Small cell networks are regarded as a promising candidate to meet the exponential growth of mobile data traffic in cellular networks. With a dense deployment of access points, spatial reuse will be improved, and uniform coverage can be provided. However, such performance gains cannot be achieved without effective intercell interference management. In this paper, a novel interference coordination strategy, called user-centric intercell interference nulling, is proposed for small cell networks. A main merit of the proposed strategy is its ability to effectively identify and mitigate the dominant interference for each user. Different from existing works, each user selects the coordinating base stations (BSs) based on the relative distance between the home BS and the interfering BSs, called the interference nulling (IN) range, and thus interference nulling adapts to each user's own interference situation. By adopting a random spatial network model, we derive an approximate expression of the successful transmission probability to the typical user, which is then used to determine the optimal IN range. Simulation results shall confirm the tightness of the approximation, and demonstrate significant performance gains (about 35%-40%) of the proposed coordination strategy, compared with the non-coordination case. Moreover, it is shown that the proposed strategy outperforms other interference nulling methods. Finally, the effect of imperfect channel state information (CSI) is investigated, where CSI is assumed to be obtained via limited feedback. It is shown that the proposed coordination strategy still provides significant performance gains even with a moderate number of feedback bits.