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An Isaac Newton Institute Programme

Principles of the Dynamics of Non-Equilibrium Systems

Social balance on networks: The dynamics of friendship and hatred

6th June 2006

Author: Redner, S (Boston University)


We study the evolution of social networks that contain both friendly and unfriendly links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced(frustrated) triad---a triangular loop with 1 or 3 unfriendly links---is reversed to make the triad balanced. Thus a balanced triad fulfills the adage: "friend of my friend is my friend; an enemy of my friend is my enemy; a friend of my enemy is my enemy; an enemy of my enemy is my friend." With this frustration- reducing dynamics, an infinite network undergoes a dynamics phase transition from a steady state to "utopia"---all links are friendly---as the propensity for friendly links in an update event passes through 1/2. A finite network always falls into an socially-balanced absorbing state where no imbalanced triads remain. One example of the trend to social balance was the evolution of treaties between various European countries between approximately 1880-1910 that ultimately led to the alliances that comprised the protagonists of World War I.