Social Balance on Networks: The Dynamics of Friendship and Enmity

Details Social Balance on Networks: The Dynamics of Friendship and Enmity Social Balance on Networks: The Dynamics of Friendship and Enmity

2006-05-21

arxiv.org/abs/physics/0605183v1

Physica D 224, 130 (2006)

Physics

General Physics

16 pages, 11 figures, paper based on an invited talk at Dyonet06, Dynamics on Complex Networks and Applications, Dresden, Germ

Scientific paper

10.1016/j.physd.2006.09.028

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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