. Chiara Ravazzi
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  2. Anton Proskurnikov
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Corresponding author

Correspondence to Chiara Ravazzi .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Systems Modeling & Control Group, CNR-IEIIT, Torino, Italy

    Fabrizio Dabbene

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Ravazzi, C., Proskurnikov, A. (2020). Dynamical Social Networks. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100129-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_100129-1

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

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