  For models whose evolution takes place on a network it is often necessary to
augment the mean-field approach by considering explicitly the degree dependence
of average quantities (heterogeneous mean-field). Here we introduce the degree
dependence in the pair approximation (heterogeneous pair approximation) for
analyzing voter models on uncorrelated networks. This approach gives an
essentially exact description of the dynamics, correcting some inaccurate
results of previous approaches. The heterogeneous pair approximation introduced
here can be applied in full generality to many other processes on complex
networks.
