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The designation of the cluster number K and the initial centroids is essential for K-modes clustering algorithm. However, most of the improved methods based on K-modes specify the K value manually and generate the initial centroids randomly, which makes the clustering algorithm significantly dependent on human-based decisions and unstable on the iteration time. To overcome this limitation, we propose a cohesive K-modes (CK-modes) algorithm to generate the cluster number K and the initial centroids automatically. Explicitly, we construct a labeled property graph based on index-free adjacency to capture both global and local cohesion of the node in the sample of the input datasets. The cohesive node calculated based on the property similarity is exploited to split the graph to a K-node tree that determines the K value, and then the initial centroids are selected from the split subtrees. Since the property graph construction and the cohesion calculation are only performed once, they account for a small amount of execution time of the clustering operation with multiple iterations, but significantly accelerate the clustering convergence. Experimental validation in both real-world and synthetic datasets shows that the CK-modes algorithm outperforms the state-of-the-art algorithms.