The retrieval abilities of spatially uniform attractor networks can be measured by the global overlap between patterns and neural states. However, we found that nonuniform networks, for instance, small-world networks, can retrieve fragments of patterns (blocks) without performing global retrieval. We propose a way to measure the local retrieval using a parameter that is related to the fluctuation of the block overlaps. Simulation of neural dynamics shows a competition between local and global retrieval. The phase diagram shows a transition from local retrieval to global retrieval when the storage ratio increases and the topology becomes more random. A theoretical approach confirms the simulation results and predicts that the stability of blocks can be improved by dilution.