Dynamics of Social Balance on Networks

Details Dynamics of Social Balance on Networks Dynamics of Social Balance on Networks

2005-06-19

arxiv.org/abs/cond-mat/0506476v1

Phys. Rev. E 72, 036121 (2005)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 7 figures, 2-column revtex4 format

Scientific paper

10.1103/PhysRevE.72.036121

We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with 1 or 3 unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2. A finite network always falls into a socially-balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network does not increase in an update is imposed, then the network quickly reaches a balanced final state.

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