Social Balance on Networks: The Dynamics of Friendship and Enmity
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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.
16 pages, 11 figures, paper based on an invited talk at Dyonet06, Dynamics on Complex Networks and Applications, Dresden, Germany, Feburary 2006
16 pages, 11 figures, paper based on an invited talk at Dyonet06, Dynamics on Complex Networks and Applications, Dresden, Germany, Feburary 2006