Graph-structured databases have numerous recent applications including the Semantic Web, biological databases and XML, among many others. In this paper, we study the maintenance problem of a popular structural index, namely bisimulation, of a possibly cyclic data graph. In comparison, previous work mainly focuses on acyclic graphs. In the context of database applications, it is natural to compute minimal bisimulation with merging algorithms. First, we propose a maintenance algorithm for a minimal bisimulation of a cyclic graph, in the style of merging. Second, to prune the computation on non-bisimilar SCCs, we propose a feature-based optimization. The features are designed to be constructed and used more efficiently than bisimulation minimization. Third, we conduct an experimental study that verifies the effectiveness and efficiency of our algorithm. Our features-based optimization pruned 50% (on average) unnecessary bisimulation computation. Our experiment verifies that we extend the current state-of-the-art with a capability on handling cyclic graphs in maintenance of minimal bisimulation.