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Face clustering is an essential task in computer vision due to the explosion of related applications such as augmented reality or photo album management. The main challenge of this task lies in the imperfectness of similarities among image feature representations. Given an existing feature extraction model, it is still an unresolved problem that how can the inherent characteristics of similarities of unlabelled images be leveraged to improve the clustering performance. Motivated by answering the question, we develop an effective unsupervised method, named as FaceMap, by formulating face clustering as a process of non-overlapping community detection, and minimizing the entropy of information flows on a network of images. The entropy is denoted by the map equation and its minimum represents the least description of paths among images in expectation. Inspired by observations on the ranked transition probabilities in the affinity graph constructed from facial images, we develop an outlier detection strategy to adaptively adjust transition probabilities among images. Experiments with ablation studies demonstrate that FaceMap significantly outperforms existing methods and achieves new state-of-the-arts on three popular large-scale datasets for face clustering, e.g., an absolute improvement of more than $10\%$ and $4\%$ comparing with prior unsupervised and supervised methods respectively in terms of average of Pairwise F-score. Our code is publicly available on github.