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This paper presents two novel graph-clustering algorithms, Clustering based on a Near Neighbor Graph (CNNG) and Clustering based on a Grid Cell Graph (CGCG). CNNG algorithm inspired by the idea of near neighbors is an improved graph-clustering method based on Minimum Spanning Tree (MST). In order to analyze massive data sets more efficiently, CGCG algorithm, which is a kind of graph-clustering method based on MST on the level of grid cells, is presented. To clearly describe the two algorithms, we give some important concepts, such as near neighbor point set, near neighbor undirected graph, grid cell, and so on. To effectively implement the two algorithms, we use some efficient partitioning and index methods, such as multidimensional grid partition method, multidimensional index tree, and so on. From simulation experiments of some artificial data sets and seven real data sets, we observe that the time cost of CNNG algorithm can be decreased by using some improving techniques and approximate methods while attaining an acceptable clustering quality, and CGCG algorithm can approximately analyze some dense data sets with linear time cost. Moreover, comparing some classical clustering algorithms, CNNG algorithm can often get better clustering quality or quicker clustering speed.