Most network models for neural behavior assume a predefined network topology and consist of almost identical elements exhibiting little heterogeneity. In this paper, we propose a self-organized network consisting of heterogeneous neurons with different behaviors or degrees of excitability. The synaptic connections evolve according to the spike-timing dependent plasticity mechanism and finally a sparse and active-neuron-dominant structure is observed. That is, strong connections are mainly distributed to the synapses from active neurons to inactive ones. We argue that this self-emergent topology essentially reflects the competition of different neurons and encodes the heterogeneity. This structure is shown to significantly enhance the coherence resonance and stochastic resonance of the entire network, indicating its high efficiency in information processing.