Community detection by fuzzy clustering

•Rule I fit the similarity of same groups is stronger than that of different groups.•Rule II fit the similarity of same groups is weaker than that of different groups.•Fuzzy clustering adapts to vaguer community detection.

How to measure the similarity between nodes is of great importance for fuzzy clustering when we use the approach to uncover communities in complex networks. In this paper, we first measure the similarity between nodes in a network based on edge centralities and model the network as a fuzzy relation. Then, two fuzzy transitive rules (Rule I and Rule II) are applied on the relation respectively, by which the similarity information can be transferred from one node to another in the network until the relation reaches a stable state. By choosing different thresholds, our method finally can partition the network into several non-overlapping subgroups. We compare our method with some state of the art methods on the LFR benchmark and real-world networks. We find that our method based on Rule I can correctly identify communities when the similarity between nodes of same groups is greater than that of different groups, while it is just opposite to Rule II. Our method achieves better results than the state of the art methods when the pre-planted communities of the random networks are vaguer.