We present a method for graph clustering that is analogous to gradient ascent methods previously proposed for clustering points in space. The algorithm, which can be viewed as a max-degree hill-climbing procedure on the graph, iteratively moves each node to a neighboring node of highest degree. We show that, when applied to a random geometric graph whose nodes correspond to data drawn i.i.d. from a density with Morse regularity, the method is asymptotically consistent. Here, consistency is in the sense of Fukunaga and Hostetler, meaning, with respect to the partition of the support of the density defined by the basins of attraction of the density gradient flow.

翻译：我们提出了一种图聚类方法，该方法类似于先前提出的用于空间点聚类的梯度上升方法。该算法可视为在图上的最大度爬山过程，迭代地将每个节点移动到度最高的相邻节点。我们证明，当应用于节点对应于从具有莫尔斯正则性的密度中独立同分布抽取的数据的随机几何图时，该方法具有渐近一致性。此处的"一致性"遵循福永和霍斯泰特勒的定义，即相对于由密度梯度流的吸引域定义的密度支撑集划分而言。