A maximal clique (MC) is a complete subgraph satisfying that no other cliques can take it as their proper subgraph. Given an uncertain graph, the top-K MCs enumeration problem studies how to return k MCs with the highest rank value. Existing algorithms rank MCs according to their probabilities, thus usually return MCs with higher probabilities but less number of vertices, and fail to return large MCs that convey more useful information. Considering this problem, this paper studies the problem

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... enumerating top-K MCs. Our approach returns k MCs with the most number of vertices satisfying that their probabilities ≥ α, where each MC is called an α-MC, and computing k largest α-MCs is called as (k, α)-MCs. We propose an efficient (k, α)-MCs enumeration algorithm, Top-KMC, which works in three steps, including partition, enumeration and verification. Here, partition means that we compute the set M of all MCs without considering the probability information, as if the graph is partitioned into a set of subgraphs. Enumeration means that we compute α-MCs from each MC of M. As each such subgraph is an MC, the cost of computing common neighbors for finding α-MCs can be reduced. Verification means that we need to verify whether an α-MC is a subgraph of another α-MC. If not, it is an α-MC; otherwise, it is a useless α-MC and should be removed. We further propose an optimized algorithm Top-KMC+ to reduce both time and space by merging the above three steps into a whole step. The experimental results on real datasets show that both Top-KMC and Top-KMC+ can return k largest α-MCs efficiently.