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Social Balance on Networks: The Dynamics of Friendship and Enmity

T. Antal·P. L. Krapivsky·S. Redner
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Abstract

How do social networks evolve when both friendly and unfriendly relations exist? Here we propose a simple dynamics for social networks in which the sense of a relationship can change so as to eliminate imbalanced triads--relationship triangles that contains 1 or 3 unfriendly links. In this dynamics, a friendly link changes to unfriendly or vice versa in an imbalanced triad to make the triad balanced. Such networks undergo a dynamic phase transition from a steady state to "utopia"--all friendly links--as the amount of network friendliness is changed. Basic features of the long-time dynamics and the phase transition are discussed.

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T. Antal, P. L. Krapivsky, S. Redner. 2006-05-21. Social Balance on Networks: The Dynamics of Friendship and Enmity. https://doi.org/10.1016/j.physd.2006.09.028

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