Recent research efforts have made notable progress in improving the performance of (exhaustive) maximal clique enumeration (MCE). However, existing algorithms still suffer from exploring the huge search space of MCE. Furthermore, their results are often undesirable as many of the returned maximal cliques have large overlapping parts. This redundancy leads to problems in both computational efficiency and usefulness of MCE.

In this paper, we aim at providing a concise and complete summary of the set of maximal cliques, which is useful to many applications. We propose the notion of τ-visible MCE to achieve this goal and design algorithms to realize the notion. Based on the refined output space, we further consider applications including an efficient computation of the top-k results with diversity and an interactive clique exploration process. Our experimental results demonstrate that our approach is capable of producing output of high usability and our algorithms achieve superior efficiency over classic MCE algorithms.