Title: Clustering Structure Identification With Ordering Graph. Abstract: In machine learning, data is often presented in the form of a graph or similarity (or distance) values between samples. Graph-based clustering methods such as spectral clustering are defined for general weighted graphs to identify the clustering structure. Graph construction research has developed significantly for decades, but the graph-based partition study still requires more attention because of its poor performance. For example, spectral clustering needs a post-processing (e.g., K-Means) step to uncover the clustering indicators. Yet, K-Means is sensitive to the initial center setting and easily falls into a local optimum. In this paper, we investigate a new type of graph-based clustering approach. Firstly, we introduce a new algorithm for the purpose of cluster analysis which does not explicitly produce a clustering of a dataset but instead creates an augmented graph representing its density-based ordered clustering structure. This ordered graph contains information equivalent to density-based clustering corresponding to a broad range of parameter settings. Secondly, we found that the graph matrix is shown in a block-diagonal form because of the nature of ordering. We propose a partition method to learn the graph matrix's block-diagonal structure and identify the clustering directly. The global optimality is guaranteed theoretically. We test the proposed method on synthetic datasets and five high-dimensional datasets. Experimental results show that the proposed method outperforms state-of-the-art graph-based clustering methods and improves their performance by roughly 10%-50%. 