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The interaction between substitutional nitrogen atoms in graphene is studied by performing first-principles calculations. The effective nearest-neighbor interaction between nitrogen dopants is found to be highly repulsive because of the strong electrostatic repulsion between nitrogen atoms. This interaction prevents the full nitrogen-carbon phase separation in nitrogen-doped graphene. Interestingly, there are two relatively stable nitrogen-nitrogen pair configurations, whose stability can be attributed to the anisotropy in the charge redistribution induced by nitrogen doping. We reveal two stable, ordered, semiconducting N-doped graphene structures, C_{3}N and C_{12}N, through the cluster-expansion technique and particle-swarm optimization method. In particular, we show that C_{12}N has a direct band gap of 0.98 eV. The heterojunctions between C_{12}N and graphene nanoribbons might be a promising basis for organic solar cells.