A major goal in the study of neural networks is to create novel information-processing algorithms inferred from the real brain. Recent neurophysiological evidence of graded persistent activity suggests that the brain possesses neural mechanisms for retrieval of graded information, which could be described by the neural-network dynamics with attractors that are continuously dependent on the initial state. Theoretical studies have also demonstrated that model neurons with a multihysteretic response property can generate robust continuous attractors. Inspired by these lines of evidence, we proposed an algorithm given by the multihysteretic neuron-network dynamics, devised to retrieve graded information specific to a given topic (i.e., context, represented by the initial state). To demonstrate the validity of the proposed algorithm, we examined keyword extraction from documents, which is best fitted for evaluating the appropriateness of retrieval of graded information. The performance of keyword extraction by using our algorithm was significantly high (measured by the average precision of document retrieval, for which the appropriateness of keyword extraction is crucial) compared with standard document-retrieval methods. Moreover, our algorithm exhibited much higher performance than the neural-network dynamics with bistable neurons, which can also produce robust continuous attractors but only represent dichotomous information at the single-cell level. These findings indicate that the capability to manage graded information at the single-cell level was essential for obtaining a high performing algorithm.