SummaryRole mining was recently proposed to automatically find roles among user‐permission assignments using data mining technologies. However, the current studies about role mining mainly focus on how to find roles, without considering the constraints that are essentially required in role‐based access control systems. In this paper, we present a role mining algorithm with constraints, especially for the cardinality constraints. We illustrate it is essential for role mining to take cardinality constraints into account, and introduce the concepts of the cardinality constraints of roles and permissions. We further propose a role mining algorithm to generate roles based on these two kinds of cardinality constraints. The algorithm uses graph theory to model the role mining problem and maps the relation of two roles to the relation of graph elements. We set an optimization goal for role mining and employ graph optimization theory to find roles that satisfy the aforementioned cardinality constraints. We carry out the experiments to evaluate our approach. The experimental results demonstrate the rationality and effectiveness of the proposed algorithm. Copyright © 2015 John Wiley & Sons, Ltd.