On the Logic of Balance in Social Networks

Xiong, Zuojun; Ågotnes, Thomas

doi:10.1007/s10849-019-09297-0

Cited by 11 publications

(13 citation statements)

References 22 publications

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“…Pedersen et al (2020Pedersen et al ( , 2021 proposed different ways of defining properties related to the concept of balance in signed social networks, where relations can be either positive or negative. To be able to formally reason about the social phenomenon of group polarization based on balance theory, they used positive and negative relations logic (Xiong and Ågotnes, 2020). Positive and negative relations between nodes are interpreted as agreement or disagreement on a given issue.…”

Section: Signed Network and Balance Theorymentioning

confidence: 99%

Network polarization, filter bubbles, and echo chambers: an annotated review of measures and reduction methods

Interian

Marzo

Bernardini

et al. 2022

Int Trans Operational Res

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Polarization arises when the underlying network connecting the members of a community or society becomes characterized by highly connected groups with weak intergroup connectivity. The increasing polarization, the strengthening of echo chambers, and the isolation caused by information filters in social networks are increasingly attracting the attention of researchers from different areas of knowledge such as computer science, economics, and social and political sciences. This work presents an annotated review of network polarization measures and models used to handle the polarization. Several approaches for measuring polarization in graphs and networks were identified, including those based on homophily, modularity, random walks, and balance theory. The strategies used for reducing polarization include methods that propose edge or node editions (including insertions or deletions as well as edge weight modifications), changes in social network design, or changes in the recommendation systems embedded in these networks.

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Section: Signed Network and Balance Theorymentioning

confidence: 99%

Network polarization, filter bubbles, and echo chambers: an annotated review of measures and reduction methods

Interian

Marzo

Bernardini

et al. 2022

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…Pedersen et al [104,105] proposed different ways of defining properties related to the concept of balance in signed social networks, where relations can be either positive or negative. To be able to formally reason about the social phenomenon of group polarization based on balance theory, they used positive and negative relations logic [131]. Positive and negative relations between nodes are interpreted as agreement or disagreement on a given issue.…”

Section: Signed Network and Balance Theorymentioning

confidence: 99%

Network polarization, filter bubbles, and echo chambers: An annotated review of measures, models, and case studies

Interian¹,

Marzo²,

Bernardini³

et al. 2022

Preprint

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Polarization arises when the underlying network connecting the members of a society is formed by highly connected groups with weak intergroup connectivity. The increasing polarization, the strengthening of echo chambers, and the isolation caused by information filters in social networks are increasingly attracting the attention of researchers from different areas of knowledge such as computer science, economics, social and political sciences. Despite hundreds of publications in this area, there was little effort to systematize or present the knowledge developed in the field in an organized way. This study presents an annotated review of network polarization measures, models used to handle existing polarization, their applications, and case studies. Altogether, 405 scientific articles and conference papers were examined, with 74 filtered for this review. Several approaches for measuring polarization in graphs and networks were identified, including those based on homophily, modularity, random walks, and balance theory. The models used for reducing polarization included methods that propose edge or node editions (including edge insertions or deletions, and edge weight modifications), changes in social network design, or changes in the recommendation systems embedded in these networks. This review will be helpful to researchers investigating polarized social networks from a theoretical and applied perspective.

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“…Positive and negative relations logic (PNL) [42,43] models signed networks as Kripke frames 4 with a set of possible worlds representing agents and two distinct positive "+" and negative "−" binary relations representing friendships and enmities, respectively. See Fig.…”

Section: Preliminaries: Balance and Pnlmentioning

confidence: 99%

“…Definition 3 (Signed Frame and Model [42]). Let A be a non-empty set of agents and R + and R − be two symmetric and non-overlapping binary relations on A where R + is reflexive.…”

Section: Syntax and Semantics Of Pnlmentioning

confidence: 99%

“…We are interested in formal reasoning about polarization and therefore about balance. First steps in this direction have been made: positive and negative relations logic (PNL) [42,43] is a basic modal logic that uses Kripke frames with two distinct relations to model networks where agents can be related positively or negatively, but not both, and is used to axiomatize the class of networks that are balanced (to a certain degree). While PNL can be seen as a logical foundation for reasoning about balance, it has two particular downsides.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modal Logics and Group Polarization

Pedersen

Smets

Ågotnes

2021

Journal of Logic and Computation

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This paper proposes different ways of modally defining properties related to the concept of balance in signed social networks where relations can be either positive or negative. The motivation is to be able to formally reason about the social phenomenon of group polarization based on balance theory. The starting point is a recently developed basic modal logic that axiomatizes the class of social networks that are balanced up to a certain degree. This property is not modally definable but can be captured using a deduction rule. In this work, we examine different possibilities for extending this basic language to define frame properties such as balance and related properties such as non-overlapping positive and negative relations and collective connectedness as axioms. Furthermore, we define the property of full balance rather than balanced-up-to-a-degree. We look into the complexity of the model checking problem and show a non-compactness result of the extended language. Along the way, we provide axioms for weak balance. We also look at a full hybrid extension and reason about network changes with dynamic modalities. Then, to explore the measures of how far a network is from polarization, we consider variations of measures in relation to balance.

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On the Logic of Balance in Social Networks

Cited by 11 publications

References 22 publications

Network polarization, filter bubbles, and echo chambers: an annotated review of measures and reduction methods

Network polarization, filter bubbles, and echo chambers: an annotated review of measures and reduction methods

Network polarization, filter bubbles, and echo chambers: An annotated review of measures, models, and case studies

Modal Logics and Group Polarization

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