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For models whose evolution takes place on a network it is often necessary toaugment the mean-field approach by considering explicitly the degree dependenceof average quantities (heterogeneous mean-field). Here we introduce the degreedependence in the pair approximation (heterogeneous pair approximation) foranalyzing voter models on uncorrelated networks. This approach gives anessentially exact description of the dynamics, correcting some inaccurateresults of previous approaches. The heterogeneous pair approximation introducedhere can be applied in full generality to many other processes on complexnetworks.

Heterogeneous pair approximation for voter models on networks