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