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We introduce a homogeneous pair approximation to the Naming Game (NG) modelby deriving a six-dimensional ODE for the two-word Naming Game. Our ODE revealsthe change in dynamical behavior of the Naming Game as a function of theaverage degree < k > of an uncorrelated network. This result is in goodagreement with the numerical results. We also analyze the extended NG modelthat allows for presence of committed nodes and show that there is a shift ofthe tipping point for social consensus in sparse networks.

Analytic Treatment of Tipping Points for Social Consensus in Large Random Networks